Daily Papers

Advancements in LLMs have significantly expanded their capabilities across various domains. However, mathematical reasoning remains a challenging area, prompting the development of math-specific LLMs. These models typically follow a two-stage training paradigm: pre-training with math-related corpora and post-training with problem datasets for SFT. Despite these efforts, the improvements in mathematical reasoning achieved through continued pre-training (CPT) are often less significant compared to those obtained via SFT. This study addresses this discrepancy by exploring alternative strategies during the pre-training phase, focusing on the use of problem-solving data over general mathematical corpora. We investigate three primary research questions: (1) Can problem-solving data enhance the model's mathematical reasoning capabilities more effectively than general mathematical corpora during CPT? (2) Are synthetic data from the same source equally effective, and which synthesis methods are most efficient? (3) How do the capabilities developed from the same problem-solving data differ between the CPT and SFT stages, and what factors contribute to these differences? Our findings indicate that problem-solving data significantly enhances the model's mathematical capabilities compared to general mathematical corpora. We also identify effective data synthesis methods, demonstrating that the tutorship amplification synthesis method achieves the best performance. Furthermore, while SFT facilitates instruction-following abilities, it underperforms compared to CPT with the same data, which can be partially attributed to its poor learning capacity for hard multi-step problem-solving data. These insights provide valuable guidance for optimizing the mathematical reasoning capabilities of LLMs, culminating in our development of a powerful mathematical base model called JiuZhang-8B.

Recent claims about the impressive abilities of large language models (LLMs) are often supported by evaluating publicly available benchmarks. Since LLMs train on wide swaths of the internet, this practice raises concerns of data contamination, i.e., evaluating on examples that are explicitly or implicitly included in the training data. Data contamination remains notoriously challenging to measure and mitigate, even with partial attempts like controlled experimentation of training data, canary strings, or embedding similarities. In this work, we conduct the first thorough longitudinal analysis of data contamination in LLMs by using the natural experiment of training cutoffs in GPT models to look at benchmarks released over time. Specifically, we consider two code/mathematical problem-solving datasets, Codeforces and Project Euler, and find statistically significant trends among LLM pass rate vs. GitHub popularity and release date that provide strong evidence of contamination. By open-sourcing our dataset, raw results, and evaluation framework, our work paves the way for rigorous analyses of data contamination in modern models. We conclude with a discussion of best practices and future steps for publicly releasing benchmarks in the age of LLMs that train on webscale data.

Reinforcement Learning (RL) plays a crucial role in aligning large language models (LLMs) with human preferences and improving their ability to perform complex tasks. However, current approaches either require significant computational resources due to the use of multiple models and extensive online sampling for training (e.g., PPO) or are framed as bandit problems (e.g., DPO, DRO), which often struggle with multi-step reasoning tasks, such as math problem-solving and complex reasoning that involve long chains of thought. To overcome these limitations, we introduce Direct Q-function Optimization (DQO), which formulates the response generation process as a Markov Decision Process (MDP) and utilizes the soft actor-critic (SAC) framework to optimize a Q-function directly parameterized by the language model. The MDP formulation of DQO offers structural advantages over bandit-based methods, enabling more effective process supervision. Experimental results on two math problem-solving datasets, GSM8K and MATH, demonstrate that DQO outperforms previous methods, establishing it as a promising offline reinforcement learning approach for aligning language models.

We propose RaDeR, a set of reasoning-based dense retrieval models trained with data derived from mathematical problem solving using large language models (LLMs). Our method leverages retrieval-augmented reasoning trajectories of an LLM and self-reflective relevance evaluation, enabling the creation of both diverse and hard-negative samples for reasoning-intensive relevance. RaDeR retrievers, trained for mathematical reasoning, effectively generalize to diverse reasoning tasks in the BRIGHT and RAR-b benchmarks, consistently outperforming strong baselines in overall performance. Notably, RaDeR achieves significantly higher performance than baselines on the Math and Coding splits. In addition, RaDeR presents the first dense retriever that outperforms BM25 when queries are Chain-of-Thought reasoning steps, underscoring the critical role of reasoning-based retrieval to augment reasoning language models. Furthermore, RaDeR achieves comparable or superior performance while using only 2.5% of the training data used by the concurrent work REASONIR, highlighting the quality of our synthesized training data.

This paper presents a critical examination of current approaches to replicating OpenAI's O1 model capabilities, with particular focus on the widespread but often undisclosed use of knowledge distillation techniques. While our previous work explored the fundamental technical path to O1 replication, this study reveals how simple distillation from O1's API, combined with supervised fine-tuning, can achieve superior performance on complex mathematical reasoning tasks. Through extensive experiments, we show that a base model fine-tuned on simply tens of thousands of samples O1-distilled long-thought chains outperforms O1-preview on the American Invitational Mathematics Examination (AIME) with minimal technical complexity. Moreover, our investigation extends beyond mathematical reasoning to explore the generalization capabilities of O1-distilled models across diverse tasks: hallucination, safety and open-domain QA. Notably, despite training only on mathematical problem-solving data, our models demonstrated strong generalization to open-ended QA tasks and became significantly less susceptible to sycophancy after fine-tuning. We deliberately make this finding public to promote transparency in AI research and to challenge the current trend of obscured technical claims in the field. Our work includes: (1) A detailed technical exposition of the distillation process and its effectiveness, (2) A comprehensive benchmark framework for evaluating and categorizing O1 replication attempts based on their technical transparency and reproducibility, (3) A critical discussion of the limitations and potential risks of over-relying on distillation approaches, our analysis culminates in a crucial bitter lesson: while the pursuit of more capable AI systems is important, the development of researchers grounded in first-principles thinking is paramount.

Large Language Model (LLM)-based agents have demonstrated remarkable effectiveness. However, their performance can be compromised in data science scenarios that require real-time data adjustment, expertise in optimization due to complex dependencies among various tasks, and the ability to identify logical errors for precise reasoning. In this study, we introduce the Data Interpreter, a solution designed to solve with code that emphasizes three pivotal techniques to augment problem-solving in data science: 1) dynamic planning with hierarchical graph structures for real-time data adaptability;2) tool integration dynamically to enhance code proficiency during execution, enriching the requisite expertise;3) logical inconsistency identification in feedback, and efficiency enhancement through experience recording. We evaluate the Data Interpreter on various data science and real-world tasks. Compared to open-source baselines, it demonstrated superior performance, exhibiting significant improvements in machine learning tasks, increasing from 0.86 to 0.95. Additionally, it showed a 26% increase in the MATH dataset and a remarkable 112% improvement in open-ended tasks. The solution will be released at https://github.com/geekan/MetaGPT.

This paper presents an in-depth exploration of Meta Prompting, a novel technique that revolutionizes the way large language models (LLMs), multi-modal foundation models, and AI systems approach problem-solving and data interpretation. Meta Prompting, rooted in type theory and category theory, prioritizes the structure and syntax of information, providing a unique framework that transcends traditional content-focused methods. We delve into the formal definitions of Meta Prompting, contrasting it with Few-Shot Prompting, and highlight its applicability and superiority in various AI applications. Key to this exploration is the expansion of Meta Prompting into the realm of complex reasoning. Here, we demonstrate how this technique adeptly breaks down intricate problems into manageable sub-problems, facilitating a step-by-step, detailed approach to problem-solving. This method proves especially advantageous in terms of token efficiency and offering a fair comparison in problem-solving scenarios, standing out against few-shot example approaches. Furthermore, the paper breaks new ground by extending Meta Prompting into multi-modal foundation model settings. This extension addresses the integration of diverse data types, such as images, audio, and video, within the structured framework of Meta Prompting, highlighting both the challenges and the vast potential of this approach in handling complex, multi-faceted data (The code is available at https://github.com/meta-prompting/meta-prompting).

Recent advances in large language model (LLM) training have highlighted the need for diverse, high-quality instruction data. Recently, many works are exploring synthetic data generation using LLMs. However, they primarily focus on prompt engineering with standard supervised instruction-finetuned models, which contains a fundamental limitation: these models are optimized for general question-answering/problem-solving rather than data generation. We propose a paradigm shift named NOMAD by investigating how to specifically train models for data generation, demonstrating that this task differs significantly from training a classical LM. We identify two key factors: no-prompt-masked training and proper training set size selection. Our method, NOMAD, shows substantial improvements over baselines, achieving >4\% gains in TriviaQA and >2\% in GSM8K with limited training data. Finally, we offer new insights by interpreting synthetic data through the lenses of "relevance" and "novelty".

Large language models (LLMs) have significantly advanced natural language understanding and demonstrated strong problem-solving abilities. Despite these successes, most LLMs still struggle with solving mathematical problems due to the intricate reasoning required. This paper investigates the mathematical problem-solving capabilities of LLMs using the newly developed "MathOdyssey" dataset. The dataset includes diverse mathematical problems at high school and university levels, created by experts from notable institutions to rigorously test LLMs in advanced problem-solving scenarios and cover a wider range of subject areas. By providing the MathOdyssey dataset as a resource to the AI community, we aim to contribute to the understanding and improvement of AI capabilities in complex mathematical problem-solving. We conduct benchmarking on open-source models, such as Llama-3 and DBRX-Instruct, and closed-source models from the GPT series and Gemini models. Our results indicate that while LLMs perform well on routine and moderately difficult tasks, they face significant challenges with Olympiad-level problems and complex university-level questions. Our analysis shows a narrowing performance gap between open-source and closed-source models, yet substantial challenges remain, particularly with the most demanding problems. This study highlights the ongoing need for research to enhance the mathematical reasoning of LLMs. The dataset, results, and code are publicly available.

Fine-tuning language models~(LMs) on human-generated data remains a prevalent practice. However, the performance of such models is often limited by the quantity and diversity of high-quality human data. In this paper, we explore whether we can go beyond human data on tasks where we have access to scalar feedback, for example, on math problems where one can verify correctness. To do so, we investigate a simple self-training method based on expectation-maximization, which we call ReST^{EM}, where we (1) generate samples from the model and filter them using binary feedback, (2) fine-tune the model on these samples, and (3) repeat this process a few times. Testing on advanced MATH reasoning and APPS coding benchmarks using PaLM-2 models, we find that ReST^{EM} scales favorably with model size and significantly surpasses fine-tuning only on human data. Overall, our findings suggest self-training with feedback can substantially reduce dependence on human-generated data.

Mathematical geometric problem solving (GPS) often requires effective integration of multimodal information and verifiable logical coherence. Despite the fast development of large language models in general problem solving, it remains unresolved regarding with both methodology and benchmarks, especially given the fact that exiting synthetic GPS benchmarks are often not self-verified and contain noise and self-contradicted information due to the illusion of LLMs. In this paper, we propose a scalable data engine called TrustGeoGen for problem generation, with formal verification to provide a principled benchmark, which we believe lays the foundation for the further development of methods for GPS. The engine synthesizes geometric data through four key innovations: 1) multimodal-aligned generation of diagrams, textual descriptions, and stepwise solutions; 2) formal verification ensuring rule-compliant reasoning paths; 3) a bootstrapping mechanism enabling complexity escalation via recursive state generation and 4) our devised GeoExplore series algorithms simultaneously produce multi-solution variants and self-reflective backtracking traces. By formal logical verification, TrustGeoGen produces GeoTrust-200K dataset with guaranteed modality integrity, along with GeoTrust-test testset. Experiments reveal the state-of-the-art models achieve only 49.17\% accuracy on GeoTrust-test, demonstrating its evaluation stringency. Crucially, models trained on GeoTrust achieve OOD generalization on GeoQA, significantly reducing logical inconsistencies relative to pseudo-label annotated by OpenAI-o1. Our code is available at https://github.com/Alpha-Innovator/TrustGeoGen

Many intellectual endeavors require mathematical problem solving, but this skill remains beyond the capabilities of computers. To measure this ability in machine learning models, we introduce MATH, a new dataset of 12,500 challenging competition mathematics problems. Each problem in MATH has a full step-by-step solution which can be used to teach models to generate answer derivations and explanations. To facilitate future research and increase accuracy on MATH, we also contribute a large auxiliary pretraining dataset which helps teach models the fundamentals of mathematics. Even though we are able to increase accuracy on MATH, our results show that accuracy remains relatively low, even with enormous Transformer models. Moreover, we find that simply increasing budgets and model parameter counts will be impractical for achieving strong mathematical reasoning if scaling trends continue. While scaling Transformers is automatically solving most other text-based tasks, scaling is not currently solving MATH. To have more traction on mathematical problem solving we will likely need new algorithmic advancements from the broader research community.

Understanding a student's problem-solving strategy can have a significant impact on effective math learning using Intelligent Tutoring Systems (ITSs) and Adaptive Instructional Systems (AISs). For instance, the ITS/AIS can better personalize itself to correct specific misconceptions that are indicated by incorrect strategies, specific problems can be designed to improve strategies and frustration can be minimized by adapting to a student's natural way of thinking rather than trying to fit a standard strategy for all. While it may be possible for human experts to identify strategies manually in classroom settings with sufficient student interaction, it is not possible to scale this up to big data. Therefore, we leverage advances in Machine Learning and AI methods to perform scalable strategy prediction that is also fair to students at all skill levels. Specifically, we develop an embedding called MVec where we learn a representation based on the mastery of students. We then cluster these embeddings with a non-parametric clustering method where we progressively learn clusters such that we group together instances that have approximately symmetrical strategies. The strategy prediction model is trained on instances sampled from these clusters. This ensures that we train the model over diverse strategies and also that strategies from a particular group do not bias the DNN model, thus allowing it to optimize its parameters over all groups. Using real world large-scale student interaction datasets from MATHia, we implement our approach using transformers and Node2Vec for learning the mastery embeddings and LSTMs for predicting strategies. We show that our approach can scale up to achieve high accuracy by training on a small sample of a large dataset and also has predictive equality, i.e., it can predict strategies equally well for learners at diverse skill levels.

The quest for human imitative AI has been an enduring topic in AI research since its inception. The technical evolution and emerging capabilities of the latest cohort of large language models (LLMs) have reinvigorated the subject beyond academia to the cultural zeitgeist. While recent NLP evaluation benchmark tasks test some aspects of human-imitative behaviour (e.g., BIG-bench's 'human-like behavior' tasks), few, if not none, examine creative problem solving abilities. Creative problem solving in humans is a well-studied topic in cognitive neuroscience with standardized tests that predominantly use the ability to associate (heterogeneous) connections among clue words as a metric for creativity. Exposure to misleading stimuli - distractors dubbed red herrings - impede human performance in such tasks via the fixation effect and Einstellung paradigm. In cognitive neuroscience studies, such fixations are experimentally induced by pre-exposing participants to orthographically similar incorrect words to subsequent word-fragments or clues. The popular British quiz show Only Connect's Connecting Wall segment essentially mimics Mednick's Remote Associates Test (RAT) formulation with built-in, deliberate red herrings, which makes it an ideal proxy dataset to explore and study fixation effect and Einstellung paradigm from cognitive neuroscience in LLMs. In addition to presenting the novel Only Connect Wall (OCW) dataset, we also report results from our evaluation of selected pre-trained language models and LLMs (including OpenAI's GPT series) on creative problem solving tasks like grouping clue words by heterogeneous connections, and identifying correct open knowledge domain connections in respective groups. The code and link to the dataset are available at https://github.com/TaatiTeam/OCW.

Large language models (LLMs) have shown excellent mastering of human language, but still struggle in real-world applications that require mathematical problem-solving. While many strategies and datasets to enhance LLMs' mathematics are developed, it remains a challenge to simultaneously maintain and improve both language and mathematical capabilities in deployed LLM systems.In this work, we tailor the Self-Critique pipeline, which addresses the challenge in the feedback learning stage of LLM alignment. We first train a general Math-Critique model from the LLM itself to provide feedback signals. Then, we sequentially employ rejective fine-tuning and direct preference optimization over the LLM's own generations for data collection. Based on ChatGLM3-32B, we conduct a series of experiments on both academic and our newly created challenging dataset, MathUserEval. Results show that our pipeline significantly enhances the LLM's mathematical problem-solving while still improving its language ability, outperforming LLMs that could be two times larger. Related techniques have been deployed to ChatGLM\url{https://chatglm.cn}, an online serving LLM. Related evaluation dataset and scripts are released at https://github.com/THUDM/ChatGLM-Math.

Recently, large language models (LLMs) have become increasingly powerful and have become capable of solving a plethora of tasks through proper instructions in natural language. However, the vast majority of testing suites assume that the instructions are written in English, the de facto prompting language. Code intelligence and problem solving still remain a difficult task, even for the most advanced LLMs. Currently, there are no datasets to measure the generalization power for code-generation models in a language other than English. In this work, we present RoCode, a competitive programming dataset, consisting of 2,642 problems written in Romanian, 11k solutions in C, C++ and Python and comprehensive testing suites for each problem. The purpose of RoCode is to provide a benchmark for evaluating the code intelligence of language models trained on Romanian / multilingual text as well as a fine-tuning set for pretrained Romanian models. Through our results and review of related works, we argue for the need to develop code models for languages other than English.

Large Language Models (LLMs) have shown impressive progress in mathematical reasoning. While data augmentation is promising to enhance mathematical problem-solving ability, current approaches are predominantly limited to instance-level modifications-such as rephrasing or generating syntactic variations-which fail to capture and leverage the intrinsic relational structures inherent in mathematical knowledge. Inspired by human learning processes, where mathematical proficiency develops through systematic exposure to interconnected concepts, we introduce MathFusion, a novel framework that enhances mathematical reasoning through cross-problem instruction synthesis. MathFusion implements this through three fusion strategies: (1) sequential fusion, which chains related problems to model solution dependencies; (2) parallel fusion, which combines analogous problems to reinforce conceptual understanding; and (3) conditional fusion, which creates context-aware selective problems to enhance reasoning flexibility. By applying these strategies, we generate a new dataset, MathFusionQA, followed by fine-tuning models (DeepSeekMath-7B, Mistral-7B, Llama3-8B) on it. Experimental results demonstrate that MathFusion achieves substantial improvements in mathematical reasoning while maintaining high data efficiency, boosting performance by 18.0 points in accuracy across diverse benchmarks while requiring only 45K additional synthetic instructions, representing a substantial improvement over traditional single-instruction approaches. Our datasets, models, and code are publicly available at https://github.com/QizhiPei/mathfusion.

Recently, the release of INSTRUCTEVAL has provided valuable insights into the performance of large language models (LLMs) that utilize encoder-decoder or decoder-only architecture. Interestingly, despite being introduced four years ago, T5-based LLMs, such as FLAN-T5, continue to outperform the latest decoder-based LLMs, such as LLAMA and VICUNA, on tasks that require general problem-solving skills. This performance discrepancy can be attributed to three key factors: (1) Pre-training data, (2) Backbone architecture, and (3) Instruction dataset. In this technical report, our main focus is on investigating the impact of the third factor by leveraging VICUNA, a large language model based on LLAMA, which has undergone fine-tuning on ChatGPT conversations. To achieve this objective, we fine-tuned VICUNA using a customized instruction dataset collection called FLANMINI. This collection includes a subset of the large-scale instruction dataset known as FLAN, as well as various code-related datasets and conversational datasets derived from ChatGPT/GPT-4. This dataset comprises a large number of tasks that demand problem-solving skills. Our experimental findings strongly indicate that the enhanced problem-solving abilities of our model, FLACUNA, are obtained through fine-tuning VICUNA on the FLAN dataset, leading to significant improvements across numerous benchmark datasets in INSTRUCTEVAL. FLACUNA is publicly available at https://huggingface.co/declare-lab/flacuna-13b-v1.0.

The art of mathematical reasoning stands as a fundamental pillar of intellectual progress and is a central catalyst in cultivating human ingenuity. Researchers have recently published a plethora of works centered around the task of solving Math Word Problems (MWP) - a crucial stride towards general AI. These existing models are susceptible to dependency on shallow heuristics and spurious correlations to derive the solution expressions. In order to ameliorate this issue, in this paper, we propose a framework for MWP solvers based on the generation of linguistic variants of the problem text. The approach involves solving each of the variant problems and electing the predicted expression with the majority of the votes. We use DeBERTa (Decoding-enhanced BERT with disentangled attention) as the encoder to leverage its rich textual representations and enhanced mask decoder to construct the solution expressions. Furthermore, we introduce a challenging dataset, Psmall{ARAMAWPS}, consisting of paraphrased, adversarial, and inverse variants of selectively sampled MWPs from the benchmark Msmall{AWPS} dataset. We extensively experiment on this dataset along with other benchmark datasets using some baseline MWP solver models. We show that training on linguistic variants of problem statements and voting on candidate predictions improve the mathematical reasoning and robustness of the model. We make our code and data publicly available.

Geometry problem solving has attracted much attention in the NLP community recently. The task is challenging as it requires abstract problem understanding and symbolic reasoning with axiomatic knowledge. However, current datasets are either small in scale or not publicly available. Thus, we construct a new large-scale benchmark, Geometry3K, consisting of 3,002 geometry problems with dense annotation in formal language. We further propose a novel geometry solving approach with formal language and symbolic reasoning, called Interpretable Geometry Problem Solver (Inter-GPS). Inter-GPS first parses the problem text and diagram into formal language automatically via rule-based text parsing and neural object detecting, respectively. Unlike implicit learning in existing methods, Inter-GPS incorporates theorem knowledge as conditional rules and performs symbolic reasoning step by step. Also, a theorem predictor is designed to infer the theorem application sequence fed to the symbolic solver for the more efficient and reasonable searching path. Extensive experiments on the Geometry3K and GEOS datasets demonstrate that Inter-GPS achieves significant improvements over existing methods. The project with code and data is available at https://lupantech.github.io/inter-gps.

Despite recent advancements in large language models (LLMs), their performance on complex reasoning problems requiring multi-step thinking and combining various skills is still limited. To address this, we propose a novel framework HDFlow for complex reasoning with LLMs that combines fast and slow thinking modes in an adaptive manner. Our approach consists of two key components: 1) a new approach for slow, deliberate reasoning called Dynamic Workflow, which automatically decomposes complex problems into more manageable sub-tasks and dynamically designs a workflow to assemble specialized LLM or symbolic reasoning tools to solve sub-tasks; 2) Hybrid Thinking, a general framework that dynamically combines fast and slow thinking based on problem complexity. Finally, we propose an easy-to-scale method for automatically synthesizing a large-scale dataset of 27K challenging reasoning problems for complex reasoning and a hybrid thinking tuning method that trains smaller LLMs on this dataset to internalize the fast/slow hybrid reasoning strategies. Experiments on four reasoning benchmark datasets demonstrate that our slow thinking with dynamic workflows significantly outperforms Chain-of-Thought, and hybrid thinking achieves the highest accuracy while providing an effective balance between computational efficiency and performance. Fine-tuning using our hybrid thinking approach also significantly boosts the complex reasoning capabilities of open-source language models. The results showcase the promise of slow thinking, dynamic workflows, and hybrid thinking in expanding the frontier of complex problem-solving with LLMsCode and data will be released at \url{https://github.com/wenlinyao/HDFlow.}.

Large Language Models (LLMs) have transformed natural language processing, yet improving their problem-solving capabilities, particularly for complex, reasoning-intensive tasks, remains a persistent challenge. This paper introduces the REAP (Reflection, Explicit Problem Deconstruction, and Advanced Prompting) method, an innovative approach within the dynamic context generation framework. REAP guides LLMs through reflection on the query, deconstructing it into manageable components, and generating relevant context to enhance the solution process. We evaluated REAP using a dataset designed to expose LLM limitations, comparing zero-shot prompting with REAP-enhanced prompts across six state-of-the-art models: OpenAI's o1-preview, o1-mini, GPT-4o, GPT-4o-mini, Google's Gemini 1.5 Pro, and Claude 3.5 Sonnet. The results demonstrate notable performance gains, with o1-mini improving by 40.97%, GPT-4o by 66.26%, and GPT-4o-mini by 112.93%. Despite the already strong baseline performance of OpenAI's o1-preview, modest gains were observed. Beyond performance improvements, REAP offers a cost-effective solution; for example, GPT-4o-mini, which is approximately 100 times cheaper than o1-preview, delivered competitive results. REAP also improves the clarity of model outputs, making it easier for humans to understand the reasoning behind the results and simplifying the process of identifying and addressing any issues. These findings demonstrate REAP's potential to greatly improve the capabilities of LLMs, providing both better performance and increased cost-efficiency across a wide range of applications.

In this study, we investigated the effects of self-reflection in large language models (LLMs) on problem-solving performance. We instructed nine popular LLMs to answer a series of multiple-choice questions to provide a performance baseline. For each incorrectly answered question, we instructed eight types of self-reflecting LLM agents to reflect on their mistakes and provide themselves with guidance to improve problem-solving. Then, using this guidance, each self-reflecting agent attempted to re-answer the same questions. Our results indicate that LLM agents are able to significantly improve their problem-solving performance through self-reflection (p < 0.001). In addition, we compared the various types of self-reflection to determine their individual contribution to performance. All code and data are available on GitHub at https://github.com/matthewrenze/self-reflection

Chain-of-Thought (CoT) plays a crucial role in reasoning for math problem solving. We conduct a comprehensive examination of methods for designing CoT, comparing conventional natural language CoT with various program CoTs, including the self-describing program, the comment-describing program, and the non-describing program. Furthermore, we investigate the impact of programming language on program CoTs, comparing Python and Wolfram Language. Through extensive experiments on GSM8K, MATHQA, and SVAMP, we find that program CoTs often have superior effectiveness in math problem solving. Notably, the best performing combination with 30B parameters beats GPT-3.5-turbo by a significant margin. The results show that self-describing program offers greater diversity and thus can generally achieve higher performance. We also find that Python is a better choice of language than Wolfram for program CoTs. The experimental results provide a valuable guideline for future CoT designs that take into account both programming language and coding style for further advancements. Our datasets and code are publicly available.

We introduce a large-scale dataset of math word problems and an interpretable neural math problem solver that learns to map problems to operation programs. Due to annotation challenges, current datasets in this domain have been either relatively small in scale or did not offer precise operational annotations over diverse problem types. We introduce a new representation language to model precise operation programs corresponding to each math problem that aim to improve both the performance and the interpretability of the learned models. Using this representation language, our new dataset, MathQA, significantly enhances the AQuA dataset with fully-specified operational programs. We additionally introduce a neural sequence-to-program model enhanced with automatic problem categorization. Our experiments show improvements over competitive baselines in our MathQA as well as the AQuA dataset. The results are still significantly lower than human performance indicating that the dataset poses new challenges for future research. Our dataset is available at: https://math-qa.github.io/math-QA/

This paper presents GPSM4K, a comprehensive geometry multimodal dataset tailored to augment the problem-solving capabilities of Large Vision Language Models (LVLMs). GPSM4K encompasses 2157 multimodal question-answer pairs manually extracted from mathematics textbooks spanning grades 7-12 and is further augmented to 5340 problems, consisting of both numerical and theorem-proving questions. In contrast to PGPS9k, Geometry3K, and Geo170K which feature only objective-type questions, GPSM4K offers detailed step-by-step solutions in a consistent format, facilitating a comprehensive evaluation of problem-solving approaches. This dataset serves as an excellent benchmark for assessing the geometric reasoning capabilities of LVLMs. Evaluation of our test set shows that there is scope for improvement needed in open-source language models in geometry problem-solving. Finetuning on our training set increases the geometry problem-solving capabilities of models. Further, We also evaluate the effectiveness of techniques such as image captioning and Retrieval Augmentation generation (RAG) on model performance. We leveraged LLM to automate the task of final answer evaluation by providing ground truth and predicted solutions. This research will help to assess and improve the geometric reasoning capabilities of LVLMs.

Code generation by Llama 3.1 models, such as Meta's Llama 3.1 405B, represents a significant advancement in the field of artificial intelligence, particularly in natural language processing and programming automation. This paper explores the capabilities and applications of Llama-driven code generation, highlighting its ability to translate natural language prompts into executable code across multiple programming languages. Key features include contextual awareness, multi-language support, and enhanced debugging and optimization functionalities. By examining these aspects, we illustrate how Llama can serve as a versatile tool for developers of all skill levels, improving productivity and efficiency in software development. The potential implications for education, industry, and the future of coding practices are also discussed, underscoring the transformative impact of AI in programming. Experimentation shows that while Llama 3.1 405B performs well with simple algorithmic and data structure based problems, it still struggles with problems on Quantum Computing, Bioinformatics, and Artificial Intelligence.

Diffusion models have recently achieved success in solving Bayesian inverse problems with learned data priors. Current methods build on top of the diffusion sampling process, where each denoising step makes small modifications to samples from the previous step. However, this process struggles to correct errors from earlier sampling steps, leading to worse performance in complicated nonlinear inverse problems, such as phase retrieval. To address this challenge, we propose a new method called Decoupled Annealing Posterior Sampling (DAPS) that relies on a novel noise annealing process. Specifically, we decouple consecutive steps in a diffusion sampling trajectory, allowing them to vary considerably from one another while ensuring their time-marginals anneal to the true posterior as we reduce noise levels. This approach enables the exploration of a larger solution space, improving the success rate for accurate reconstructions. We demonstrate that DAPS significantly improves sample quality and stability across multiple image restoration tasks, particularly in complicated nonlinear inverse problems. For example, we achieve a PSNR of 30.72dB on the FFHQ 256 dataset for phase retrieval, which is an improvement of 9.12dB compared to existing methods.

Recent advances in large language models (LLMs) have demonstrated notable progress on many mathematical benchmarks. However, most of these benchmarks only feature problems grounded in junior and senior high school subjects, contain only multiple-choice questions, and are confined to a limited scope of elementary arithmetic operations. To address these issues, this paper introduces an expansive benchmark suite SciBench that aims to systematically examine the reasoning capabilities required for complex scientific problem solving. SciBench contains two carefully curated datasets: an open set featuring a range of collegiate-level scientific problems drawn from mathematics, chemistry, and physics textbooks, and a closed set comprising problems from undergraduate-level exams in computer science and mathematics. Based on the two datasets, we conduct an in-depth benchmark study of two representative LLMs with various prompting strategies. The results reveal that current LLMs fall short of delivering satisfactory performance, with an overall score of merely 35.80%. Furthermore, through a detailed user study, we categorize the errors made by LLMs into ten problem-solving abilities. Our analysis indicates that no single prompting strategy significantly outperforms others and some strategies that demonstrate improvements in certain problem-solving skills result in declines in other skills. We envision that SciBench will catalyze further developments in the reasoning abilities of LLMs, thereby ultimately contributing to scientific research and discovery.

The increasing adoption of artificial intelligence in telecommunications has raised interest in the capability of Large Language Models (LLMs) to address domain-specific, mathematically intensive tasks. Although recent advancements have improved the performance of LLMs in general mathematical reasoning, their effectiveness within specialized domains, such as signal processing, network optimization, and performance analysis, remains largely unexplored. To address this gap, we introduce TeleMath, the first benchmark dataset specifically designed to evaluate LLM performance in solving mathematical problems with numerical solutions in the telecommunications domain. Comprising 500 question-answer (QnA) pairs, TeleMath covers a wide spectrum of topics in the telecommunications field. This paper outlines the proposed QnAs generation pipeline, starting from a selected seed of problems crafted by Subject Matter Experts. The evaluation of a wide range of open-source LLMs reveals that best performance on TeleMath is achieved by recent models explicitly designed for mathematical or logical reasoning. In contrast, general-purpose models, even those with a large number of parameters, often struggle with these challenges. We have released the dataset and the evaluation code to ease result reproducibility and support future research.

Recently, deep learning models have made great progress in MWP solving on answer accuracy. However, they are uninterpretable since they mainly rely on shallow heuristics to achieve high performance without understanding and reasoning the grounded math logic. To address this issue and make a step towards interpretable MWP solving, we first construct a high-quality MWP dataset named InterMWP which consists of 11,495 MWPs and annotates interpretable logical formulas based on algebraic knowledge as the grounded linguistic logic of each solution equation. Different from existing MWP datasets, our InterMWP benchmark asks for a solver to not only output the solution expressions but also predict the corresponding logical formulas. We further propose a novel approach with logical prompt and interpretation generation, called LogicSolver. For each MWP, our LogicSolver first retrieves some highly-correlated algebraic knowledge and then passes them to the backbone model as prompts to improve the semantic representations of MWPs. With these improved semantic representations, our LogicSolver generates corresponding solution expressions and interpretable knowledge formulas in accord with the generated solution expressions, simultaneously. Experimental results show that our LogicSolver has stronger logical formula-based interpretability than baselines while achieving higher answer accuracy with the help of logical prompts, simultaneously. The source code and dataset is available at https://github.com/yangzhch6/InterMWP.

Solving math word problems requires deductive reasoning over the quantities in the text. Various recent research efforts mostly relied on sequence-to-sequence or sequence-to-tree models to generate mathematical expressions without explicitly performing relational reasoning between quantities in the given context. While empirically effective, such approaches typically do not provide explanations for the generated expressions. In this work, we view the task as a complex relation extraction problem, proposing a novel approach that presents explainable deductive reasoning steps to iteratively construct target expressions, where each step involves a primitive operation over two quantities defining their relation. Through extensive experiments on four benchmark datasets, we show that the proposed model significantly outperforms existing strong baselines. We further demonstrate that the deductive procedure not only presents more explainable steps but also enables us to make more accurate predictions on questions that require more complex reasoning.

Many students struggle with math word problems (MWPs), often finding it difficult to identify key information and select the appropriate mathematical operations.Schema-based instruction (SBI) is an evidence-based strategy that helps students categorize problems based on their structure, improving problem-solving accuracy. Building on this, we propose a Schema-Based Instruction Retrieval-Augmented Generation (SBI-RAG) framework that incorporates a large language model (LLM).Our approach emphasizes step-by-step reasoning by leveraging schemas to guide solution generation. We evaluate its performance on the GSM8K dataset, comparing it with GPT-4 and GPT-3.5 Turbo, and introduce a "reasoning score" metric to assess solution quality. Our findings suggest that SBI-RAG enhances reasoning clarity and problem-solving accuracy, potentially providing educational benefits for students

We introduce KnowledgeMath, a novel benchmark designed to evaluate LLMs' capabilities in applying financial knowledge to solve complex math word problems. Compared to prior works, this study features three core advancements. First, KnowledgeMath includes 1,259 problems with a hybrid of textual and tabular content and require college-level knowledge in the finance domain for effective resolution. Second, we provide expert-annotated, detailed solution references in Python program format, ensuring a high-quality benchmark for LLM assessment. Finally, we evaluate a wide spectrum of 14 LLMs with different prompting strategies like Chain-of-Thoughts and Program-of-Thoughts. The current best-performing system (i.e., GPT-4 with Program-of-Thoughts) achieves only 45.4% accuracy, leaving substantial room for improvement. While knowledge-augmented LLMs can improve the performance (e.g., from 23.9% to 32.0% for GPT-3.5), it is still significantly lower the estimated human expert performance of 94%. We believe that KnowledgeMath can facilitate future research on domain-specific knowledge retrieval and augmentation into the math word problem-solving process. We will release the benchmark and code at https://github.com/yale-nlp/KnowledgeMath.

Large Language Models (LLMs) have demonstrated strong capabilities in text-based tasks but struggle with the complex reasoning required for physics problems, particularly in advanced arithmetic and conceptual understanding. While some research has explored ways to enhance LLMs in physics education using techniques such as prompt engineering and Retrieval Augmentation Generation (RAG), not enough effort has been made in addressing their limitations in physics reasoning. This paper presents a novel approach to improving LLM performance on physics questions using Reinforcement Learning with Human and Artificial Intelligence Feedback (RLHAIF). We evaluate several reinforcement learning methods, including Proximal Policy Optimization (PPO), Direct Preference Optimization (DPO), and Remax optimization. These methods are chosen to investigate RL policy performance with different settings on the PhyQA dataset, which includes challenging physics problems from high school textbooks. Our RLHAIF model, tested on leading LLMs like LLaMA2 and Mistral, achieved superior results, notably with the MISTRAL-PPO model, demonstrating marked improvements in reasoning and accuracy. It achieved high scores, with a 58.67 METEOR score and a 0.74 Reasoning score, making it a strong example for future physics reasoning research in this area.

Solving mathematical problems requires advanced reasoning abilities and presents notable challenges for large language models. Previous works usually synthesize data from proprietary models to augment existing datasets, followed by instruction tuning to achieve top-tier results. However, our analysis of these datasets reveals severe biases towards easy queries, with frequent failures to generate any correct response for the most challenging queries. Hypothesizing that difficult queries are crucial to learn complex reasoning, we propose Difficulty-Aware Rejection Tuning (DART), a method that allocates difficult queries more trials during the synthesis phase, enabling more extensive training on difficult samples. Utilizing DART, we have created new datasets for mathematical problem-solving that focus more on difficult queries and are substantially smaller than previous ones. Remarkably, our synthesis process solely relies on a 7B-sized open-weight model, without reliance on the commonly used proprietary GPT-4. We fine-tune various base models on our datasets ranging from 7B to 70B in size, resulting in a series of strong models called DART-MATH. In comprehensive in-domain and out-of-domain evaluation on 6 mathematical benchmarks, DART-MATH outperforms vanilla rejection tuning significantly, being superior or comparable to previous arts, despite using much smaller datasets and no proprietary models. Furthermore, our results position our synthetic datasets as the most effective and cost-efficient publicly available resources for advancing mathematical problem-solving.

Existing approaches to mathematical reasoning with large language models (LLMs) rely on Chain-of-Thought (CoT) for generalizability or Tool-Integrated Reasoning (TIR) for precise computation. While efforts have been made to combine these methods, they primarily rely on post-selection or predefined strategies, leaving an open question: whether LLMs can autonomously adapt their reasoning strategy based on their inherent capabilities. In this work, we propose TATA (Teaching LLMs According to Their Aptitude), an adaptive framework that enables LLMs to personalize their reasoning strategy spontaneously, aligning it with their intrinsic aptitude. TATA incorporates base-LLM-aware data selection during supervised fine-tuning (SFT) to tailor training data to the model's unique abilities. This approach equips LLMs to autonomously determine and apply the appropriate reasoning strategy at test time. We evaluate TATA through extensive experiments on six mathematical reasoning benchmarks, using both general-purpose and math-specialized LLMs. Empirical results demonstrate that TATA effectively combines the complementary strengths of CoT and TIR, achieving superior or comparable performance with improved inference efficiency compared to TIR alone. Further analysis underscores the critical role of aptitude-aware data selection in enabling LLMs to make effective and adaptive reasoning decisions and align reasoning strategies with model capabilities.

The rapid advancement of large language models (LLMs) has empowered intelligent agents to leverage diverse external tools for solving complex real-world problems. However, as agents increasingly depend on multiple tools, they encounter new challenges: extended contexts from disparate sources and noisy or irrelevant tool outputs can undermine system reliability and accuracy. These challenges underscore the necessity for enhanced stability in agent-based systems. To address this, we introduce dynamic supervision and maneuvering mechanisms, constructing a robust and dynamic Multi-Agent System (MAS) architecture within the AWorld framework. In our approach, the Execution Agent invokes the Guard Agent at critical steps to verify and correct the reasoning process, effectively reducing errors arising from noise and bolstering problem-solving robustness. Extensive experiments on the GAIA test dataset reveal that our dynamic maneuvering mechanism significantly improves both the effectiveness and stability of solutions, outperforming single-agent system (SAS) and standard tool-augmented systems. As a result, our dynamic MAS system achieved first place among open-source projects on the prestigious GAIA leaderboard. These findings highlight the practical value of collaborative agent roles in developing more reliable and trustworthy intelligent systems.

Employing Large Language Models (LLMs) to address mathematical problems is an intriguing research endeavor, considering the abundance of math problems expressed in natural language across numerous science and engineering fields. While several prior works have investigated solving elementary mathematics using LLMs, this work explores the frontier of using GPT-4 for solving more complex and challenging math problems. We evaluate various ways of using GPT-4. Some of them are adapted from existing work, and one is \MathChat, a conversational problem-solving framework newly proposed in this work. We perform the evaluation on difficult high school competition problems from the MATH dataset, which shows the advantage of the proposed conversational approach.

In most current research, large language models (LLMs) are able to perform reasoning tasks by generating chains of thought through the guidance of specific prompts. However, there still exists a significant discrepancy between their capability in solving complex reasoning problems and that of humans. At present, most approaches focus on chains of thought (COT) and tool use, without considering the adoption and application of human cognitive frameworks. It is well-known that when confronting complex reasoning challenges, humans typically employ various cognitive abilities, and necessitate interaction with all aspects of tools, knowledge, and the external environment information to accomplish intricate tasks. This paper introduces a novel intelligent framework, referred to as OlaGPT. OlaGPT carefully studied a cognitive architecture framework, and propose to simulate certain aspects of human cognition. The framework involves approximating different cognitive modules, including attention, memory, reasoning, learning, and corresponding scheduling and decision-making mechanisms. Inspired by the active learning mechanism of human beings, it proposes a learning unit to record previous mistakes and expert opinions, and dynamically refer to them to strengthen their ability to solve similar problems. The paper also outlines common effective reasoning frameworks for human problem-solving and designs Chain-of-Thought (COT) templates accordingly. A comprehensive decision-making mechanism is also proposed to maximize model accuracy. The efficacy of OlaGPT has been stringently evaluated on multiple reasoning datasets, and the experimental outcomes reveal that OlaGPT surpasses state-of-the-art benchmarks, demonstrating its superior performance. Our implementation of OlaGPT is available on GitHub: https://github.com/oladata-team/OlaGPT.

LLMs exhibit advanced reasoning capabilities, offering the potential to transform natural language questions into mathematical models. However, existing open-source datasets in operations research domain lack detailed annotations of the modeling process, such as variable definitions, focusing solely on objective values, which hinders reinforcement learning applications. To address this, we release the StructuredOR dataset, annotated with comprehensive labels that capture the complete mathematical modeling process. We further propose BPP-Search, a algorithm that integrates reinforcement learning into a tree-of-thought structure using Beam search, a Process reward model, and a pairwise Preference algorithm. This approach enables efficient exploration of tree structures, avoiding exhaustive search while improving accuracy. Extensive experiments on StructuredOR, NL4OPT, and MAMO-ComplexLP datasets show that BPP-Search significantly outperforms state-of-the-art methods. In tree-based reasoning, BPP-Search excels in accuracy and efficiency, enabling faster retrieval of correct solutions.

Large language models (LLMs) are known to struggle with complicated reasoning tasks such as math word problems (MWPs). In this paper, we present how analogy from similarly structured questions can improve LLMs' problem-solving capabilities for MWPs. Specifically, we rely on the retrieval of problems with similar computational graphs to the given question to serve as exemplars in the prompt, providing the correct reasoning path for the generation model to refer to. Empirical results across six math word problem datasets demonstrate the effectiveness of our proposed method, which achieves a significant improvement of up to 6.7 percent on average in absolute value, compared to baseline methods. These results highlight our method's potential in addressing the reasoning challenges in current LLMs.

This is the first paper in a series of work we have accomplished over the past three years. In this paper, we have constructed a consistent formal plane geometry system. This will serve as a crucial bridge between IMO-level plane geometry challenges and readable AI automated reasoning. Within this formal framework, we have been able to seamlessly integrate modern AI models with our formal system. AI is now capable of providing deductive reasoning solutions to IMO-level plane geometry problems, just like handling other natural languages, and these proofs are readable, traceable, and verifiable. We propose the geometry formalization theory (GFT) to guide the development of the geometry formal system. Based on the GFT, we have established the FormalGeo, which consists of 88 geometric predicates and 196 theorems. It can represent, validate, and solve IMO-level geometry problems. we also have crafted the FGPS (formal geometry problem solver) in Python. It serves as both an interactive assistant for verifying problem-solving processes and an automated problem solver. We've annotated the formalgeo7k and formalgeo-imo datasets. The former contains 6,981 (expand to 133,818 through data augmentation) geometry problems, while the latter includes 18 (expand to 2,627 and continuously increasing) IMO-level challenging geometry problems. All annotated problems include detailed formal language descriptions and solutions. Implementation of the formal system and experiments validate the correctness and utility of the GFT. The backward depth-first search method only yields a 2.42% problem-solving failure rate, and we can incorporate deep learning techniques to achieve lower one. The source code of FGPS and datasets are available at https://github.com/BitSecret/FGPS.

Problem-solving has been a fundamental driver of human progress in numerous domains. With advancements in artificial intelligence, Large Language Models (LLMs) have emerged as powerful tools capable of tackling complex problems across diverse domains. Unlike traditional computational systems, LLMs combine raw computational power with an approximation of human reasoning, allowing them to generate solutions, make inferences, and even leverage external computational tools. However, applying LLMs to real-world problem-solving presents significant challenges, including multi-step reasoning, domain knowledge integration, and result verification. This survey explores the capabilities and limitations of LLMs in complex problem-solving, examining techniques including Chain-of-Thought (CoT) reasoning, knowledge augmentation, and various LLM-based and tool-based verification techniques. Additionally, we highlight domain-specific challenges in various domains, such as software engineering, mathematical reasoning and proving, data analysis and modeling, and scientific research. The paper further discusses the fundamental limitations of the current LLM solutions and the future directions of LLM-based complex problems solving from the perspective of multi-step reasoning, domain knowledge integration and result verification.

Plane geometry problem solving (PGPS) has recently gained significant attention as a benchmark to assess the multi-modal reasoning capabilities of large vision-language models. Despite the growing interest in PGPS, the research community still lacks a comprehensive overview that systematically synthesizes recent work in PGPS. To fill this gap, we present a survey of existing PGPS studies. We first categorize PGPS methods into an encoder-decoder framework and summarize the corresponding output formats used by their encoders and decoders. Subsequently, we classify and analyze these encoders and decoders according to their architectural designs. Finally, we outline major challenges and promising directions for future research. In particular, we discuss the hallucination issues arising during the encoding phase within encoder-decoder architectures, as well as the problem of data leakage in current PGPS benchmarks.

Recent advances in Multimodal Large Language Models (MLLMs) have achieved remarkable progress in general domains and demonstrated promise in multimodal mathematical reasoning. However, applying MLLMs to geometry problem solving (GPS) remains challenging due to lack of accurate step-by-step solution data and severe hallucinations during reasoning. In this paper, we propose GeoGen, a pipeline that can automatically generates step-wise reasoning paths for geometry diagrams. By leveraging the precise symbolic reasoning, GeoGen produces large-scale, high-quality question-answer pairs. To further enhance the logical reasoning ability of MLLMs, we train GeoLogic, a Large Language Model (LLM) using synthetic data generated by GeoGen. Serving as a bridge between natural language and symbolic systems, GeoLogic enables symbolic tools to help verifying MLLM outputs, making the reasoning process more rigorous and alleviating hallucinations. Experimental results show that our approach consistently improves the performance of MLLMs, achieving remarkable results on benchmarks for geometric reasoning tasks. This improvement stems from our integration of the strengths of LLMs and symbolic systems, which enables a more reliable and interpretable approach for the GPS task. Codes are available at https://github.com/ycpNotFound/GeoGen.

Recent advances in large language models (LLMs) have predominantly focused on maximizing accuracy and reasoning capabilities, often overlooking crucial computational efficiency considerations. While this approach has yielded impressive accuracy improvements, it has led to methods that may be impractical for real-world deployment due to computational overhead and latency constraints. This paper investigates the potential synergy between reasoning enhancement and computational efficiency by analyzing the integration of two contrasting approaches: Quiet-STaR (Self-Taught Reasoner) and REBASE (REward BAlanced SEarch). Through comprehensive empirical analysis using the Mistral-7B model on the GSM8K dataset, we demonstrate that while each method excels in its primary objective-Quiet-STaR achieving superior accuracy (32.03%) despite high computational cost (554.66s runtime, 12.73T FLOPs), and REBASE providing exceptional efficiency (8.47s runtime, 2.35T FLOPs) while maintaining baseline-comparable accuracy (10.94%)-their integration reveals fundamental challenges in reconciling reasoning depth with computational efficiency. The combined approach unexpectedly results in degraded performance (9.38% accuracy, 143.66s runtime), highlighting critical insights about the complex interplay between reasoning enhancement and efficiency optimization in LLMs. Our findings illuminate the need for novel architectures and algorithms specifically designed to bridge the gap between these competing objectives, while providing concrete directions for future research in compute-efficient reasoning methods.

Large language models (LLMs) have demonstrated transformative potential across various domains, yet they face significant challenges in knowledge integration and complex problem reasoning, often leading to hallucinations and unreliable outputs. Retrieval-Augmented Generation (RAG) has emerged as a promising solution to enhance LLMs accuracy by incorporating external knowledge. However, traditional RAG systems struggle with processing complex relational information and multi-step reasoning, limiting their effectiveness in advanced problem-solving tasks. To address these limitations, we propose CogGRAG, a cognition inspired graph-based RAG framework, designed to improve LLMs performance in Knowledge Graph Question Answering (KGQA). Inspired by the human cognitive process of decomposing complex problems and performing self-verification, our framework introduces a three-stage methodology: decomposition, retrieval, and reasoning with self-verification. By integrating these components, CogGRAG enhances the accuracy of LLMs in complex problem solving. We conduct systematic experiments with three LLM backbones on four benchmark datasets, where CogGRAG outperforms the baselines.

Code synthesis, which requires a deep understanding of complex natural language problem descriptions, generation of code instructions for complex algorithms and data structures, and the successful execution of comprehensive unit tests, presents a significant challenge. While large language models (LLMs) demonstrate impressive proficiency in natural language processing, their performance in code generation tasks remains limited. In this paper, we introduce a new approach to code generation tasks leveraging multi-agent prompting that uniquely replicates the full cycle of program synthesis as observed in human developers. Our framework, MapCoder, consists of four LLM agents specifically designed to emulate the stages of this cycle: recalling relevant examples, planning, code generation, and debugging. After conducting thorough experiments, with multiple LLM ablations and analyses across eight challenging competitive problem-solving and program synthesis benchmarks, MapCoder showcases remarkable code generation capabilities, achieving new state-of-the-art results (pass@1) on HumanEval (93.9%), MBPP (83.1%), APPS (22.0%), CodeContests (28.5%), and xCodeEval (45.3%). Moreover, our method consistently delivers superior performance across various programming languages and varying problem difficulties. We open-source our framework at https://github.com/Md-Ashraful-Pramanik/MapCoder.

Large Language Models (LLMs) have attained human-level accuracy on medical question-answer (QA) benchmarks. However, their limitations in navigating open-ended clinical scenarios have recently been shown, raising concerns about the robustness and generalizability of LLM reasoning across diverse, real-world medical tasks. To probe potential LLM failure modes in clinical problem-solving, we present the medical abstraction and reasoning corpus (M-ARC). M-ARC assesses clinical reasoning through scenarios designed to exploit the Einstellung effect -- the fixation of thought arising from prior experience, targeting LLM inductive biases toward inflexible pattern matching from their training data rather than engaging in flexible reasoning. We find that LLMs, including current state-of-the-art o1 and Gemini models, perform poorly compared to physicians on M-ARC, often demonstrating lack of commonsense medical reasoning and a propensity to hallucinate. In addition, uncertainty estimation analyses indicate that LLMs exhibit overconfidence in their answers, despite their limited accuracy. The failure modes revealed by M-ARC in LLM medical reasoning underscore the need to exercise caution when deploying these models in clinical settings.

We present the Process Engineering Operations Assistant (PEOA), an AI-driven framework designed to solve complex problems in the chemical and process industries. The framework employs a modular architecture orchestrated by a meta-agent, which serves as the central coordinator, managing an action generator and instruction-tuned small-scale language models (expert models). The action generator decomposes complex problems into sub-tasks and identifies suitable expert models to execute each, delivering precise solutions for multi-step problem-solving. Key techniques include advanced knowledge modeling using property graphs for improved information retrieval, facilitating more accurate and contextually relevant solutions. Additionally, the framework utilizes a teacher-student transfer-learning approach with GPT-4 (Omni) to fine-tune the action generator and expert models for domain adaptation, alongside an iterative problem-solving mechanism with sophisticated error handling. Custom datasets were developed to evaluate the framework against leading proprietary language models on various engineering tasks. The results demonstrate the framework effectiveness in automating calculations, accelerating prototyping, and providing AI-augmented decision support for industrial processes, marking a significant advancement in process engineering capabilities.

Metacognitive knowledge refers to humans' intuitive knowledge of their own thinking and reasoning processes. Today's best LLMs clearly possess some reasoning processes. The paper gives evidence that they also have metacognitive knowledge, including ability to name skills and procedures to apply given a task. We explore this primarily in context of math reasoning, developing a prompt-guided interaction procedure to get a powerful LLM to assign sensible skill labels to math questions, followed by having it perform semantic clustering to obtain coarser families of skill labels. These coarse skill labels look interpretable to humans. To validate that these skill labels are meaningful and relevant to the LLM's reasoning processes we perform the following experiments. (a) We ask GPT-4 to assign skill labels to training questions in math datasets GSM8K and MATH. (b) When using an LLM to solve the test questions, we present it with the full list of skill labels and ask it to identify the skill needed. Then it is presented with randomly selected exemplar solved questions associated with that skill label. This improves accuracy on GSM8k and MATH for several strong LLMs, including code-assisted models. The methodology presented is domain-agnostic, even though this article applies it to math problems.

Although pre-trained language models~(PLMs) have recently advanced the research progress in mathematical reasoning, they are not specially designed as a capable multi-task solver, suffering from high cost for multi-task deployment (\eg a model copy for a task) and inferior performance on complex mathematical problems in practical applications. To address these issues, in this paper, we propose JiuZhang~2.0, a unified Chinese PLM specially for multi-task mathematical problem solving. Our idea is to maintain a moderate-sized model and employ the cross-task knowledge sharing to improve the model capacity in a multi-task setting. Specially, we construct a Mixture-of-Experts~(MoE) architecture for modeling mathematical text, so as to capture the common mathematical knowledge across tasks. For optimizing the MoE architecture, we design multi-task continual pre-training and multi-task fine-tuning strategies for multi-task adaptation. These training strategies can effectively decompose the knowledge from the task data and establish the cross-task sharing via expert networks. In order to further improve the general capacity of solving different complex tasks, we leverage large language models~(LLMs) as complementary models to iteratively refine the generated solution by our PLM, via in-context learning. Extensive experiments have demonstrated the effectiveness of our model.

Large language models have made significant progress in various language tasks, yet they still struggle with complex mathematics. In this paper, we propose ToRA a series of Tool-integrated Reasoning Agents designed to solve challenging mathematical problems by seamlessly integrating natural language reasoning with the utilization of external tools (e.g., computation libraries and symbolic solvers), thereby amalgamating the analytical prowess of language and the computational efficiency of tools. To train ToRA, we curate interactive tool-use trajectories on mathematical datasets, apply imitation learning on the annotations, and propose output space shaping to further refine models' reasoning behavior. As a result, ToRA models significantly outperform open-source models on 10 mathematical reasoning datasets across all scales with 13%-19% absolute improvements on average. Notably, ToRA-7B reaches 44.6% on the competition-level dataset MATH, surpassing the best open-source model WizardMath-70B by 22% absolute. ToRA-34B is also the first open-source model that achieves an accuracy exceeding 50% on MATH, which significantly outperforms GPT-4's CoT result, and is competitive with GPT-4 solving problems with programs. Additionally, we conduct a comprehensive analysis of the benefits and remaining challenges of tool interaction for mathematical reasoning, providing valuable insights for future research.

The performance of large language models (LLMs) on existing reasoning benchmarks has significantly improved over the past years. In response, we present JEEBench, a considerably more challenging benchmark dataset for evaluating the problem solving abilities of LLMs. We curate 515 challenging pre-engineering mathematics, physics and chemistry problems from the highly competitive IIT JEE-Advanced exam. Long-horizon reasoning on top of deep in-domain knowledge is essential for solving problems in this benchmark. Our evaluation on various open-source and proprietary models reveals that the highest performance, even after using techniques like self-consistency, self-refinement and chain-of-thought prompting, is less than 40%. The typical failure modes of GPT-4, the best model, are errors in algebraic manipulation, difficulty in grounding abstract concepts into mathematical equations accurately and failure in retrieving relevant domain-specific concepts. We also observe that by mere prompting, GPT-4 is unable to assess risk introduced by negative marking for incorrect answers. For this, we develop a post-hoc confidence-thresholding method over self-consistency, which enables effective response selection. We hope that our challenging benchmark will guide future re-search in problem-solving using LLMs.

Scaling test-time compute has emerged as a key strategy for enhancing the reasoning capabilities of large language models (LLMs), particularly in tasks like mathematical problem-solving. A traditional approach, Self-Consistency (SC), generates multiple solutions to a problem and selects the most common answer via majority voting. Another common method involves scoring each solution with a reward model (verifier) and choosing the best one. Recent advancements in Generative Reward Models (GenRM) reframe verification as a next-token prediction task, enabling inference-time scaling along a new axis. Specifically, GenRM generates multiple verification chains-of-thought to score each solution. Under a limited inference budget, this introduces a fundamental trade-off: should you spend the budget on scaling solutions via SC or generate fewer solutions and allocate compute to verification via GenRM? To address this, we evaluate GenRM against SC under a fixed inference budget. Interestingly, we find that SC is more compute-efficient than GenRM for most practical inference budgets across diverse models and datasets. For instance, GenRM first matches SC after consuming up to 8x the inference compute and requires significantly more compute to outperform it. Furthermore, we derive inference scaling laws for the GenRM paradigm, revealing that compute-optimal inference favors scaling solution generation more aggressively than scaling the number of verifications. Our work provides practical guidance on optimizing test-time scaling by balancing solution generation and verification. The code is available at https://github.com/nishadsinghi/sc-genrm-scaling.

Multimodal scientific problems (MSPs) involve complex issues that require the integration of multiple modalities, such as text and diagrams, presenting a significant challenge in artificial intelligence. While progress has been made in addressing traditional scientific problems, MSPs still face two primary issues: the challenge of multi-modal comprehensive reasoning in scientific problem-solving and the lack of reflective and rethinking capabilities. To address these issues, we introduce a Multi-Agent framework based on the Big Seven Personality and Socratic guidance (MAPS). This framework employs seven distinct agents that leverage feedback mechanisms and the Socratic method to guide the resolution of MSPs. To tackle the first issue, we propose a progressive four-agent solving strategy, where each agent focuses on a specific stage of the problem-solving process. For the second issue, we introduce a Critic agent, inspired by Socratic questioning, which prompts critical thinking and stimulates autonomous learning. We conduct extensive experiments on the EMMA, Olympiad, and MathVista datasets, achieving promising results that outperform the current SOTA model by 15.84% across all tasks. Meanwhile, the additional analytical experiments also verify the model's progress as well as generalization ability.

Most existing chain-of-thought (CoT) prompting methods suffer from the issues of generalizability and consistency, as they often rely on instance-specific solutions that may not be applicable to other cases and lack task-level consistency in their reasoning steps. To address these limitations, we propose a comprehensive framework, StrategyLLM, harnessing the capabilities of LLMs to construct generalizable and consistent few-shot prompts for various tasks automatically. To this end, StrategyLLM employs four LLM-based agents: strategy generator, executor, optimizer, and evaluator, working together to generate, evaluate, and select promising strategies for a given task. The experimental results demonstrate that StrategyLLM outperforms the competitive baseline CoT-SC that requires human-annotated solutions on 13 datasets across 4 challenging tasks without human involvement, including math reasoning (34.21% rightarrow 38.79%), commonsense reasoning (70.3% rightarrow 72.5%), algorithmic reasoning (51.7% rightarrow 62.0%), and symbolic reasoning (30.0% rightarrow 79.2%).

Automatic math word problem solving has attracted growing attention in recent years. The evaluation datasets used by previous works have serious limitations in terms of scale and diversity. In this paper, we release a new large-scale and template-rich math word problem dataset named Ape210K. It consists of 210K Chinese elementary school-level math problems, which is 9 times the size of the largest public dataset Math23K. Each problem contains both the gold answer and the equations needed to derive the answer. Ape210K is also of greater diversity with 56K templates, which is 25 times more than Math23K. Our analysis shows that solving Ape210K requires not only natural language understanding but also commonsense knowledge. We expect Ape210K to be a benchmark for math word problem solving systems. Experiments indicate that state-of-the-art models on the Math23K dataset perform poorly on Ape210K. We propose a copy-augmented and feature-enriched sequence to sequence (seq2seq) model, which outperforms existing models by 3.2% on the Math23K dataset and serves as a strong baseline of the Ape210K dataset. The gap is still significant between human and our baseline model, calling for further research efforts. We make Ape210K dataset publicly available at https://github.com/yuantiku/ape210k

Large multimodal models have demonstrated impressive problem-solving abilities in vision and language tasks, and have the potential to encode extensive world knowledge. However, it remains an open challenge for these models to perceive, reason, plan, and act in realistic environments. In this work, we introduce Can-Do, a benchmark dataset designed to evaluate embodied planning abilities through more diverse and complex scenarios than previous datasets. Our dataset includes 400 multimodal samples, each consisting of natural language user instructions, visual images depicting the environment, state changes, and corresponding action plans. The data encompasses diverse aspects of commonsense knowledge, physical understanding, and safety awareness. Our fine-grained analysis reveals that state-of-the-art models, including GPT-4V, face bottlenecks in visual perception, comprehension, and reasoning abilities. To address these challenges, we propose NeuroGround, a neurosymbolic framework that first grounds the plan generation in the perceived environment states and then leverages symbolic planning engines to augment the model-generated plans. Experimental results demonstrate the effectiveness of our framework compared to strong baselines. Our code and dataset are available at https://embodied-planning.github.io.

Recent LLMs have demonstrated remarkable performance in solving exam-like math word problems. However, the degree to which these numerical reasoning skills are effective in real-world scenarios, particularly in expert domains, is still largely unexplored. This paper introduces DocMath-Eval, a comprehensive benchmark specifically designed to evaluate the numerical reasoning and problem-solving capabilities of LLMs in the context of understanding and analyzing financial documents containing both text and tables. We evaluate a wide spectrum of 19 LLMs, including those specialized in coding and finance. We also incorporate different prompting strategies (i.e., Chain-of-Thoughts and Program-of-Thoughts) to comprehensively assess the capabilities and limitations of existing LLMs in DocMath-Eval. We found that, although the current best-performing system (i.e., GPT-4), can perform well on simple problems such as calculating the rate of increase in a financial metric within a short document context, it significantly lags behind human experts in more complex problems grounded in longer contexts. We believe DocMath-Eval can be used as a valuable benchmark to evaluate LLMs' capabilities to solve challenging numerical reasoning problems in expert domains. We will release the benchmark and code at https://github.com/yale-nlp/DocMath-Eval.

Solving parametric partial differential equations (PDEs) and associated PDE-based, inverse problems is a central task in engineering and physics, yet existing neural operator methods struggle with high-dimensional, discontinuous inputs and require large amounts of {\em labeled} training data. We propose the Deep Generative Neural Operator (DGNO), a physics-aware framework that addresses these challenges by leveraging a deep, generative, probabilistic model in combination with a set of lower-dimensional, latent variables that simultaneously encode PDE-inputs and PDE-outputs. This formulation can make use of unlabeled data and significantly improves inverse problem-solving, particularly for discontinuous or discrete-valued input functions. DGNO enforces physics constraints without labeled data by incorporating as virtual observables, weak-form residuals based on compactly supported radial basis functions (CSRBFs). These relax regularity constraints and eliminate higher-order derivatives from the objective function. We also introduce MultiONet, a novel neural operator architecture, which is a more expressive generalization of the popular DeepONet that significantly enhances the approximating power of the proposed model. These innovations make DGNO particularly effective for challenging forward and inverse, PDE-based problems, such as those involving multi-phase media. Numerical experiments demonstrate that DGNO achieves higher accuracy across multiple benchmarks while exhibiting robustness to noise and strong generalization to out-of-distribution cases. Its adaptability, and the ability to handle sparse, noisy data while providing probabilistic estimates, make DGNO a powerful tool for scientific and engineering applications.

While closed-source Large Language Models (LLMs) demonstrate strong mathematical problem-solving abilities, open-source models continue to struggle with such tasks. To bridge this gap, we propose a data augmentation approach and introduce PersonaMathQA, a dataset derived from MATH and GSM8K, on which we train the PersonaMath models. Our approach consists of two stages: the first stage is learning from Persona Diversification, and the second stage is learning from Reflection. In the first stage, we regenerate detailed chain-of-thought (CoT) solutions as instructions using a closed-source LLM and introduce a novel persona-driven data augmentation technique to enhance the dataset's quantity and diversity. In the second stage, we incorporate reflection to fully leverage more challenging and valuable questions. Evaluation of our PersonaMath models on MATH and GSM8K reveals that the PersonaMath-7B model (based on LLaMA-2-7B) achieves an accuracy of 24.2% on MATH and 68.7% on GSM8K, surpassing all baseline methods and achieving state-of-the-art performance. Notably, our dataset contains only 70.3K data points-merely 17.8% of MetaMathQA and 27% of MathInstruct-yet our model outperforms these baselines, demonstrating the high quality and diversity of our dataset, which enables more efficient model training. We open-source the PersonaMathQA dataset, PersonaMath models, and our code for public usage.

Data science tasks involving tabular data present complex challenges that require sophisticated problem-solving approaches. We propose AutoKaggle, a powerful and user-centric framework that assists data scientists in completing daily data pipelines through a collaborative multi-agent system. AutoKaggle implements an iterative development process that combines code execution, debugging, and comprehensive unit testing to ensure code correctness and logic consistency. The framework offers highly customizable workflows, allowing users to intervene at each phase, thus integrating automated intelligence with human expertise. Our universal data science toolkit, comprising validated functions for data cleaning, feature engineering, and modeling, forms the foundation of this solution, enhancing productivity by streamlining common tasks. We selected 8 Kaggle competitions to simulate data processing workflows in real-world application scenarios. Evaluation results demonstrate that AutoKaggle achieves a validation submission rate of 0.85 and a comprehensive score of 0.82 in typical data science pipelines, fully proving its effectiveness and practicality in handling complex data science tasks.

Despite the effectiveness of data selection for large language models (LLMs) during pretraining and instruction fine-tuning phases, improving data efficiency in supervised fine-tuning (SFT) for specialized domains poses significant challenges due to the complexity of fine-tuning data. To bridge this gap, we introduce an effective and scalable data selection method for SFT, SmallToLarge (S2L), which leverages training trajectories from small models to guide the data selection for larger models. We demonstrate through extensive experiments that S2L significantly improves data efficiency in SFT for mathematical problem-solving, reducing the training data to just 11% of the original MathInstruct dataset (Yue et al., 2023) to match full dataset performance while outperforming state-of-the-art data selection algorithms by an average of 4.7% across 6 in- and out-domain evaluation datasets. Remarkably, selecting only 50K data for SFT, S2L achieves a 32.7% accuracy on the most challenging MATH (Hendrycks et al., 2021) benchmark, improving Phi-2 (Li et al., 2023b) by 16.6%. In clinical text summarization on the MIMIC-III dataset (Johnson et al., 2016), S2L again outperforms training on the full dataset using only 50% of the data. Notably, S2L can perform data selection using a reference model 40x smaller than the target model, proportionally reducing the cost of data selection.

The rapid advancement of large language models (LLMs) such as GPT-3, PaLM, and Llama has significantly transformed natural language processing, showcasing remarkable capabilities in understanding and generating language. However, these models often struggle with tasks requiring complex reasoning, particularly in mathematical problem-solving, due in part to the scarcity of large-scale, high-quality, domain-specific datasets necessary for training sophisticated reasoning abilities. To address this limitation, we introduce Template-based Data Generation (TDG), a novel approach that leverages LLMs (GPT-4) to automatically generate parameterized meta-templates, which are then used to synthesize a vast array of high-quality problems and solutions. Leveraging TDG, we create TemplateMath Part I: TemplateGSM, a dataset comprising over 7 million synthetically generated grade school math problems--each accompanied by code-based and natural language solutions--with the potential to generate an effectively unlimited number more. This dataset alleviates the scarcity of large-scale mathematical datasets and serves as a valuable resource for pre-training, fine-tuning, and evaluating LLMs in mathematical reasoning. Our method not only enables the generation of virtually infinite data but also elevates data augmentation to a new level by using GPT-4 for meta-template generation, ensuring diverse and high-quality problem structures. The TemplateMath Part I: TemplateGSM dataset is publicly available at https://huggingface.co/datasets/math-ai/TemplateGSM. The code is available at https://github.com/iiis-ai/TemplateMath.

Reinforcement Learning with Verifiable Rewards (RLVR) has emerged as a powerful paradigm for enhancing the reasoning capabilities of LLMs. Existing research has predominantly concentrated on isolated reasoning domains such as mathematical problem-solving, coding tasks, or logical reasoning. However, real world reasoning scenarios inherently demand an integrated application of multiple cognitive skills. Despite this, the interplay among these reasoning skills under reinforcement learning remains poorly understood. To bridge this gap, we present a systematic investigation of multi-domain reasoning within the RLVR framework, explicitly focusing on three primary domains: mathematical reasoning, code generation, and logical puzzle solving. We conduct a comprehensive study comprising four key components: (1) Leveraging the GRPO algorithm and the Qwen-2.5-7B model family, our study thoroughly evaluates the models' in-domain improvements and cross-domain generalization capabilities when trained on single-domain datasets. (2) Additionally, we examine the intricate interactions including mutual enhancements and conflicts that emerge during combined cross-domain training. (3) To further understand the influence of SFT on RL, we also analyze and compare performance differences between base and instruct models under identical RL configurations. (4) Furthermore, we delve into critical RL training details, systematically exploring the impacts of curriculum learning strategies, variations in reward design, and language-specific factors. Through extensive experiments, our results offer significant insights into the dynamics governing domain interactions, revealing key factors influencing both specialized and generalizable reasoning performance. These findings provide valuable guidance for optimizing RL methodologies to foster comprehensive, multi-domain reasoning capabilities in LLMs.

The emergence of large reasoning models (LRMs) has transformed Natural Language Processing by excelling in complex tasks such as mathematical problem-solving and code generation. These models leverage chain-of-thought (CoT) processes, enabling them to emulate human-like reasoning strategies. However, the advancement of LRMs is hindered by the lack of comprehensive CoT datasets. Current resources often fail to provide extensive reasoning problems with coherent CoT processes distilled from multiple teacher models and do not account for multifaceted properties describing the internal characteristics of CoTs. To address these challenges, we introduce OmniThought, a large-scale dataset featuring 2 million CoT processes generated and validated by two powerful LRMs as teacher models. Each CoT process in OmniThought is annotated with novel Reasoning Verbosity (RV) and Cognitive Difficulty (CD) scores, which describe the appropriateness of CoT verbosity and cognitive difficulty level for models to comprehend these reasoning processes. We further establish a self-reliant pipeline to curate this dataset. Extensive experiments using Qwen2.5 models of various sizes demonstrate the positive impact of our proposed scores on LRM training effectiveness. Based on the proposed OmniThought dataset, we further train and release a series of high-performing LRMs, specifically equipped with stronger reasoning abilities and optimal CoT output length and difficulty level. Our contributions significantly enhance the development and training of LRMs for solving complex tasks.

Software engineering (SWE) has recently emerged as a crucial testbed for next-generation LLM agents, demanding inherent capabilities in two critical dimensions: sustained iterative problem-solving (e.g., >50 interaction rounds) and long-context dependency resolution (e.g., >32k tokens). However, the data curation process in SWE remains notoriously time-consuming, as it heavily relies on manual annotation for code file filtering and the setup of dedicated runtime environments to execute and validate unit tests. Consequently, most existing datasets are limited to only a few thousand GitHub-sourced instances. To this end, we propose an incremental, automated data-curation pipeline that systematically scales both the volume and diversity of SWE datasets. Our dataset comprises 10,169 real-world Python task instances from 2,531 distinct GitHub repositories, each accompanied by a task specified in natural language and a dedicated runtime-environment image for automated unit-test validation. We have carefully curated over 8,000 successfully runtime-validated training trajectories from our proposed SWE dataset. When fine-tuning the Skywork-SWE model on these trajectories, we uncover a striking data scaling phenomenon: the trained model's performance for software engineering capabilities in LLMs continues to improve as the data size increases, showing no signs of saturation. Notably, our Skywork-SWE model achieves 38.0% pass@1 accuracy on the SWE-bench Verified benchmark without using verifiers or multiple rollouts, establishing a new state-of-the-art (SOTA) among the Qwen2.5-Coder-32B-based LLMs built on the OpenHands agent framework. Furthermore, with the incorporation of test-time scaling techniques, the performance further improves to 47.0% accuracy, surpassing the previous SOTA results for sub-32B parameter models. We release the Skywork-SWE-32B model checkpoint to accelerate future research.

Recent advancements in machine learning have significantly improved the identification of disease-associated genes from gene expression datasets. However, these processes often require extensive expertise and manual effort, limiting their scalability. Large Language Model (LLM)-based agents have shown promise in automating these tasks due to their increasing problem-solving abilities. To support the evaluation and development of such methods, we introduce GenoTEX, a benchmark dataset for the automated analysis of gene expression data. GenoTEX provides annotated code and results for solving a wide range of gene identification problems, encompassing dataset selection, preprocessing, and statistical analysis, in a pipeline that follows computational genomics standards. The benchmark includes expert-curated annotations from bioinformaticians to ensure accuracy and reliability. To provide baselines for these tasks, we present GenoAgent, a team of LLM-based agents that adopt a multi-step programming workflow with flexible self-correction, to collaboratively analyze gene expression datasets. Our experiments demonstrate the potential of LLM-based methods in analyzing genomic data, while error analysis highlights the challenges and areas for future improvement. We propose GenoTEX as a promising resource for benchmarking and enhancing automated methods for gene expression data analysis. The benchmark is available at https://github.com/Liu-Hy/GenoTex.

Given the increasing use of synthetic data in language model (LM) post-training, an LM's ability to generate high-quality data has become nearly as crucial as its ability to solve problems directly. While prior works have focused on developing effective data generation methods, they lack systematic comparison of different LMs as data generators in a unified setting. To address this gap, we propose AgoraBench, a benchmark that provides standardized settings and metrics to evaluate LMs' data generation abilities. Through synthesizing 1.26 million training instances using 6 LMs and training 99 student models, we uncover key insights about LMs' data generation capabilities. First, we observe that LMs exhibit distinct strengths. For instance, GPT-4o excels at generating new problems, while Claude-3.5-Sonnet performs better at enhancing existing ones. Furthermore, our analysis reveals that an LM's data generation ability doesn't necessarily correlate with its problem-solving ability. Instead, multiple intrinsic features of data quality-including response quality, perplexity, and instruction difficulty-collectively serve as better indicators. Finally, we demonstrate that strategic choices in output format and cost-conscious model selection significantly impact data generation effectiveness.

Foundation models have shown remarkable success across scientific domains, yet their impact in chemistry remains limited due to the absence of diverse, large-scale, high-quality datasets that reflect the field's multifaceted nature. We present the ChemPile, an open dataset containing over 75 billion tokens of curated chemical data, specifically built for training and evaluating general-purpose models in the chemical sciences. The dataset mirrors the human learning journey through chemistry -- from educational foundations to specialized expertise -- spanning multiple modalities and content types including structured data in diverse chemical representations (SMILES, SELFIES, IUPAC names, InChI, molecular renderings), scientific and educational text, executable code, and chemical images. ChemPile integrates foundational knowledge (textbooks, lecture notes), specialized expertise (scientific articles and language-interfaced data), visual understanding (molecular structures, diagrams), and advanced reasoning (problem-solving traces and code) -- mirroring how human chemists develop expertise through diverse learning materials and experiences. Constructed through hundreds of hours of expert curation, the ChemPile captures both foundational concepts and domain-specific complexity. We provide standardized training, validation, and test splits, enabling robust benchmarking. ChemPile is openly released via HuggingFace with a consistent API, permissive license, and detailed documentation. We hope the ChemPile will serve as a catalyst for chemical AI, enabling the development of the next generation of chemical foundation models.

Solving mechanics problems using numerical methods requires comprehensive intelligent capability of retrieving relevant knowledge and theory, constructing and executing codes, analyzing the results, a task that has thus far mainly been reserved for humans. While emerging AI methods can provide effective approaches to solve end-to-end problems, for instance via the use of deep surrogate models or various data analytics strategies, they often lack physical intuition since knowledge is baked into the parametric complement through training, offering less flexibility when it comes to incorporating mathematical or physical insights. By leveraging diverse capabilities of multiple dynamically interacting large language models (LLMs), we can overcome the limitations of conventional approaches and develop a new class of physics-inspired generative machine learning platform, here referred to as MechAgents. A set of AI agents can solve mechanics tasks, here demonstrated for elasticity problems, via autonomous collaborations. A two-agent team can effectively write, execute and self-correct code, in order to apply finite element methods to solve classical elasticity problems in various flavors (different boundary conditions, domain geometries, meshes, small/finite deformation and linear/hyper-elastic constitutive laws, and others). For more complex tasks, we construct a larger group of agents with enhanced division of labor among planning, formulating, coding, executing and criticizing the process and results. The agents mutually correct each other to improve the overall team-work performance in understanding, formulating and validating the solution. Our framework shows the potential of synergizing the intelligence of language models, the reliability of physics-based modeling, and the dynamic collaborations among diverse agents, opening novel avenues for automation of solving engineering problems.

As multi-modal large language models (MLLMs) frequently exhibit errors when solving scientific problems, evaluating the validity of their reasoning processes is critical for ensuring reliability and uncovering fine-grained model weaknesses. Since human evaluation is laborious and costly, prompting MLLMs as automated process judges has become a common practice. However, the reliability of these model-based judges remains uncertain. To address this, we introduce ProJudgeBench, the first comprehensive benchmark specifically designed for evaluating abilities of MLLM-based process judges. ProJudgeBench comprises 2,400 test cases and 50,118 step-level labels, spanning four scientific disciplines with diverse difficulty levels and multi-modal content. In ProJudgeBench, each step is meticulously annotated by human experts for correctness, error type, and explanation, enabling a systematic evaluation of judges' capabilities to detect, classify and diagnose errors. Evaluation on ProJudgeBench reveals a significant performance gap between open-source and proprietary models. To bridge this gap, we further propose ProJudge-173k, a large-scale instruction-tuning dataset, and a Dynamic Dual-Phase fine-tuning strategy that encourages models to explicitly reason through problem-solving before assessing solutions. Both contributions significantly enhance the process evaluation capabilities of open-source models. All the resources will be released to foster future research of reliable multi-modal process evaluation.

NLP has recently made exciting progress toward training language models (LMs) with strong scientific problem-solving skills. However, model development has not focused on real-life use-cases of LMs for science, including applications in education that require processing long scientific documents. To address this, we introduce TutorEval and TutorChat. TutorEval is a diverse question-answering benchmark consisting of questions about long chapters from STEM textbooks, written by experts. TutorEval helps measure real-life usability of LMs as scientific assistants, and it is the first benchmark combining long contexts, free-form generation, and multi-disciplinary scientific knowledge. Moreover, we show that fine-tuning base models with existing dialogue datasets leads to poor performance on TutorEval. Therefore, we create TutorChat, a dataset of 80,000 long synthetic dialogues about textbooks. We use TutorChat to fine-tune Llemma models with 7B and 34B parameters. These LM tutors specialized in math have a 32K-token context window, and they excel at TutorEval while performing strongly on GSM8K and MATH. Our datasets build on open-source materials, and we release our models, data, and evaluations.

We present a design framework called Conversational Learning with Analytical Step-by-Step Strategies (CLASS) for developing high-performance Intelligent Tutoring Systems (ITS). The CLASS framework aims to empower ITS with with two critical capabilities: imparting tutor-like step-by-step guidance and enabling tutor-like conversations in natural language to effectively engage learners. To empower ITS with the aforementioned capabilities, the CLASS framework employs two carefully curated synthetic datasets. The first scaffolding dataset encompasses a variety of elements, including problems, their corresponding subproblems, hints, incorrect solutions, and tailored feedback. This dataset provides ITS with essential problem-solving strategies necessary for guiding students through each step of the conversation. The second conversational dataset contains simulated student-tutor conversations that involve the application of problem-solving strategies learned from the first dataset. In the second dataset, the tutoring system adheres to a pre-defined response template, which helps to maintain consistency and structure in ITS's responses during its interactions. This structured methodology facilitates seamless integration of user feedback and yields valuable insights into ITS's internal decision-making process, allowing for continuous refinement and improvement of the system. We also present a proof-of-concept ITS, referred to as SPOCK, trained using the CLASS framework with a focus on college level introductory biology content. A carefully constructed protocol was developed for SPOCK's preliminary evaluation, examining aspects such as the factual accuracy and relevance of its responses. Experts in the field of biology offered favorable remarks, particularly highlighting SPOCK's capability to break down questions into manageable subproblems and provide step-by-step guidance to students.

In this paper, we explore the capabilities of state-of-the-art large language models (LLMs) such as GPT-4, Claude 3 Opus, and Gemini 1.0 Ultra in solving undergraduate-level control problems. Controls provides an interesting case study for LLM reasoning due to its combination of mathematical theory and engineering design. We introduce ControlBench, a benchmark dataset tailored to reflect the breadth, depth, and complexity of classical control design. We use this dataset to study and evaluate the problem-solving abilities of these LLMs in the context of control engineering. We present evaluations conducted by a panel of human experts, providing insights into the accuracy, reasoning, and explanatory prowess of LLMs in control engineering. Our analysis reveals the strengths and limitations of each LLM in the context of classical control, and our results imply that Claude 3 Opus has become the state-of-the-art LLM for solving undergraduate control problems. Our study serves as an initial step towards the broader goal of employing artificial general intelligence in control engineering.

One way to enhance the reasoning capability of Large Language Models (LLMs) is to conduct Supervised Fine-Tuning (SFT) using Chain-of-Thought (CoT) annotations. This approach does not show sufficiently strong generalization ability, however, because the training only relies on the given CoT data. In math problem-solving, for example, there is usually only one annotated reasoning path for each question in the training data. Intuitively, it would be better for the algorithm to learn from multiple annotated reasoning paths given a question. To address this issue, we propose a simple yet effective approach called Reinforced Fine-Tuning (ReFT) to enhance the generalizability of learning LLMs for reasoning, with math problem-solving as an example. ReFT first warmups the model with SFT, and then employs on-line reinforcement learning, specifically the PPO algorithm in this paper, to further fine-tune the model, where an abundance of reasoning paths are automatically sampled given the question and the rewards are naturally derived from the ground-truth answers. Extensive experiments on GSM8K, MathQA, and SVAMP datasets show that ReFT significantly outperforms SFT, and the performance can be potentially further boosted by combining inference-time strategies such as majority voting and re-ranking. Note that ReFT obtains the improvement by learning from the same training questions as SFT, without relying on extra or augmented training questions. This indicates a superior generalization ability for ReFT.

Medical tasks such as diagnosis and treatment planning require precise and complex reasoning, particularly in life-critical domains. Unlike mathematical reasoning, medical reasoning demands meticulous, verifiable thought processes to ensure reliability and accuracy. However, there is a notable lack of datasets that provide transparent, step-by-step reasoning to validate and enhance the medical reasoning ability of AI models. To bridge this gap, we introduce MedReason, a large-scale high-quality medical reasoning dataset designed to enable faithful and explainable medical problem-solving in large language models (LLMs). We utilize a structured medical knowledge graph (KG) to convert clinical QA pairs into logical chains of reasoning, or ``thinking paths'', which trace connections from question elements to answers via relevant KG entities. Each path is validated for consistency with clinical logic and evidence-based medicine. Our pipeline generates detailed reasoning for various medical questions from 7 medical datasets, resulting in a dataset of 32,682 question-answer pairs, each with detailed, step-by-step explanations. Experiments demonstrate that fine-tuning with our dataset consistently boosts medical problem-solving capabilities, achieving significant gains of up to 7.7% for DeepSeek-Ditill-8B. Our top-performing model, MedReason-8B, outperforms the Huatuo-o1-8B, a state-of-the-art medical reasoning model, by up to 4.2% on the clinical benchmark MedBullets. We also engage medical professionals from diverse specialties to assess our dataset's quality, ensuring MedReason offers accurate and coherent medical reasoning. Our data, models, and code will be publicly available.

Recent developments, particularly OpenAI's O1 model, have demonstrated the remarkable potential of Large Language Models (LLMs) for complex reasoning tasks. Through analysis of O1's outputs and provided sample Chain-of-Thought (CoT) demonstrations, we observe that it approaches problem-solving in a distinctly human-like manner, systematically brainstorming ideas, testing hypotheses, verifying results, and planning comprehensive solutions. These sophisticated reasoning capabilities remain notably absent in other state-of-the-art language models. In this paper, we hypothesize that this performance gap stems from the limited availability of high-quality reasoning process data in current training sets. We demonstrate that by constructing a specialized dataset focused on explicit problem-solving workflows ("worked solutions"), we can elicit substantially improved planning capabilities from existing models. Additionally, we propose the Reasoning Enhancement Loop (REL), a method for generating synthetic worked solutions.

Dialogue-based language models mark a huge milestone in the field of artificial intelligence, by their impressive ability to interact with users, as well as a series of challenging tasks prompted by customized instructions. However, the prevalent large-scale dialogue-based language models like ChatGPT still have room for improvement, such as unstable responses to questions and the inability to think cooperatively like humans. Considering the ability of dialogue-based language models in conversation and their inherent randomness in thinking, we propose ChatLLM network that allows multiple dialogue-based language models to interact, provide feedback, and think together. We design the network of ChatLLMs based on ChatGPT. Specifically, individual instances of ChatGPT may possess distinct perspectives towards the same problem, and by consolidating these diverse viewpoints via a separate ChatGPT, the ChatLLM network system can conduct decision-making more objectively and comprehensively. In addition, a language-based feedback mechanism comparable to backpropagation is devised to update the ChatGPTs within the network. Experiments on two datasets demonstrate that our network attains significant improvements in problem-solving, leading to observable progress amongst each member.

Geometric ability is a significant challenge for large language models (LLMs) due to the need for advanced spatial comprehension and abstract thinking. Existing datasets primarily evaluate LLMs on their final answers, but they cannot truly measure their true understanding of geometric structures, as LLMs can arrive at correct answers by coincidence. To fill this gap, we introduce the GeomRel dataset, designed to evaluate LLMs' understanding of geometric structures by isolating the core step of geometric relationship identification in problem-solving. Using this benchmark, we conduct thorough evaluations of diverse LLMs and identify key limitations in understanding geometric structures. We further propose the Geometry Chain-of-Thought (GeoCoT) method, which enhances LLMs' ability to identify geometric relationships, resulting in significant performance improvements.

Mathematical problem-solving is a key field in artificial intelligence (AI) and a critical benchmark for evaluating the capabilities of large language models (LLMs). While extensive research has focused on mathematical problem-solving, most existing work and datasets concentrate on computational tasks, leaving gaps in areas like mathematical analysis, which demands rigorous proofs and formal reasoning. We developed the DEMI-MathAnalysis dataset, comprising proof-based problems from mathematical analysis topics such as Sequences and Limits, Infinite Series, and Convex Functions. We also designed a guiding framework to rigorously enhance LLMs' ability to solve these problems. Through fine-tuning LLMs on this dataset and employing our framework, we observed significant improvements in their capability to generate logical, complete, and elegant proofs. This work addresses critical gaps in mathematical reasoning and contributes to advancing trustworthy AI capable of handling formalized mathematical language. The code is publicly accessible at LLMs for Mathematical Analysis.

With the rapid advancement of powerful large language models (LLMs) in recent years, a wide range of software engineering tasks can now be addressed using LLMs, significantly enhancing productivity and scalability. Numerous benchmark datasets have been developed to evaluate the coding capabilities of these models, while they primarily focus on problem-solving and issue-resolution tasks. In contrast, we introduce a new coding benchmark MIGRATION-BENCH with a distinct focus: code migration. MIGRATION-BENCH aims to serve as a comprehensive benchmark for migration from Java 8 to the latest long-term support (LTS) versions (Java 17, 21), MIGRATION-BENCH includes a full dataset and its subset selected with 5,102 and 300 repositories respectively. Selected is a representative subset curated for complexity and difficulty, offering a versatile resource to support research in the field of code migration. Additionally, we provide a comprehensive evaluation framework to facilitate rigorous and standardized assessment of LLMs on this challenging task. We further propose SD-Feedback and demonstrate that LLMs can effectively tackle repository-level code migration to Java 17. For the selected subset with Claude-3.5-Sonnet-v2, SD-Feedback achieves 62.33% and 27.00% success rate (pass@1) for minimal and maximal migration respectively. The benchmark dataset and source code are available at: https://huggingface.co/collections/AmazonScience and https://github.com/amazon-science/self_debug respectively.

While language models are powerful and versatile, they often fail to address highly complex problems. This is because solving complex problems requires deliberate thinking, which has been only minimally guided during training. In this paper, we propose a new method called Cumulative Reasoning (CR), which employs language models in a cumulative and iterative manner to emulate human thought processes. By decomposing tasks into smaller components, CR streamlines the problem-solving process, rendering it both more manageable and effective. For logical inference tasks, CR consistently outperforms existing methods with an improvement up to 9.3%, and achieves the astonishing accuracy of 98.04% on the curated FOLIO wiki dataset. In the context of the Game of 24, CR achieves an accuracy of 98%, which signifies a substantial enhancement of 24% over the previous state-of-the-art method. Finally, on the MATH dataset, we establish new state-of-the-art results with 58.0% overall accuracy, surpassing the previous best approach by a margin of 4.2%, and achieving 43% relative improvement on the hardest level 5 problems (22.4% to 32.1%). Code is available at https://github.com/iiis-ai/cumulative-reasoning.

The Massive Multitask Language Understanding (MMLU) benchmark has been widely used to evaluate language models across various domains. However, existing MMLU datasets primarily focus on high-resource languages such as English, which leaves low-resource languages like Bengali underrepresented. In this paper, we introduce BnMMLU, a benchmark to evaluate the multitask language understanding capabilities of Bengali in language models. The dataset spans 23 domains, including science, humanities, mathematics and general knowledge and is structured in a multiple-choice format to assess factual knowledge, application-based problem-solving and reasoning abilities of language models. It consists of 138,949 question-option pairs. We benchmark several proprietary and open-source large language models (LLMs) on the BnMMLU test set. Additionally, we annotate the test set with three cognitive categories-factual knowledge, procedural application and reasoning-to gain deeper insights into model strengths and weaknesses across various cognitive tasks. The results reveal significant performance gaps, highlighting the need for improved pre-training and fine-tuning strategies tailored to Bengali data. We release the dataset and benchmark results to facilitate further research in this area.

Large Language Models (LLMs) are transforming how people find information, and many users turn nowadays to chatbots to obtain answers to their questions. Despite the instant access to abundant information that LLMs offer, it is still important to promote critical thinking and problem-solving skills. Automatic hint generation is a new task that aims to support humans in answering questions by themselves by creating hints that guide users toward answers without directly revealing them. In this context, hint evaluation focuses on measuring the quality of hints, helping to improve the hint generation approaches. However, resources for hint research are currently spanning different formats and datasets, while the evaluation tools are missing or incompatible, making it hard for researchers to compare and test their models. To overcome these challenges, we introduce HintEval, a Python library that makes it easy to access diverse datasets and provides multiple approaches to generate and evaluate hints. HintEval aggregates the scattered resources into a single toolkit that supports a range of research goals and enables a clear, multi-faceted, and reliable evaluation. The proposed library also includes detailed online documentation, helping users quickly explore its features and get started. By reducing barriers to entry and encouraging consistent evaluation practices, HintEval offers a major step forward for facilitating hint generation and analysis research within the NLP/IR community.

With the development of Large Language Models (LLM), numerous prompts have been proposed, each with a rich set of features and their own merits. This paper summarizes the prompt words for large language models (LLMs), categorizing them into stimulating and framework types, and proposes an Auto-Prompt Graphical Paradigm(APGP) that combines both stimulating and framework prompts to enhance the problem-solving capabilities of LLMs across multiple domains, then exemplifies it with a framework that adheres to this paradigm. The framework involves automated prompt generation and consideration of emotion-stimulus factors, guiding LLMs in problem abstraction, diversified solutions generation, comprehensive optimization, and self-verification after providing answers, ensuring solution accuracy. Compared to traditional stimuli and framework prompts, this framework integrates the advantages of both by adopting automated approaches inspired by APE work, overcoming the limitations of manually designed prompts. Test results on the ruozhiba and BBH datasets demonstrate that this framework can effectively improve the efficiency and accuracy of LLMs in problem-solving, paving the way for new applications of LLMs.

Automatic math problem solving has recently attracted increasing attention as a long-standing AI benchmark. In this paper, we focus on solving geometric problems, which requires a comprehensive understanding of textual descriptions, visual diagrams, and theorem knowledge. However, the existing methods were highly dependent on handcraft rules and were merely evaluated on small-scale datasets. Therefore, we propose a Geometric Question Answering dataset GeoQA, containing 4,998 geometric problems with corresponding annotated programs, which illustrate the solving process of the given problems. Compared with another publicly available dataset GeoS, GeoQA is 25 times larger, in which the program annotations can provide a practical testbed for future research on explicit and explainable numerical reasoning. Moreover, we introduce a Neural Geometric Solver (NGS) to address geometric problems by comprehensively parsing multimodal information and generating interpretable programs. We further add multiple self-supervised auxiliary tasks on NGS to enhance cross-modal semantic representation. Extensive experiments on GeoQA validate the effectiveness of our proposed NGS and auxiliary tasks. However, the results are still significantly lower than human performance, which leaves large room for future research. Our benchmark and code are released at https://github.com/chen-judge/GeoQA .

Large language models (LLMs) have shown impressive performance in various reasoning benchmarks with the emergence of Chain-of-Thought (CoT) and its derivative methods, particularly in tasks involving multi-choice questions (MCQs). However, current works all process data uniformly without considering the problem-solving difficulty, which means an excessive focus on simple questions while insufficient to intricate ones. To address this challenge, we inspired by humans using heuristic strategies to categorize tasks and handle them individually, propose to apply the Divide and Conquer to LLMs reasoning. First, we divide questions into different subsets based on the statistical confidence score (CS), then fix nearly resolved sets and conquer demanding nuanced process ones with elaborately designed methods, including Prior Knowledge based Reasoning (PKR) and Filter Choices based Reasoning (FCR), as well as their integration variants. Our experiments demonstrate that this proposed strategy significantly boosts the models' reasoning abilities across nine datasets involving arithmetic, commonsense, and logic tasks. For instance, compared to baseline, we make a striking improvement on low confidence subsets of 8.72\% for AQuA, 15.07\% for ARC Challenge and 7.71\% for RiddleSense. In addition, through extensive analysis on length of rationale and number of options, we verify that longer reasoning paths in PKR could prevent models from referring infer-harmful shortcuts, and also find that removing irrelevant choices in FCR would substantially avoid models' confusion. The code is at https://github.com/AiMijie/Divide-and-Conquer

Natural language image-caption datasets, widely used for training Large Multimodal Models, mainly focus on natural scenarios and overlook the intricate details of mathematical figures that are critical for problem-solving, hindering the advancement of current LMMs in multimodal mathematical reasoning. To this end, we propose leveraging code as supervision for cross-modal alignment, since code inherently encodes all information needed to generate corresponding figures, establishing a precise connection between the two modalities. Specifically, we co-develop our image-to-code model and dataset with model-in-the-loop approach, resulting in an image-to-code model, FigCodifier and ImgCode-8.6M dataset, the largest image-code dataset to date. Furthermore, we utilize FigCodifier to synthesize novel mathematical figures and then construct MM-MathInstruct-3M, a high-quality multimodal math instruction fine-tuning dataset. Finally, we present MathCoder-VL, trained with ImgCode-8.6M for cross-modal alignment and subsequently fine-tuned on MM-MathInstruct-3M for multimodal math problem solving. Our model achieves a new open-source SOTA across all six metrics. Notably, it surpasses GPT-4o and Claude 3.5 Sonnet in the geometry problem-solving subset of MathVista, achieving improvements of 8.9% and 9.2%. The dataset and models will be released at https://github.com/mathllm/MathCoder.

Multiple-choice question (MCQ) datasets like Massive Multitask Language Understanding (MMLU) are widely used to evaluate the commonsense, understanding, and problem-solving abilities of large language models (LLMs). However, the open-source nature of these benchmarks and the broad sources of training data for LLMs have inevitably led to benchmark contamination, resulting in unreliable evaluation results. To alleviate this issue, we propose a contamination-free and more challenging MCQ benchmark called MMLU-CF. This benchmark reassesses LLMs' understanding of world knowledge by averting both unintentional and malicious data leakage. To avoid unintentional data leakage, we source data from a broader domain and design three decontamination rules. To prevent malicious data leakage, we divide the benchmark into validation and test sets with similar difficulty and subject distributions. The test set remains closed-source to ensure reliable results, while the validation set is publicly available to promote transparency and facilitate independent verification. Our evaluation of mainstream LLMs reveals that the powerful GPT-4o achieves merely a 5-shot score of 73.4% and a 0-shot score of 71.9% on the test set, which indicates the effectiveness of our approach in creating a more rigorous and contamination-free evaluation standard. The GitHub repository is available at https://github.com/microsoft/MMLU-CF and the dataset refers to https://huggingface.co/datasets/microsoft/MMLU-CF.

Large Language Models (LLMs) have demonstrated proficiency in their reasoning abilities, yet their large size presents scalability challenges and limits any further customization. In contrast, compact models offer customized training but often fall short in solving complex reasoning tasks. This study focuses on distilling the LLMs' decomposition skills into compact models using offline reinforcement learning. We leverage the advancements in the LLM`s capabilities to provide feedback and generate a specialized task-specific dataset for training compact models. The development of an AI-generated dataset and the establishment of baselines constitute the primary contributions of our work, underscoring the potential of compact models in replicating complex problem-solving skills.

Mathematical reasoning represents a critical frontier in advancing large language models (LLMs). While step-by-step approaches have emerged as the dominant paradigm for mathematical problem-solving in LLMs, the quality of reasoning steps in training data fundamentally constrains the performance of the models. Recent studies has demonstrated that more detailed intermediate steps can enhance model performance, yet existing methods for step expansion either require more powerful external models or incur substantial computational costs. In this paper, we introduce MathFimer, a novel framework for mathematical reasoning step expansion inspired by the "Fill-in-the-middle" task from code completion. By decomposing solution chains into prefix-suffix pairs and training models to reconstruct missing intermediate steps, we develop a specialized model, MathFimer-7B, on our carefully curated NuminaMath-FIM dataset. We then apply these models to enhance existing mathematical reasoning datasets by inserting detailed intermediate steps into their solution chains, creating MathFimer-expanded versions. Through comprehensive experiments on multiple mathematical reasoning datasets, including MathInstruct, MetaMathQA and etc., we demonstrate that models trained on MathFimer-expanded data consistently outperform their counterparts trained on original data across various benchmarks such as GSM8K and MATH. Our approach offers a practical, scalable solution for enhancing mathematical reasoning capabilities in LLMs without relying on powerful external models or expensive inference procedures.

Large language models (LLMs) have demonstrated remarkable performance across a wide range of tasks. Advances in prompt engineering and fine-tuning techniques have further enhanced their ability to address complex reasoning challenges. However, these advanced capabilities are often exclusive to models exceeding 100 billion parameters. Although Chain-of-Thought (CoT) fine-tuning methods have been explored for smaller models (under 10 billion parameters), they typically depend on extensive CoT training data, which can introduce inconsistencies and limit effectiveness in low-data settings. To overcome these limitations, this paper introduce a new reasoning strategy Solution Guidance (SG) and a plug-and-play training paradigm Solution-Guidance Fine-Tuning (SGFT) for enhancing the reasoning capabilities of small language models. SG focuses on problem understanding and decomposition at the semantic and logical levels, rather than specific computations, which can effectively improve the SLMs' generalization and reasoning abilities. With only a small amount of SG training data, SGFT can fine-tune a SLM to produce accurate problem-solving guidances, which can then be flexibly fed to any SLM as prompts, enabling it to generate correct answers directly. Experimental results demonstrate that our method significantly improves the performance of SLMs on various reasoning tasks, enhancing both their practicality and efficiency within resource-constrained environments.

Iterative human engagement is a common and effective means of leveraging the advanced language processing power of large language models (LLMs). Using well-structured prompts in a conversational manner, human users can effectively influence an LLM to develop more thoughtful and accurate responses. Motivated by this insight, we propose the Iteration of Thought (IoT) framework for enhancing LLM responses by generating "thought"-provoking prompts vis a vis an input query and the current iteration of an LLM's response. Unlike static or semi-static approaches, e.g. Chain of Thought (CoT) or Tree of Thoughts (ToT), IoT adapts its reasoning path dynamically, based on evolving context, and without generating alternate explorative thoughts which are ultimately discarded. The three components of the IoT framework are (1) an Inner Dialogue Agent (IDA) responsible for generating instructive, context-specific prompts; (2) an LLM Agent (LLMA) that processes these prompts to refine its responses; and (3) an iterative prompting loop that implements a conversation between the former two components. We introduce two variants of our framework: Autonomous Iteration of Thought (AIoT), where an LLM decides when to stop iterating, and Guided Iteration of Thought (GIoT), which always forces a fixed number iterations. We investigate the performance of IoT across various datasets, spanning complex reasoning tasks from the GPQA dataset, explorative problem-solving in Game of 24, puzzle solving in Mini Crosswords, and multi-hop question answering from the HotpotQA dataset. Our results show that IoT represents a viable paradigm for autonomous response refinement in LLMs, showcasing significant improvements over CoT and thereby enabling more adaptive and efficient reasoning systems that minimize human intervention.

Large Language Models (LLMs) have demonstrated remarkable performance across a spectrum of tasks. Recently, Direct Preference Optimization (DPO) has emerged as an RL-free approach to optimize the policy model on human preferences. However, several limitations hinder the widespread adoption of this method. To address these shortcomings, various versions of DPO have been introduced. Yet, a comprehensive evaluation of these variants across diverse tasks is still lacking. In this study, we aim to bridge this gap by investigating the performance of alignment methods across three distinct scenarios: (1) keeping the Supervised Fine-Tuning (SFT) part, (2) skipping the SFT part, and (3) skipping the SFT part and utilizing an instruction-tuned model. Furthermore, we explore the impact of different training sizes on their performance. Our evaluation spans a range of tasks including dialogue systems, reasoning, mathematical problem-solving, question answering, truthfulness, and multi-task understanding, encompassing 13 benchmarks such as MT-Bench, Big Bench, and Open LLM Leaderboard. Key observations reveal that alignment methods achieve optimal performance with smaller training data subsets, exhibit limited effectiveness in reasoning tasks yet significantly impact mathematical problem-solving, and employing an instruction-tuned model notably influences truthfulness. We anticipate that our findings will catalyze further research aimed at developing more robust models to address alignment challenges.

This Perspective explores the transformative potential of Multi-Agent Systems (MAS) powered by Large Language Models (LLMs) in the geosciences. Users of geoscientific data repositories face challenges due to the complexity and diversity of data formats, inconsistent metadata practices, and a considerable number of unprocessed datasets. MAS possesses transformative potential for improving scientists' interaction with geoscientific data by enabling intelligent data processing, natural language interfaces, and collaborative problem-solving capabilities. We illustrate this approach with "PANGAEA GPT", a specialized MAS pipeline integrated with the diverse PANGAEA database for Earth and Environmental Science, demonstrating how MAS-driven workflows can effectively manage complex datasets and accelerate scientific discovery. We discuss how MAS can address current data challenges in geosciences, highlight advancements in other scientific fields, and propose future directions for integrating MAS into geoscientific data processing pipelines. In this Perspective, we show how MAS can fundamentally improve data accessibility, promote cross-disciplinary collaboration, and accelerate geoscientific discoveries.

Large language models (LLMs) have exhibited their problem-solving abilities in mathematical reasoning. Solving realistic optimization (OPT) problems in application scenarios requires advanced and applied mathematics ability. However, current OPT benchmarks that merely solve linear programming are far from complex realistic situations. In this work, we propose OptiBench, a benchmark for End-to-end optimization problem-solving with human-readable inputs and outputs. OptiBench contains rich optimization problems, including linear and nonlinear programming with or without tabular data, which can comprehensively evaluate LLMs' solving ability. In our benchmark, LLMs are required to call a code solver to provide precise numerical answers. Furthermore, to alleviate the data scarcity for optimization problems, and to bridge the gap between open-source LLMs on a small scale (e.g., Llama-3-8b) and closed-source LLMs (e.g., GPT-4), we further propose a data synthesis method namely ReSocratic. Unlike general data synthesis methods that proceed from questions to answers, \ReSocratic first incrementally synthesizes formatted optimization demonstration with mathematical formulations step by step and then back-translates the generated demonstrations into questions. Based on this, we synthesize the ReSocratic-29k dataset. We further conduct supervised fine-tuning with ReSocratic-29k on multiple open-source models. Experimental results show that ReSocratic-29k significantly improves the performance of open-source models.

Multi-modal Large Language Models (MLLMs) have recently emerged as a significant focus in academia and industry. Despite their proficiency in general multi-modal scenarios, the mathematical problem-solving capabilities in visual contexts remain insufficiently explored. We identify three key areas within MLLMs that need to be improved: visual encoding of math diagrams, diagram-language alignment, and mathematical reasoning skills. This draws forth an urgent demand for large-scale, high-quality data and training pipelines in visual mathematics. In this paper, we propose MAVIS, the first MAthematical VISual instruction tuning paradigm for MLLMs, involving a series of mathematical visual datasets and specialized MLLMs. Targeting the three issues, MAVIS contains three progressive training stages from scratch. First, we curate MAVIS-Caption, consisting of 558K diagram-caption pairs, to fine-tune a math-specific vision encoder (CLIP-Math) through contrastive learning, tailored for improved diagram visual encoding. Second, we utilize MAVIS-Caption to align the CLIP-Math with a large language model (LLM) by a projection layer, enhancing vision-language alignment in mathematical domains. Third, we introduce MAVIS-Instruct, including 900K meticulously collected and annotated visual math problems, which is adopted to finally instruct-tune the MLLM for robust mathematical reasoning skills. In MAVIS-Instruct, we incorporate complete chain-of-thought (CoT) rationales for each problem, and minimize textual redundancy, thereby concentrating the model towards the visual elements. Data and Models are released at https://github.com/ZrrSkywalker/MAVIS

We introduce MAmmoTH, a series of open-source large language models (LLMs) specifically tailored for general math problem-solving. The MAmmoTH models are trained on MathInstruct, our meticulously curated instruction tuning dataset. MathInstruct is compiled from 13 math datasets with intermediate rationales, six of which have rationales newly curated by us. It presents a unique hybrid of chain-of-thought (CoT) and program-of-thought (PoT) rationales, and also ensures extensive coverage of diverse fields in math. The hybrid of CoT and PoT not only unleashes the potential of tool use but also allows different thought processes for different math problems. As a result, the MAmmoTH series substantially outperform existing open-source models on nine mathematical reasoning datasets across all scales with an average accuracy gain between 13% and 29%. Remarkably, our MAmmoTH-7B model reaches 35% on MATH (a competition-level dataset), which exceeds the best open-source 7B model (WizardMath) by 25%, and the MAmmoTH-34B model achieves 46% accuracy on MATH, even surpassing GPT-4's CoT result. Our work underscores the importance of diverse problem coverage and the use of hybrid rationales in developing superior math generalist models.

Cognitive textual and visual reasoning tasks, such as puzzles, series, and analogies, demand the ability to quickly reason, decipher, and evaluate patterns both textually and spatially. While LLMs and VLMs, through extensive training on large amounts of human-curated data, have attained a high level of pseudo-human intelligence in some common sense reasoning tasks, they still struggle with more complex reasoning tasks that require cognitive understanding. In this work, we introduce a new dataset, NTSEBench, designed to evaluate the cognitive multi-modal reasoning and problem-solving skills of large models. The dataset comprises 2,728 multiple-choice questions comprising of a total of 4,642 images across 26 categories sampled from the NTSE examination conducted nationwide in India, featuring both visual and textual general aptitude questions that do not rely on rote learning. We establish baselines on the dataset using state-of-the-art LLMs and VLMs. To facilitate a comparison between open source and propriety models, we propose four distinct modeling strategies to handle different modalities (text and images) in the dataset instances.

A common method to solve complex problems in software engineering, is to divide the problem into multiple sub-problems. Inspired by this, we propose a Modular Architecture for Software-engineering AI (MASAI) agents, where different LLM-powered sub-agents are instantiated with well-defined objectives and strategies tuned to achieve those objectives. Our modular architecture offers several advantages: (1) employing and tuning different problem-solving strategies across sub-agents, (2) enabling sub-agents to gather information from different sources scattered throughout a repository, and (3) avoiding unnecessarily long trajectories which inflate costs and add extraneous context. MASAI enabled us to achieve the highest performance (28.33% resolution rate) on the popular and highly challenging SWE-bench Lite dataset consisting of 300 GitHub issues from 11 Python repositories. We conduct a comprehensive evaluation of MASAI relative to other agentic methods and analyze the effects of our design decisions and their contribution to the success of MASAI.

Fine-tuning pretrained LLMs has been shown to be an effective strategy for reaching state-of-the-art performance on specific tasks like machine translation. However, this process of adaptation often implies sacrificing general-purpose capabilities, such as conversational reasoning and instruction-following, hampering the utility of the system in real-world applications that require a mixture of skills. In this paper, we introduce Tower+, a suite of models designed to deliver strong performance across both translation and multilingual general-purpose text capabilities. We achieve a Pareto frontier between translation specialization and multilingual general-purpose capabilities by introducing a novel training recipe that builds on Tower (Alves et al., 2024), comprising continued pretraining, supervised fine-tuning, preference optimization, and reinforcement learning with verifiable rewards. At each stage of training, we carefully generate and curate data to strengthen performance on translation as well as general-purpose tasks involving code generation, mathematics problem solving, and general instruction-following. We develop models at multiple scales: 2B, 9B, and 72B. Our smaller models often outperform larger general-purpose open-weight and proprietary LLMs (e.g., Llama 3.3 70B, GPT-4o). Our largest model delivers best-in-class translation performance for high-resource languages and top results in multilingual Arena Hard evaluations and in IF-MT, a benchmark we introduce for evaluating both translation and instruction-following. Our findings highlight that it is possible to rival frontier models in general capabilities, while optimizing for specific business domains, such as translation and localization.

Recent advancements in LLM-based agents have led to significant progress in automatic software engineering, particularly in software maintenance and evolution. Despite these encouraging advances, current research faces two major challenges. First, SOTA performance primarily depends on closed-source models, which significantly limits the technology's accessibility, and potential for customization in diverse SE tasks. Second, these models are predominantly trained on static code data, lacking a deep understanding of the dynamic interactions, iterative problem-solving processes, and evolutionary characteristics inherent in software development. To address these challenges, our study adopts a software engineering perspective. We recognize that real-world software maintenance and evolution processes encompass not only static code data but also developers' thought processes, utilization of external tools, and the interaction between different functional personnel. Consequently, we introduce the Lingma SWE-GPT series, comprising Lingma SWE-GPT 7B and 72B. By learning from and simulating real-world code submission activities, Lingma SWE-GPT systematically incorporates the dynamic interactions and iterative problem-solving inherent in software development process, thereby achieving a more comprehensive understanding of software improvement processes. We conducted experimental evaluations using SWE-bench Verified benchmark. The results demonstrate that Lingma SWE-GPT 72B successfully resolves 30.20% of the GitHub issues, marking a significant improvement in automatic issue resolution (22.76% relative improvement compared to Llama 3.1 405B), approaching the performance of closed-source models (31.80\% issues of GPT-4o resolved). Notably, Lingma SWE-GPT 7B resolves 18.20% of the issues, highlighting the potential for applying smaller models to ASE tasks.

The recent release of OpenAI's o1 models and other similar frameworks showcasing test-time scaling laws has demonstrated their exceptional capability to tackle complex reasoning tasks. Inspired by this, subsequent research has revealed that such test-time scaling laws hinge on the model's ability to search both within a single response (intra-response) and across multiple responses (inter-response) during training. Crucially, beyond selecting a single optimal response, the model must also develop robust self-correction capabilities within its own outputs. However, training models to achieve effective self-evaluation and self-correction remains a significant challenge, heavily dependent on the quality of self-reflection data. In this paper, we address this challenge by focusing on enhancing the quality of self-reflection data generation for complex problem-solving, which can subsequently improve the training of next-generation large language models (LLMs). Specifically, we explore how manually triggering a model's self-correction mechanisms can improve performance on challenging reasoning tasks. To this end, we propose a novel iterative deepening sampling algorithm framework designed to enhance self-correction and generate higher-quality samples. Through extensive experiments on Math500 and AIME benchmarks, we demonstrate that our method achieves a higher success rate on difficult tasks and provide detailed ablation studies to analyze its effectiveness across diverse settings.

Mathematical reasoning serves as a cornerstone for assessing the fundamental cognitive capabilities of human intelligence. In recent times, there has been a notable surge in the development of Large Language Models (LLMs) geared towards the automated resolution of mathematical problems. However, the landscape of mathematical problem types is vast and varied, with LLM-oriented techniques undergoing evaluation across diverse datasets and settings. This diversity makes it challenging to discern the true advancements and obstacles within this burgeoning field. This survey endeavors to address four pivotal dimensions: i) a comprehensive exploration of the various mathematical problems and their corresponding datasets that have been investigated; ii) an examination of the spectrum of LLM-oriented techniques that have been proposed for mathematical problem-solving; iii) an overview of factors and concerns affecting LLMs in solving math; and iv) an elucidation of the persisting challenges within this domain. To the best of our knowledge, this survey stands as one of the first extensive examinations of the landscape of LLMs in the realm of mathematics, providing a holistic perspective on the current state, accomplishments, and future challenges in this rapidly evolving field.

Large Language Models (LLMs) have shown the potential to revolutionize natural language processing tasks in various domains, sparking great interest in vertical-specific large models. However, unlike proprietary models such as BloombergGPT and FinGPT, which have leveraged their unique data accumulations to make strides in the finance domain, there hasn't not many similar large language models in the Chinese legal domain to facilitate its digital transformation. In this paper, we propose an open-source legal large language model named ChatLaw. Due to the importance of data quality, we carefully designed a legal domain fine-tuning dataset. Additionally, to overcome the problem of model hallucinations in legal data screening during reference data retrieval, we introduce a method that combines vector database retrieval with keyword retrieval to effectively reduce the inaccuracy of relying solely on vector database retrieval. Furthermore, we propose a self-attention method to enhance the ability of large models to overcome errors present in reference data, further optimizing the issue of model hallucinations at the model level and improving the problem-solving capabilities of large models. We also open-sourced our model and part of the data at https://github.com/PKU-YuanGroup/ChatLaw.

Recent LLMs have significantly improved reasoning capabilities, primarily by including an explicit, lengthy Thinking process as part of generation. In this paper, we question whether this explicit thinking is necessary. Using the state-of-the-art DeepSeek-R1-Distill-Qwen, we find that bypassing the thinking process via simple prompting, denoted as NoThinking, can be surprisingly effective. When controlling for the number of tokens, NoThinking outperforms Thinking across a diverse set of seven challenging reasoning datasets--including mathematical problem solving, formal theorem proving, and coding--especially in low-budget settings, e.g., 51.3 vs. 28.9 on ACM 23 with 700 tokens. Notably, the performance of NoThinking becomes more competitive with pass@k as k increases. Building on this observation, we demonstrate that a parallel scaling approach that uses NoThinking to generate N outputs independently and aggregates them is highly effective. For aggregation, we use task-specific verifiers when available, or we apply simple best-of-N strategies such as confidence-based selection. Our method outperforms a range of baselines with similar latency using Thinking, and is comparable to Thinking with significantly longer latency (up to 9x). Together, our research encourages a reconsideration of the necessity of lengthy thinking processes, while also establishing a competitive reference for achieving strong reasoning performance in low-budget settings or at low latency using parallel scaling.

Programming often involves converting detailed and complex specifications into code, a process during which developers typically utilize visual aids to more effectively convey concepts. While recent developments in Large Multimodal Models have demonstrated remarkable abilities in visual reasoning and mathematical tasks, there is little work on investigating whether these models can effectively interpret visual elements for code generation. To this end, we present MMCode, the first multi-modal coding dataset for evaluating algorithmic problem-solving skills in visually rich contexts. MMCode contains 3,548 questions and 6,620 images collected from real-world programming challenges harvested from 10 code competition websites, presenting significant challenges due to the extreme demand for reasoning abilities. Our experiment results show that current state-of-the-art models struggle to solve these problems. The results highlight the lack of powerful vision-code models, and we hope MMCode can serve as an inspiration for future works in this domain. The data and code are publicly available at https://github.com/happylkx/MMCode.

The recent GPT-4 has demonstrated extraordinary multi-modal abilities, such as directly generating websites from handwritten text and identifying humorous elements within images. These features are rarely observed in previous vision-language models. We believe the primary reason for GPT-4's advanced multi-modal generation capabilities lies in the utilization of a more advanced large language model (LLM). To examine this phenomenon, we present MiniGPT-4, which aligns a frozen visual encoder with a frozen LLM, Vicuna, using just one projection layer. Our findings reveal that MiniGPT-4 possesses many capabilities similar to those exhibited by GPT-4 like detailed image description generation and website creation from hand-written drafts. Furthermore, we also observe other emerging capabilities in MiniGPT-4, including writing stories and poems inspired by given images, providing solutions to problems shown in images, teaching users how to cook based on food photos, etc. In our experiment, we found that only performing the pretraining on raw image-text pairs could produce unnatural language outputs that lack coherency including repetition and fragmented sentences. To address this problem, we curate a high-quality, well-aligned dataset in the second stage to finetune our model using a conversational template. This step proved crucial for augmenting the model's generation reliability and overall usability. Notably, our model is highly computationally efficient, as we only train a projection layer utilizing approximately 5 million aligned image-text pairs. Our code, pre-trained model, and collected dataset are available at https://minigpt-4.github.io/.

Recent advances in large language models (LLMs) have increased the demand for comprehensive benchmarks to evaluate their capabilities as human-like agents. Existing benchmarks, while useful, often focus on specific application scenarios, emphasizing task completion but failing to dissect the underlying skills that drive these outcomes. This lack of granularity makes it difficult to deeply discern where failures stem from. Additionally, setting up these environments requires considerable effort, and issues of unreliability and reproducibility sometimes arise, especially in interactive tasks. To address these limitations, we introduce the Massive Multitask Agent Understanding (MMAU) benchmark, featuring comprehensive offline tasks that eliminate the need for complex environment setups. It evaluates models across five domains, including teal{Tool-use}, teal{Directed Acyclic Graph (DAG) QA}, teal{Data Science and Machine Learning coding}, teal{Contest-level programming} and teal{Mathematics}, and covers five essential capabilities: orange{Understanding}, orange{Reasoning}, orange{Planning}, orange{Problem-solving}, and orange{Self-correction}. With a total of 20 meticulously designed tasks encompassing over 3K distinct prompts, MMAU provides a comprehensive framework for evaluating the strengths and limitations of LLM agents. By testing 18 representative models on MMAU, we provide deep and insightful analyses. Ultimately, MMAU not only sheds light on the capabilities and limitations of LLM agents but also enhances the interpretability of their performance. Datasets and evaluation scripts of MMAU are released at https://github.com/apple/axlearn/docs/research/mmau.

Large language models and autonomous AI agents have evolved rapidly, resulting in a diverse array of evaluation benchmarks, frameworks, and collaboration protocols. However, the landscape remains fragmented and lacks a unified taxonomy or comprehensive survey. Therefore, we present a side-by-side comparison of benchmarks developed between 2019 and 2025 that evaluate these models and agents across multiple domains. In addition, we propose a taxonomy of approximately 60 benchmarks that cover general and academic knowledge reasoning, mathematical problem-solving, code generation and software engineering, factual grounding and retrieval, domain-specific evaluations, multimodal and embodied tasks, task orchestration, and interactive assessments. Furthermore, we review AI-agent frameworks introduced between 2023 and 2025 that integrate large language models with modular toolkits to enable autonomous decision-making and multi-step reasoning. Moreover, we present real-world applications of autonomous AI agents in materials science, biomedical research, academic ideation, software engineering, synthetic data generation, chemical reasoning, mathematical problem-solving, geographic information systems, multimedia, healthcare, and finance. We then survey key agent-to-agent collaboration protocols, namely the Agent Communication Protocol (ACP), the Model Context Protocol (MCP), and the Agent-to-Agent Protocol (A2A). Finally, we discuss recommendations for future research, focusing on advanced reasoning strategies, failure modes in multi-agent LLM systems, automated scientific discovery, dynamic tool integration via reinforcement learning, integrated search capabilities, and security vulnerabilities in agent protocols.

This paper introduces the novel task of multimodal puzzle solving, framed within the context of visual question-answering. We present a new dataset, AlgoPuzzleVQA designed to challenge and evaluate the capabilities of multimodal language models in solving algorithmic puzzles that necessitate both visual understanding, language understanding, and complex algorithmic reasoning. We create the puzzles to encompass a diverse array of mathematical and algorithmic topics such as boolean logic, combinatorics, graph theory, optimization, search, etc., aiming to evaluate the gap between visual data interpretation and algorithmic problem-solving skills. The dataset is generated automatically from code authored by humans. All our puzzles have exact solutions that can be found from the algorithm without tedious human calculations. It ensures that our dataset can be scaled up arbitrarily in terms of reasoning complexity and dataset size. Our investigation reveals that large language models (LLMs) such as GPT4V and Gemini exhibit limited performance in puzzle-solving tasks. We find that their performance is near random in a multi-choice question-answering setup for a significant number of puzzles. The findings emphasize the challenges of integrating visual, language, and algorithmic knowledge for solving complex reasoning problems.

Large language models (LLMs) have shown remarkable proficiency in human-level reasoning and generation capabilities, which encourages extensive research on their application in mathematical problem solving. However, current work has been largely focused on text-based mathematical problems, with limited investigation in problems involving geometric information. Addressing this gap, we aim to enable LLMs to solve geometric problems by understanding image input. We first analyze the limitations of current Multimodal Large Language Models (MLLMs) in this area: they struggle to accurately comprehending basic geometric elements and their relationships. To overcome these challenges, we take advantage of the unique characteristics of geometric problems (such as unique geometric logical form, and geometric scalability) and the capacity of the textual LLMs to build an enriched multimodal geometry dataset based on existing data. The augmented dataset, Geo170K, contains more than 170K geometric image-caption and question-answer pairs. Utilizing our constructed Geo170K dataset, we develop G-LLaVA, which demonstrates exceptional performance in solving geometric problems, significantly outperforming GPT-4-V on the MathVista benchmark with only 7B parameters.

Post-training quantization (PTQ) is widely regarded as one of the most efficient compression methods practically, benefitting from its data privacy and low computation costs. We argue that an overlooked problem of oscillation is in the PTQ methods. In this paper, we take the initiative to explore and present a theoretical proof to explain why such a problem is essential in PTQ. And then, we try to solve this problem by introducing a principled and generalized framework theoretically. In particular, we first formulate the oscillation in PTQ and prove the problem is caused by the difference in module capacity. To this end, we define the module capacity (ModCap) under data-dependent and data-free scenarios, where the differentials between adjacent modules are used to measure the degree of oscillation. The problem is then solved by selecting top-k differentials, in which the corresponding modules are jointly optimized and quantized. Extensive experiments demonstrate that our method successfully reduces the performance drop and is generalized to different neural networks and PTQ methods. For example, with 2/4 bit ResNet-50 quantization, our method surpasses the previous state-of-the-art method by 1.9%. It becomes more significant on small model quantization, e.g. surpasses BRECQ method by 6.61% on MobileNetV2*0.5.

Source separation involves the ill-posed problem of retrieving a set of source signals that have been observed through a mixing operator. Solving this problem requires prior knowledge, which is commonly incorporated by imposing regularity conditions on the source signals, or implicitly learned through supervised or unsupervised methods from existing data. While data-driven methods have shown great promise in source separation, they often require large amounts of data, which rarely exists in planetary space missions. To address this challenge, we propose an unsupervised source separation scheme for domains with limited data access that involves solving an optimization problem in the wavelet scattering covariance representation spacex2014an interpretable, low-dimensional representation of stationary processes. We present a real-data example in which we remove transient, thermally-induced microtiltsx2014known as glitchesx2014from data recorded by a seismometer during NASA's InSight mission on Mars. Thanks to the wavelet scattering covariances' ability to capture non-Gaussian properties of stochastic processes, we are able to separate glitches using only a few glitch-free data snippets.

A vector database is used to store high-dimensional data that cannot be characterized by traditional DBMS. Although there are not many articles describing existing or introducing new vector database architectures, the approximate nearest neighbor search problem behind vector databases has been studied for a long time, and considerable related algorithmic articles can be found in the literature. This article attempts to comprehensively review relevant algorithms to provide a general understanding of this booming research area. The basis of our framework categorises these studies by the approach of solving ANNS problem, respectively hash-based, tree-based, graph-based and quantization-based approaches. Then we present an overview of existing challenges for vector databases. Lastly, we sketch how vector databases can be combined with large language models and provide new possibilities.

Competitive programming benchmarks are widely used in scenarios such as programming contests and large language model assessments. However, the growing presence of duplicate or highly similar problems raises concerns not only about competition fairness, but also about the validity of competitive programming as a benchmark for model evaluation. In this paper, we propose a new problem -- similar question retrieval -- to address this issue. Due to the lack of both data and models, solving this problem is challenging. To this end, we introduce CPRet, a retrieval-oriented benchmark suite for competitive programming, covering four retrieval tasks: two code-centric (i.e., Text-to-Code and Code-to-Code) and two newly proposed problem-centric tasks (i.e., Problem-to-Duplicate and Simplified-to-Full), built from a combination of automatically crawled problem-solution data and manually curated annotations. Our contribution includes both high-quality training data and temporally separated test sets for reliable evaluation. In addition, we develop two task-specialized retrievers based on this dataset: CPRetriever-Code, trained with a novel Group-InfoNCE loss for problem-code alignment, and CPRetriever-Prob, fine-tuned for identifying problem-level similarity. Both models achieve strong results and are open-sourced for local use. Finally, we analyze LiveCodeBench and find that high-similarity problems inflate model pass rates and reduce differentiation, underscoring the need for similarity-aware evaluation in future benchmarks. Code and data are available at: https://github.com/coldchair/CPRet

Fine-tuning text-to-image diffusion models with human feedback is an effective method for aligning model behavior with human intentions. However, this alignment process often suffers from slow convergence due to the large size and noise present in human feedback datasets. In this work, we propose FiFA, a novel automated data filtering algorithm designed to enhance the fine-tuning of diffusion models using human feedback datasets with direct preference optimization (DPO). Specifically, our approach selects data by solving an optimization problem to maximize three components: preference margin, text quality, and text diversity. The concept of preference margin is used to identify samples that are highly informative in addressing the noisy nature of feedback dataset, which is calculated using a proxy reward model. Additionally, we incorporate text quality, assessed by large language models to prevent harmful contents, and consider text diversity through a k-nearest neighbor entropy estimator to improve generalization. Finally, we integrate all these components into an optimization process, with approximating the solution by assigning importance score to each data pair and selecting the most important ones. As a result, our method efficiently filters data automatically, without the need for manual intervention, and can be applied to any large-scale dataset. Experimental results show that FiFA significantly enhances training stability and achieves better performance, being preferred by humans 17% more, while using less than 0.5% of the full data and thus 1% of the GPU hours compared to utilizing full human feedback datasets.

RNN-like language models are getting renewed attention from NLP researchers in recent years and several models have made significant progress, which demonstrates performance comparable to traditional transformers. However, due to the recurrent nature of RNNs, this kind of language model can only store information in a set of fixed-length state vectors. As a consequence, they still suffer from forgetfulness though after a lot of improvements and optimizations, when given complex instructions or prompts. As the prompted generation is the main and most concerned function of LMs, solving the problem of forgetting in the process of generation is no wonder of vital importance. In this paper, focusing on easing the prompt forgetting during generation, we proposed an architecture to teach the model memorizing prompt during generation by synthetic gradient. To force the model to memorize the prompt, we derive the states that encode the prompt, then transform it into model parameter modification using low-rank gradient approximation, which hard-codes the prompt into model parameters temporarily. We construct a dataset for experiments, and the results have demonstrated the effectiveness of our method in solving the problem of forgetfulness in the process of prompted generation. We will release all the code upon acceptance.

In this research. we analyze the potential of Feature Density (HD) as a way to comparatively estimate machine learning (ML) classifier performance prior to training. The goal of the study is to aid in solving the problem of resource-intensive training of ML models which is becoming a serious issue due to continuously increasing dataset sizes and the ever rising popularity of Deep Neural Networks (DNN). The issue of constantly increasing demands for more powerful computational resources is also affecting the environment, as training large-scale ML models are causing alarmingly-growing amounts of CO2, emissions. Our approach 1s to optimize the resource-intensive training of ML models for Natural Language Processing to reduce the number of required experiments iterations. We expand on previous attempts on improving classifier training efficiency with FD while also providing an insight to the effectiveness of various linguistically-backed feature preprocessing methods for dialog classification, specifically cyberbullying detection.

Commit messages are natural language descriptions of code changes, which are important for program understanding and maintenance. However, writing commit messages manually is time-consuming and laborious, especially when the code is updated frequently. Various approaches utilizing generation or retrieval techniques have been proposed to automatically generate commit messages. To achieve a better understanding of how the existing approaches perform in solving this problem, this paper conducts a systematic and in-depth analysis of the state-of-the-art models and datasets. We find that: (1) Different variants of the BLEU metric are used in previous works, which affects the evaluation and understanding of existing methods. (2) Most existing datasets are crawled only from Java repositories while repositories in other programming languages are not sufficiently explored. (3) Dataset splitting strategies can influence the performance of existing models by a large margin. Some models show better performance when the datasets are split by commit, while other models perform better when the datasets are split by timestamp or by project. Based on our findings, we conduct a human evaluation and find the BLEU metric that best correlates with the human scores for the task. We also collect a large-scale, information-rich, and multi-language commit message dataset MCMD and evaluate existing models on this dataset. Furthermore, we conduct extensive experiments under different dataset splitting strategies and suggest the suitable models under different scenarios. Based on the experimental results and findings, we provide feasible suggestions for comprehensively evaluating commit message generation models and discuss possible future research directions. We believe this work can help practitioners and researchers better evaluate and select models for automatic commit message generation.

We propose a class of greedy algorithms for weighted sparse recovery by considering new loss function-based generalizations of Orthogonal Matching Pursuit (OMP). Given a (regularized) loss function, the proposed algorithms alternate the iterative construction of the signal support via greedy index selection and a signal update based on solving a local data-fitting problem restricted to the current support. We show that greedy selection rules associated with popular weighted sparsity-promoting loss functions admit explicitly computable and simple formulas. Specifically, we consider ell^0 - and ell^1 -based versions of the weighted LASSO (Least Absolute Shrinkage and Selection Operator), the Square-Root LASSO (SR-LASSO) and the Least Absolute Deviations LASSO (LAD-LASSO). Through numerical experiments on Gaussian compressive sensing and high-dimensional function approximation, we demonstrate the effectiveness of the proposed algorithms and empirically show that they inherit desirable characteristics from the corresponding loss functions, such as SR-LASSO's noise-blind optimal parameter tuning and LAD-LASSO's fault tolerance. In doing so, our study sheds new light on the connection between greedy sparse recovery and convex relaxation.

This paper investigates how far a very deep neural network is from attaining close to saturating performance on existing 2D and 3D face alignment datasets. To this end, we make the following 5 contributions: (a) we construct, for the first time, a very strong baseline by combining a state-of-the-art architecture for landmark localization with a state-of-the-art residual block, train it on a very large yet synthetically expanded 2D facial landmark dataset and finally evaluate it on all other 2D facial landmark datasets. (b) We create a guided by 2D landmarks network which converts 2D landmark annotations to 3D and unifies all existing datasets, leading to the creation of LS3D-W, the largest and most challenging 3D facial landmark dataset to date ~230,000 images. (c) Following that, we train a neural network for 3D face alignment and evaluate it on the newly introduced LS3D-W. (d) We further look into the effect of all "traditional" factors affecting face alignment performance like large pose, initialization and resolution, and introduce a "new" one, namely the size of the network. (e) We show that both 2D and 3D face alignment networks achieve performance of remarkable accuracy which is probably close to saturating the datasets used. Training and testing code as well as the dataset can be downloaded from https://www.adrianbulat.com/face-alignment/

The optimal stopping problem is a category of decision problems with a specific constrained configuration. It is relevant to various real-world applications such as finance and management. To solve the optimal stopping problem, state-of-the-art algorithms in dynamic programming, such as the least-squares Monte Carlo (LSMC), are employed. This type of algorithm relies on path simulations using only the last price of the underlying asset as a state representation. Also, the LSMC was thinking for option valuation where risk-neutral probabilities can be employed to account for uncertainty. However, the general optimal stopping problem goals may not fit the requirements of the LSMC showing auto-correlated prices. We employ a data-driven method that uses Monte Carlo simulation to train and test artificial neural networks (ANN) to solve the optimal stopping problem. Using ANN to solve decision problems is not entirely new. We propose a different architecture that uses convolutional neural networks (CNN) to deal with the dimensionality problem that arises when we transform the whole history of prices into a Markovian state. We present experiments that indicate that our proposed architecture improves results over the previous implementations under specific simulated time series function sets. Lastly, we employ our proposed method to compare the optimal exercise of the financial options problem with the LSMC algorithm. Our experiments show that our method can capture more accurate exercise opportunities when compared to the LSMC. We have outstandingly higher (above 974\% improvement) expected payoff from these exercise policies under the many Monte Carlo simulations that used the real-world return database on the out-of-sample (test) data.

Diffusion models have recently emerged as powerful generative priors for solving inverse problems. However, training diffusion models in the pixel space are both data-intensive and computationally demanding, which restricts their applicability as priors for high-dimensional real-world data such as medical images. Latent diffusion models, which operate in a much lower-dimensional space, offer a solution to these challenges. However, incorporating latent diffusion models to solve inverse problems remains a challenging problem due to the nonlinearity of the encoder and decoder. To address these issues, we propose ReSample, an algorithm that can solve general inverse problems with pre-trained latent diffusion models. Our algorithm incorporates data consistency by solving an optimization problem during the reverse sampling process, a concept that we term as hard data consistency. Upon solving this optimization problem, we propose a novel resampling scheme to map the measurement-consistent sample back onto the noisy data manifold and theoretically demonstrate its benefits. Lastly, we apply our algorithm to solve a wide range of linear and nonlinear inverse problems in both natural and medical images, demonstrating that our approach outperforms existing state-of-the-art approaches, including those based on pixel-space diffusion models.

We propose UTSP, an unsupervised learning (UL) framework for solving the Travelling Salesman Problem (TSP). We train a Graph Neural Network (GNN) using a surrogate loss. The GNN outputs a heat map representing the probability for each edge to be part of the optimal path. We then apply local search to generate our final prediction based on the heat map. Our loss function consists of two parts: one pushes the model to find the shortest path and the other serves as a surrogate for the constraint that the route should form a Hamiltonian Cycle. Experimental results show that UTSP outperforms the existing data-driven TSP heuristics. Our approach is parameter efficient as well as data efficient: the model takes sim 10\% of the number of parameters and sim 0.2\% of training samples compared with reinforcement learning or supervised learning methods.

Generalized Category Discovery (GCD) aims to identify a mix of known and novel categories within unlabeled data sets, providing a more realistic setting for image recognition. Essentially, GCD needs to remember existing patterns thoroughly to recognize novel categories. Recent state-of-the-art method SimGCD transfers the knowledge from known-class data to the learning of novel classes through debiased learning. However, some patterns are catastrophically forgot during adaptation and thus lead to poor performance in novel categories classification. To address this issue, we propose a novel learning approach, LegoGCD, which is seamlessly integrated into previous methods to enhance the discrimination of novel classes while maintaining performance on previously encountered known classes. Specifically, we design two types of techniques termed as Local Entropy Regularization (LER) and Dual-views Kullback Leibler divergence constraint (DKL). The LER optimizes the distribution of potential known class samples in unlabeled data, thus ensuring the preservation of knowledge related to known categories while learning novel classes. Meanwhile, DKL introduces Kullback Leibler divergence to encourage the model to produce a similar prediction distribution of two view samples from the same image. In this way, it successfully avoids mismatched prediction and generates more reliable potential known class samples simultaneously. Extensive experiments validate that the proposed LegoGCD effectively addresses the known category forgetting issue across all datasets, eg, delivering a 7.74% and 2.51% accuracy boost on known and novel classes in CUB, respectively. Our code is available at: https://github.com/Cliffia123/LegoGCD.

This work introduces systematic approach for enhancing large language models (LLMs) to address Bangla AI mathematical challenges. Through the assessment of diverse LLM configurations, fine-tuning with specific datasets, and the implementation of Retrieval-Augmented Generation (RAG), we enhanced the model's reasoning precision in a multilingual setting. Crucial discoveries indicate that customized prompting, dataset augmentation, and iterative reasoning improve the model's efficiency regarding Olympiad-level mathematical challenges.

The Explainable Detection of Online Sexism task presents the problem of explainable sexism detection through fine-grained categorisation of sexist cases with three subtasks. Our team experimented with different ways to combat class imbalance throughout the tasks using data augmentation and loss alteration techniques. We tackled the challenge by utilising ensembles of Transformer models trained on different datasets, which are tested to find the balance between performance and interpretability. This solution ranked us in the top 40\% of teams for each of the tracks.

Solving the inverse problem is the key step in evaluating the capacity of a physical model to describe real phenomena. In medical image computing, it aligns with the classical theme of image-based model personalization. Traditionally, a solution to the problem is obtained by performing either sampling or variational inference based methods. Both approaches aim to identify a set of free physical model parameters that results in a simulation best matching an empirical observation. When applied to brain tumor modeling, one of the instances of image-based model personalization in medical image computing, the overarching drawback of the methods is the time complexity for finding such a set. In a clinical setting with limited time between imaging and diagnosis or even intervention, this time complexity may prove critical. As the history of quantitative science is the history of compression, we align in this paper with the historical tendency and propose a method compressing complex traditional strategies for solving an inverse problem into a simple database query task. We evaluated different ways of performing the database query task assessing the trade-off between accuracy and execution time. On the exemplary task of brain tumor growth modeling, we prove that the proposed method achieves one order speed-up compared to existing approaches for solving the inverse problem. The resulting compute time offers critical means for relying on more complex and, hence, realistic models, for integrating image preprocessing and inverse modeling even deeper, or for implementing the current model into a clinical workflow.

Variational inequalities in general and saddle point problems in particular are increasingly relevant in machine learning applications, including adversarial learning, GANs, transport and robust optimization. With increasing data and problem sizes necessary to train high performing models across various applications, we need to rely on parallel and distributed computing. However, in distributed training, communication among the compute nodes is a key bottleneck during training, and this problem is exacerbated for high dimensional and over-parameterized models. Due to these considerations, it is important to equip existing methods with strategies that would allow to reduce the volume of transmitted information during training while obtaining a model of comparable quality. In this paper, we present the first theoretically grounded distributed methods for solving variational inequalities and saddle point problems using compressed communication: MASHA1 and MASHA2. Our theory and methods allow for the use of both unbiased (such as Randk; MASHA1) and contractive (such as Topk; MASHA2) compressors. New algorithms support bidirectional compressions, and also can be modified for stochastic setting with batches and for federated learning with partial participation of clients. We empirically validated our conclusions using two experimental setups: a standard bilinear min-max problem, and large-scale distributed adversarial training of transformers.

Recently, due to COVID-19 and the growing demand for remote work, video conferencing apps have become especially widespread. The most valuable features of video chats are real-time background removal and face beautification. While solving these tasks, computer vision researchers face the problem of having relevant data for the training stage. There is no large dataset with high-quality labeled and diverse images of people in front of a laptop or smartphone camera to train a lightweight model without additional approaches. To boost the progress in this area, we provide a new image dataset, EasyPortrait, for portrait segmentation and face parsing tasks. It contains 20,000 primarily indoor photos of 8,377 unique users, and fine-grained segmentation masks separated into 9 classes. Images are collected and labeled from crowdsourcing platforms. Unlike most face parsing datasets, in EasyPortrait, the beard is not considered part of the skin mask, and the inside area of the mouth is separated from the teeth. These features allow using EasyPortrait for skin enhancement and teeth whitening tasks. This paper describes the pipeline for creating a large-scale and clean image segmentation dataset using crowdsourcing platforms without additional synthetic data. Moreover, we trained several models on EasyPortrait and showed experimental results. Proposed dataset and trained models are publicly available.

Mathematical reasoning is regarded as a necessary ability for Language Models (LMs). Recent works demonstrate large LMs' impressive performance in solving math problems. The success is attributed to their Chain-of-Thought (CoT) reasoning abilities, i.e., the ability to decompose complex questions into step-by-step reasoning chains, but such ability seems only to emerge from models with abundant parameters. This work investigates how to incorporate relatively small LMs with the capabilities of multi-step reasoning. We propose to inject such abilities by continually pre-training LMs on a synthetic dataset MsAT which is composed of Multi-step Arithmetic Tasks. Our experiments on four math word problem datasets show the effectiveness of the proposed method in enhancing LMs' math reasoning abilities.

We present rectified flow, a surprisingly simple approach to learning (neural) ordinary differential equation (ODE) models to transport between two empirically observed distributions \pi_0 and \pi_1, hence providing a unified solution to generative modeling and domain transfer, among various other tasks involving distribution transport. The idea of rectified flow is to learn the ODE to follow the straight paths connecting the points drawn from \pi_0 and \pi_1 as much as possible. This is achieved by solving a straightforward nonlinear least squares optimization problem, which can be easily scaled to large models without introducing extra parameters beyond standard supervised learning. The straight paths are special and preferred because they are the shortest paths between two points, and can be simulated exactly without time discretization and hence yield computationally efficient models. We show that the procedure of learning a rectified flow from data, called rectification, turns an arbitrary coupling of \pi_0 and \pi_1 to a new deterministic coupling with provably non-increasing convex transport costs. In addition, recursively applying rectification allows us to obtain a sequence of flows with increasingly straight paths, which can be simulated accurately with coarse time discretization in the inference phase. In empirical studies, we show that rectified flow performs superbly on image generation, image-to-image translation, and domain adaptation. In particular, on image generation and translation, our method yields nearly straight flows that give high quality results even with a single Euler discretization step.

Learning neural operators for solving partial differential equations (PDEs) has attracted great attention due to its high inference efficiency. However, training such operators requires generating a substantial amount of labeled data, i.e., PDE problems together with their solutions. The data generation process is exceptionally time-consuming, as it involves solving numerous systems of linear equations to obtain numerical solutions to the PDEs. Many existing methods solve these systems independently without considering their inherent similarities, resulting in extremely redundant computations. To tackle this problem, we propose a novel method, namely Sorting Krylov Recycling (SKR), to boost the efficiency of solving these systems, thus significantly accelerating data generation for neural operators training. To the best of our knowledge, SKR is the first attempt to address the time-consuming nature of data generation for learning neural operators. The working horse of SKR is Krylov subspace recycling, a powerful technique for solving a series of interrelated systems by leveraging their inherent similarities. Specifically, SKR employs a sorting algorithm to arrange these systems in a sequence, where adjacent systems exhibit high similarities. Then it equips a solver with Krylov subspace recycling to solve the systems sequentially instead of independently, thus effectively enhancing the solving efficiency. Both theoretical analysis and extensive experiments demonstrate that SKR can significantly accelerate neural operator data generation, achieving a remarkable speedup of up to 13.9 times.

Generative models inspired by dynamical transport of measure -- such as flows and diffusions -- construct a continuous-time map between two probability densities. Conventionally, one of these is the target density, only accessible through samples, while the other is taken as a simple base density that is data-agnostic. In this work, using the framework of stochastic interpolants, we formalize how to couple the base and the target densities. This enables us to incorporate information about class labels or continuous embeddings to construct dynamical transport maps that serve as conditional generative models. We show that these transport maps can be learned by solving a simple square loss regression problem analogous to the standard independent setting. We demonstrate the usefulness of constructing dependent couplings in practice through experiments in super-resolution and in-painting.

Autonomous driving faces great safety challenges for a lack of global perspective and the limitation of long-range perception capabilities. It has been widely agreed that vehicle-infrastructure cooperation is required to achieve Level 5 autonomy. However, there is still NO dataset from real scenarios available for computer vision researchers to work on vehicle-infrastructure cooperation-related problems. To accelerate computer vision research and innovation for Vehicle-Infrastructure Cooperative Autonomous Driving (VICAD), we release DAIR-V2X Dataset, which is the first large-scale, multi-modality, multi-view dataset from real scenarios for VICAD. DAIR-V2X comprises 71254 LiDAR frames and 71254 Camera frames, and all frames are captured from real scenes with 3D annotations. The Vehicle-Infrastructure Cooperative 3D Object Detection problem (VIC3D) is introduced, formulating the problem of collaboratively locating and identifying 3D objects using sensory inputs from both vehicle and infrastructure. In addition to solving traditional 3D object detection problems, the solution of VIC3D needs to consider the temporal asynchrony problem between vehicle and infrastructure sensors and the data transmission cost between them. Furthermore, we propose Time Compensation Late Fusion (TCLF), a late fusion framework for the VIC3D task as a benchmark based on DAIR-V2X. Find data, code, and more up-to-date information at https://thudair.baai.ac.cn/index and https://github.com/AIR-THU/DAIR-V2X.

We analyze continual learning on a sequence of separable linear classification tasks with binary labels. We show theoretically that learning with weak regularization reduces to solving a sequential max-margin problem, corresponding to a special case of the Projection Onto Convex Sets (POCS) framework. We then develop upper bounds on the forgetting and other quantities of interest under various settings with recurring tasks, including cyclic and random orderings of tasks. We discuss several practical implications to popular training practices like regularization scheduling and weighting. We point out several theoretical differences between our continual classification setting and a recently studied continual regression setting.

Despite their success in many natural language tasks, solving math problems remains a significant challenge for large language models (LLMs). A large gap exists between LLMs' pass-at-one and pass-at-N performance in solving math problems, suggesting LLMs might be close to finding correct solutions, motivating our exploration of fine-tuning methods to unlock LLMs' performance. Using the challenging MATH dataset, we investigate three fine-tuning strategies: (1) solution fine-tuning, where we fine-tune to generate a detailed solution for a given math problem; (2) solution-cluster re-ranking, where the LLM is fine-tuned as a solution verifier/evaluator to choose among generated candidate solution clusters; (3) multi-task sequential fine-tuning, which integrates both solution generation and evaluation tasks together efficiently to enhance the LLM performance. With these methods, we present a thorough empirical study on a series of PaLM 2 models and find: (1) The quality and style of the step-by-step solutions used for fine-tuning can make a significant impact on the model performance; (2) While solution re-ranking and majority voting are both effective for improving the model performance when used separately, they can also be used together for an even greater performance boost; (3) Multi-task fine-tuning that sequentially separates the solution generation and evaluation tasks can offer improved performance compared with the solution fine-tuning baseline. Guided by these insights, we design a fine-tuning recipe that yields approximately 58.8% accuracy on the MATH dataset with fine-tuned PaLM 2-L models, an 11.2% accuracy improvement over the few-shot performance of pre-trained PaLM 2-L model with majority voting.

Pre-trained diffusion models have been successfully used as priors in a variety of linear inverse problems, where the goal is to reconstruct a signal from noisy linear measurements. However, existing approaches require knowledge of the linear operator. In this paper, we propose GibbsDDRM, an extension of Denoising Diffusion Restoration Models (DDRM) to a blind setting in which the linear measurement operator is unknown. GibbsDDRM constructs a joint distribution of the data, measurements, and linear operator by using a pre-trained diffusion model for the data prior, and it solves the problem by posterior sampling with an efficient variant of a Gibbs sampler. The proposed method is problem-agnostic, meaning that a pre-trained diffusion model can be applied to various inverse problems without fine-tuning. In experiments, it achieved high performance on both blind image deblurring and vocal dereverberation tasks, despite the use of simple generic priors for the underlying linear operators.

Large Language Models (LLMs) have demonstrated promising capabilities in solving mathematical reasoning tasks, leveraging Chain-of-Thought (CoT) data as a vital component in guiding answer generation. Current paradigms typically generate CoT and answers directly for a given problem, diverging from human problem-solving strategies to some extent. Humans often solve problems by recalling analogous cases and leveraging their solutions to reason about the current task. Inspired by this cognitive process, we propose MetaLadder, a novel framework that explicitly prompts LLMs to recall and reflect on meta-problems, those structurally or semantically analogous problems, alongside their CoT solutions before addressing the target problem. Additionally, we introduce a problem-restating mechanism to enhance the model's comprehension of the target problem by regenerating the original question, which further improves reasoning accuracy. Therefore, the model can achieve reasoning transfer from analogical problems, mimicking human-like "learning from examples" and generalization abilities. Extensive experiments on mathematical benchmarks demonstrate that our MetaLadder significantly boosts LLMs' problem-solving accuracy, largely outperforming standard CoT-based methods (10.3\% accuracy gain) and other methods. Our code and data has been released at https://github.com/LHL3341/MetaLadder.

Face recognition datasets are often collected by crawling Internet and without individuals' consents, raising ethical and privacy concerns. Generating synthetic datasets for training face recognition models has emerged as a promising alternative. However, the generation of synthetic datasets remains challenging as it entails adequate inter-class and intra-class variations. While advances in generative models have made it easier to increase intra-class variations in face datasets (such as pose, illumination, etc.), generating sufficient inter-class variation is still a difficult task. In this paper, we formulate the dataset generation as a packing problem on the embedding space (represented on a hypersphere) of a face recognition model and propose a new synthetic dataset generation approach, called HyperFace. We formalize our packing problem as an optimization problem and solve it with a gradient descent-based approach. Then, we use a conditional face generator model to synthesize face images from the optimized embeddings. We use our generated datasets to train face recognition models and evaluate the trained models on several benchmarking real datasets. Our experimental results show that models trained with HyperFace achieve state-of-the-art performance in training face recognition using synthetic datasets.

Language model performance depends on identifying the optimal mixture of data groups to train on (e.g., law, code, math). Prior work has proposed a diverse set of methods to efficiently learn mixture proportions, ranging from fitting regression models over training runs to dynamically updating proportions throughout training. Surprisingly, we find that no existing method consistently outperforms a simple stratified sampling baseline in terms of average test perplexity. To understand this inconsistency, we unify existing methods into a standard framework, showing they are equivalent to solving a common optimization problem: minimize average loss subject to a method-specific mixing law -- an implicit assumption on the relationship between loss and mixture proportions. This framework suggests that measuring the fidelity of a method's mixing law can offer insights into its performance. Empirically, we find that existing methods set their mixing law parameters inaccurately, resulting in the inconsistent mixing performance we observe. Using this insight, we derive a new online method named Aioli, which directly estimates the mixing law parameters throughout training and uses them to dynamically adjust proportions. Aioli outperforms stratified sampling on 6 out of 6 datasets by an average of 0.27 test perplexity points, whereas existing methods fail to consistently beat stratified sampling, doing up to 6.9 points worse. Moreover, in a practical setting where proportions are learned on shorter runs due to computational constraints, Aioli can dynamically adjust these proportions over the full training run, consistently improving performance over existing methods by up to 12.012 test perplexity points.

Solving tabular math word problems (TMWPs) has become a critical role in evaluating the mathematical reasoning ability of large language models (LLMs), where large-scale TMWP samples are commonly required for LLM fine-tuning. Since the collection of high-quality TMWP datasets is costly and time-consuming, recent research has concentrated on automatic TMWP generation. However, current generated samples usually suffer from issues of either correctness or diversity. In this paper, we propose a Template-driven LLM-paraphrased (TeLL) framework for generating high-quality TMWP samples with diverse backgrounds and accurate tables, questions, answers, and solutions. To this end, we first extract templates from existing real samples to generate initial problems, ensuring correctness. Then, we adopt an LLM to extend templates and paraphrase problems, obtaining diverse TMWP samples. Furthermore, we find the reasoning annotation is important for solving TMWPs. Therefore, we propose to enrich each solution with illustrative reasoning steps. Through the proposed framework, we construct a high-quality dataset TabMWP-TeLL by adhering to the question types in the TabMWP dataset, and we conduct extensive experiments on a variety of LLMs to demonstrate the effectiveness of TabMWP-TeLL in improving TMWP solving performance. The code and data of this paper are available at: https://github.com/Jason8Kang/TELL.

Multi-agent pathfinding (MAPF) is a challenging computational problem that typically requires to find collision-free paths for multiple agents in a shared environment. Solving MAPF optimally is NP-hard, yet efficient solutions are critical for numerous applications, including automated warehouses and transportation systems. Recently, learning-based approaches to MAPF have gained attention, particularly those leveraging deep reinforcement learning. Following current trends in machine learning, we have created a foundation model for the MAPF problems called MAPF-GPT. Using imitation learning, we have trained a policy on a set of pre-collected sub-optimal expert trajectories that can generate actions in conditions of partial observability without additional heuristics, reward functions, or communication with other agents. The resulting MAPF-GPT model demonstrates zero-shot learning abilities when solving the MAPF problem instances that were not present in the training dataset. We show that MAPF-GPT notably outperforms the current best-performing learnable-MAPF solvers on a diverse range of problem instances and is efficient in terms of computation (in the inference mode).

To augment language models with the ability to reason, researchers usually prompt or finetune them to produce chain of thought reasoning steps before producing the final answer. However, although people use natural language to reason effectively, it may be that LMs could reason more effectively with some intermediate computation that is not in natural language. In this work, we explore an alternative reasoning approach: instead of explicitly producing the chain of thought reasoning steps, we use the language model's internal hidden states to perform implicit reasoning. The implicit reasoning steps are distilled from a teacher model trained on explicit chain-of-thought reasoning, and instead of doing reasoning "horizontally" by producing intermediate words one-by-one, we distill it such that the reasoning happens "vertically" among the hidden states in different layers. We conduct experiments on a multi-digit multiplication task and a grade school math problem dataset and find that this approach enables solving tasks previously not solvable without explicit chain-of-thought, at a speed comparable to no chain-of-thought.

Scaling test-time compute is a promising axis for improving LLM capabilities. However, test-time compute can be scaled in a variety of ways, and effectively combining different approaches remains an active area of research. Here, we explore this problem in the context of solving real-world GitHub issues from the SWE-bench dataset. Our system, named CodeMonkeys, allows models to iteratively edit a codebase by jointly generating and running a testing script alongside their draft edit. We sample many of these multi-turn trajectories for every issue to generate a collection of candidate edits. This approach lets us scale "serial" test-time compute by increasing the number of iterations per trajectory and "parallel" test-time compute by increasing the number of trajectories per problem. With parallel scaling, we can amortize up-front costs across multiple downstream samples, allowing us to identify relevant codebase context using the simple method of letting an LLM read every file. In order to select between candidate edits, we combine voting using model-generated tests with a final multi-turn trajectory dedicated to selection. Overall, CodeMonkeys resolves 57.4% of issues from SWE-bench Verified using a budget of approximately 2300 USD. Our selection method can also be used to combine candidates from different sources. Selecting over an ensemble of edits from existing top SWE-bench Verified submissions obtains a score of 66.2% and outperforms the best member of the ensemble on its own. We fully release our code and data at https://scalingintelligence.stanford.edu/pubs/codemonkeys.

Multivariate Time Series (MTS) forecasting is a fundamental task with numerous real-world applications, such as transportation, climate, and epidemiology. While a myriad of powerful deep learning models have been developed for this task, few works have explored the robustness of MTS forecasting models to malicious attacks, which is crucial for their trustworthy employment in high-stake scenarios. To address this gap, we dive deep into the backdoor attacks on MTS forecasting models and propose an effective attack method named BackTime.By subtly injecting a few stealthy triggers into the MTS data, BackTime can alter the predictions of the forecasting model according to the attacker's intent. Specifically, BackTime first identifies vulnerable timestamps in the data for poisoning, and then adaptively synthesizes stealthy and effective triggers by solving a bi-level optimization problem with a GNN-based trigger generator. Extensive experiments across multiple datasets and state-of-the-art MTS forecasting models demonstrate the effectiveness, versatility, and stealthiness of attacks. The code is available at https://github.com/xiaolin-cs/BackTime.

While large-scale unsupervised language models (LMs) learn broad world knowledge and some reasoning skills, achieving precise control of their behavior is difficult due to the completely unsupervised nature of their training. Existing methods for gaining such steerability collect human labels of the relative quality of model generations and fine-tune the unsupervised LM to align with these preferences, often with reinforcement learning from human feedback (RLHF). However, RLHF is a complex and often unstable procedure, first fitting a reward model that reflects the human preferences, and then fine-tuning the large unsupervised LM using reinforcement learning to maximize this estimated reward without drifting too far from the original model. In this paper, we leverage a mapping between reward functions and optimal policies to show that this constrained reward maximization problem can be optimized exactly with a single stage of policy training, essentially solving a classification problem on the human preference data. The resulting algorithm, which we call Direct Preference Optimization (DPO), is stable, performant and computationally lightweight, eliminating the need for fitting a reward model, sampling from the LM during fine-tuning, or performing significant hyperparameter tuning. Our experiments show that DPO can fine-tune LMs to align with human preferences as well as or better than existing methods. Notably, fine-tuning with DPO exceeds RLHF's ability to control sentiment of generations and improves response quality in summarization and single-turn dialogue while being substantially simpler to implement and train.

With the recent advances in natural language processing (NLP), a vast number of applications have emerged across various use cases. Among the plethora of NLP applications, many academic researchers are motivated to do work that has a positive social impact, in line with the recent initiatives of NLP for Social Good (NLP4SG). However, it is not always obvious to researchers how their research efforts are tackling today's big social problems. Thus, in this paper, we introduce NLP4SGPAPERS, a scientific dataset with three associated tasks that can help identify NLP4SG papers and characterize the NLP4SG landscape by: (1) identifying the papers that address a social problem, (2) mapping them to the corresponding UN Sustainable Development Goals (SDGs), and (3) identifying the task they are solving and the methods they are using. Using state-of-the-art NLP models, we address each of these tasks and use them on the entire ACL Anthology, resulting in a visualization workspace that gives researchers a comprehensive overview of the field of NLP4SG. Our website is available at https://nlp4sg.vercel.app . We released our data at https://huggingface.co/datasets/feradauto/NLP4SGPapers and code at https://github.com/feradauto/nlp4sg .

Data profiling is an essential process in modern data-driven industries. One of its critical components is the discovery and validation of complex statistics, including functional dependencies, data constraints, association rules, and others. However, most existing data profiling systems that focus on complex statistics do not provide proper integration with the tools used by contemporary data scientists. This creates a significant barrier to the adoption of these tools in the industry. Moreover, existing systems were not created with industrial-grade workloads in mind. Finally, they do not aim to provide descriptive explanations, i.e. why a given pattern is not found. It is a significant issue as it is essential to understand the underlying reasons for a specific pattern's absence to make informed decisions based on the data. Because of that, these patterns are effectively rest in thin air: their application scope is rather limited, they are rarely used by the broader public. At the same time, as we are going to demonstrate in this presentation, complex statistics can be efficiently used to solve many classic data quality problems. Desbordante is an open-source data profiler that aims to close this gap. It is built with emphasis on industrial application: it is efficient, scalable, resilient to crashes, and provides explanations. Furthermore, it provides seamless Python integration by offloading various costly operations to the C++ core, not only mining. In this demonstration, we show several scenarios that allow end users to solve different data quality problems. Namely, we showcase typo detection, data deduplication, and data anomaly detection scenarios.

We introduce ``LAMBDA," a novel open-source, code-free multi-agent data analysis system that that harnesses the power of large models. LAMBDA is designed to address data analysis challenges in complex data-driven applications through the use of innovatively designed data agents that operate iteratively and generatively using natural language. At the core of LAMBDA are two key agent roles: the programmer and the inspector, which are engineered to work together seamlessly. Specifically, the programmer generates code based on the user's instructions and domain-specific knowledge, enhanced by advanced models. Meanwhile, the inspector debugs the code when necessary. To ensure robustness and handle adverse scenarios, LAMBDA features a user interface that allows direct user intervention in the operational loop. Additionally, LAMBDA can flexibly integrate external models and algorithms through our knowledge integration mechanism, catering to the needs of customized data analysis. LAMBDA has demonstrated strong performance on various machine learning datasets. It has the potential to enhance data science practice and analysis paradigm by seamlessly integrating human and artificial intelligence, making it more accessible, effective, and efficient for individuals from diverse backgrounds. The strong performance of LAMBDA in solving data science problems is demonstrated in several case studies, which are presented at https://www.polyu.edu.hk/ama/cmfai/lambda.html.

We introduce CLEVR-Math, a multi-modal math word problems dataset consisting of simple math word problems involving addition/subtraction, represented partly by a textual description and partly by an image illustrating the scenario. The text describes actions performed on the scene that is depicted in the image. Since the question posed may not be about the scene in the image, but about the state of the scene before or after the actions are applied, the solver envision or imagine the state changes due to these actions. Solving these word problems requires a combination of language, visual and mathematical reasoning. We apply state-of-the-art neural and neuro-symbolic models for visual question answering on CLEVR-Math and empirically evaluate their performances. Our results show how neither method generalise to chains of operations. We discuss the limitations of the two in addressing the task of multi-modal word problem solving.

Large Language Models (LLMs) have demonstrated significant potential in handling specialized tasks, including medical problem-solving. However, most studies predominantly focus on English-language contexts. This study introduces a novel benchmark dataset based on Polish medical licensing and specialization exams (LEK, LDEK, PES) taken by medical doctor candidates and practicing doctors pursuing specialization. The dataset was web-scraped from publicly available resources provided by the Medical Examination Center and the Chief Medical Chamber. It comprises over 24,000 exam questions, including a subset of parallel Polish-English corpora, where the English portion was professionally translated by the examination center for foreign candidates. By creating a structured benchmark from these existing exam questions, we systematically evaluate state-of-the-art LLMs, including general-purpose, domain-specific, and Polish-specific models, and compare their performance against human medical students. Our analysis reveals that while models like GPT-4o achieve near-human performance, significant challenges persist in cross-lingual translation and domain-specific understanding. These findings underscore disparities in model performance across languages and medical specialties, highlighting the limitations and ethical considerations of deploying LLMs in clinical practice.

The quality of datasets plays an increasingly crucial role in the research and development of modern artificial intelligence (AI). Despite the proliferation of open dataset platforms nowadays, data quality issues, such as insufficient documentation, inaccurate annotations, and ethical concerns, remain common in datasets widely used in AI. Furthermore, these issues are often subtle and difficult to be detected by rule-based scripts, requiring expensive manual identification and verification by dataset users or maintainers. With the increasing capability of large language models (LLMs), it is promising to streamline the curation of datasets with LLM agents. In this work, as the initial step towards this goal, we propose a dataset curation agent benchmark, DCA-Bench, to measure LLM agents' capability of detecting hidden dataset quality issues. Specifically, we collect diverse real-world dataset quality issues from eight open dataset platforms as a testbed. Additionally, to establish an automatic pipeline for evaluating the success of LLM agents, which requires a nuanced understanding of the agent outputs, we implement a dedicated Evaluator using another LLM agent. We demonstrate that the LLM-based Evaluator empirically aligns well with human evaluation, allowing reliable automatic evaluation on the proposed benchmark. We further conduct experiments on several baseline LLM agents on the proposed benchmark and demonstrate the complexity of the task, indicating that applying LLMs to real-world dataset curation still requires further in-depth exploration and innovation. Finally, the proposed benchmark can also serve as a testbed for measuring the capability of LLMs in problem discovery rather than just problem-solving. The benchmark suite is available at https://github.com/TRAIS-Lab/dca-bench.

We introduce a new type of programming challenge called programming puzzles, as an objective and comprehensive evaluation of program synthesis, and release an open-source dataset of Python Programming Puzzles (P3). Each puzzle is defined by a short Python program f, and the goal is to find an input which makes f return True. The puzzles are objective in that each one is specified entirely by the source code of its verifier f, so evaluating f is all that is needed to test a candidate solution. They do not require an answer key or input/output examples, nor do they depend on natural language understanding. The dataset is comprehensive in that it spans problems of a range of difficulties and domains, ranging from trivial string manipulation problems, to classic programming puzzles (e.g., Tower of Hanoi), to interview/competitive-programming problems (e.g., dynamic programming), to longstanding open problems in algorithms and mathematics (e.g., factoring). We develop baseline enumerative program synthesis, GPT-3 and Codex solvers that are capable of solving puzzles -- even without access to any reference solutions -- by learning from their own past solutions. Codex performs best, solving up to 18% of 397 test problems with a single try and 80% of the problems with 1,000 tries per problem. In a small user study, we find a positive correlation between puzzle-solving performance and coding experience, and between the puzzle difficulty for humans and AI solvers. Therefore, further improvements on P3 could have a significant impact on many program synthesis areas.

Automated math word problem solvers based on neural networks have successfully managed to obtain 70-80\% accuracy in solving arithmetic word problems. However, it has been shown that these solvers may rely on superficial patterns to obtain their equations. In order to determine what information math word problem solvers use to generate solutions, we remove parts of the input and measure the model's performance on the perturbed dataset. Our results show that the model is not sensitive to the removal of many words from the input and can still manage to find a correct answer when given a nonsense question. This indicates that automatic solvers do not follow the semantic logic of math word problems, and may be overfitting to the presence of specific words.

Transformers have demonstrated effectiveness in in-context solving data-fitting problems from various (latent) models, as reported by Garg et al. However, the absence of an inherent iterative structure in the transformer architecture presents a challenge in emulating the iterative algorithms, which are commonly employed in traditional machine learning methods. To address this, we propose the utilization of looped transformer architecture and its associated training methodology, with the aim of incorporating iterative characteristics into the transformer architectures. Experimental results suggest that the looped transformer achieves performance comparable to the standard transformer in solving various data-fitting problems, while utilizing less than 10\% of the parameter count.

Recently, there have been notable advancements in large language models (LLMs), demonstrating their growing abilities in complex reasoning. However, existing research largely overlooks a thorough and systematic comparison of these models' reasoning processes and outputs, particularly regarding their self-reflection pattern (also termed "Aha moment") and the interconnections across diverse domains. This paper proposes a novel framework for analyzing the reasoning characteristics of four cutting-edge large reasoning models (GPT-o1, DeepSeek-R1, Kimi-k1.5, and Grok-3) using keywords statistic and LLM-as-a-judge paradigm. Our approach connects their internal thinking processes with their final outputs. A diverse dataset consists of real-world scenario-based questions covering logical deduction, causal inference, and multi-step problem-solving. Additionally, a set of metrics is put forward to assess both the coherence of reasoning and the accuracy of the outputs. The research results uncover various patterns of how these models balance exploration and exploitation, deal with problems, and reach conclusions during the reasoning process. Through quantitative and qualitative comparisons, disparities among these models are identified in aspects such as the depth of reasoning, the reliance on intermediate steps, and the degree of similarity between their thinking processes and output patterns and those of GPT-o1. This work offers valuable insights into the trade-off between computational efficiency and reasoning robustness and provides practical recommendations for enhancing model design and evaluation in practical applications. We publicly release our project at: https://github.com/ChangWenhan/FromThinking2Output

Puzzlehunts are a genre of complex, multi-step puzzles lacking well-defined problem definitions. In contrast to conventional reasoning benchmarks consisting of tasks with clear instructions, puzzlehunts require models to discover the underlying problem structure from multimodal evidence and iterative reasoning, mirroring real-world domains such as scientific discovery, exploratory data analysis, or investigative problem-solving. Despite recent progress in foundation models, their performance on such open-ended settings remains largely untested. In this paper, we introduce PuzzleWorld, a large-scale benchmark of 667 puzzlehunt-style problems designed to assess step-by-step, open-ended, and creative multimodal reasoning. Each puzzle is annotated with the final solution, detailed reasoning traces, and cognitive skill labels, enabling holistic benchmarking and fine-grained diagnostic analysis. Most state-of-the-art models achieve only 1-2% final answer accuracy, with the best model solving only 14% of puzzles and reaching 40% stepwise accuracy. To demonstrate the value of our reasoning annotations, we show that fine-tuning a small model on reasoning traces improves stepwise reasoning from 4% to 11%, while training on final answers alone degrades performance to near zero. Our error analysis reveals that current models exhibit myopic reasoning, are bottlenecked by the limitations of language-based inference, and lack sketching capabilities crucial for visual and spatial reasoning. We release PuzzleWorld at https://github.com/MIT-MI/PuzzleWorld to support future work on building more general, open-ended, and creative reasoning systems.

Recent advancements in large language models (LLMs) have shown strong general reasoning abilities, yet their effectiveness in financial reasoning remains underexplored. In this study, we comprehensively evaluate 16 powerful reasoning and general LLMs on three complex financial tasks involving financial text, tabular data, and equations, assessing numerical reasoning, tabular interpretation, financial terminology comprehension, long-context processing, and equation-based problem solving. Our results show that while better datasets and pretraining improve financial reasoning, general enhancements like CoT fine-tuning do not always yield consistent gains. Moreover, all reasoning strategies face challenges in improving performance on long-context and multi-table tasks. To address these limitations, we develop a financial reasoning-enhanced model based on Llama-3.1-8B-Instruct, by CoT fine-tuning and reinforcement learning with domain-specific reasoning paths. Even with simple fine-tuning with one financial dataset, our model achieves a consistent 10% performance improvement across tasks, surpassing all 8B models and even Llama3-70B-Instruct and Llama3.1-70B-Instruct on average. Our results highlight the need for domain-specific adaptations in financial tasks, emphasizing future directions such as multi-table reasoning, long-context processing, and financial terminology comprehension. All our datasets, models, and codes are publicly available. Furthermore, we introduce a leaderboard for benchmarking future datasets and models.

The problem of designing NLP solvers for math word problems (MWP) has seen sustained research activity and steady gains in the test accuracy. Since existing solvers achieve high performance on the benchmark datasets for elementary level MWPs containing one-unknown arithmetic word problems, such problems are often considered "solved" with the bulk of research attention moving to more complex MWPs. In this paper, we restrict our attention to English MWPs taught in grades four and lower. We provide strong evidence that the existing MWP solvers rely on shallow heuristics to achieve high performance on the benchmark datasets. To this end, we show that MWP solvers that do not have access to the question asked in the MWP can still solve a large fraction of MWPs. Similarly, models that treat MWPs as bag-of-words can also achieve surprisingly high accuracy. Further, we introduce a challenge dataset, SVAMP, created by applying carefully chosen variations over examples sampled from existing datasets. The best accuracy achieved by state-of-the-art models is substantially lower on SVAMP, thus showing that much remains to be done even for the simplest of the MWPs.

With recent dramatic increases in AI system capabilities, there has been growing interest in utilizing machine learning for reasoning-heavy, quantitative tasks, particularly mathematics. While there are many resources capturing mathematics at the high-school, undergraduate, and graduate level, there are far fewer resources available that align with the level of difficulty and open endedness encountered by professional mathematicians working on open problems. To address this, we introduce a new collection of datasets, the Algebraic Combinatorics Dataset Repository (ACD Repo), representing either foundational results or open problems in algebraic combinatorics, a subfield of mathematics that studies discrete structures arising from abstract algebra. Further differentiating our dataset collection is the fact that it aims at the conjecturing process. Each dataset includes an open-ended research-level question and a large collection of examples (up to 10M in some cases) from which conjectures should be generated. We describe all nine datasets, the different ways machine learning models can be applied to them (e.g., training with narrow models followed by interpretability analysis or program synthesis with LLMs), and discuss some of the challenges involved in designing datasets like these.

Recent large language models (LLMs) have shown indications of mathematical reasoning ability. However it has not been clear how they would fare on more challenging competition-level problems. And while self-generated verbalizations of intermediate reasoning steps (i.e., chain-of-thought prompting) have been shown to be helpful, whether LLMs can make use of helpful side information such as problem-specific hints has not been investigated before. In this paper, we propose a challenging benchmark dataset for enabling such analyses. The Concept and Hint-Annotated Math Problems (CHAMP) consists of high school math competition problems, annotated with concepts, or general math facts, and hints, or problem-specific tricks. These annotations allow us to explore the effects of additional information, such as relevant hints, misleading concepts, or related problems. This benchmark is difficult, with the best model only scoring 58.1% in standard settings. With concepts and hints, performance sometimes improves, indicating that some models can make use of such side information. We further annotate model-generated solutions for their correctness. Using this corpus, we find that models often arrive at the correct final answer through wrong reasoning steps. In addition, we test whether models are able to verify these solutions, and find that most models struggle. The dataset and code are available on the project website.

Math word problems are critical K-8 educational tools, but writing them is time-consuming and requires domain expertise. We suggest that language models can support K-8 math education by automatically generating problems at scale. To be educational, generated problems must be 1) solvable, 2) accurate, and 3) appropriate. Existing datasets are unlabeled for these criteria, making them ill-suited for training problem generators. We introduce MATHWELL, a Llama-2 (70B) model iteratively finetuned to generate K-8 math word problems using data from expert annotation. Using MATHWELL, we generate the largest English word problem dataset to date, containing 20,490 problems. 3,484 are scored by domain experts who find MATHWELL has a 40% higher share of problems that have executable solutions and meet all criteria than alternatives, with 74% of its problems with executable solutions being solvable, accurate, and appropriate.

We introduce a new challenge to test the STEM skills of neural models. The problems in the real world often require solutions, combining knowledge from STEM (science, technology, engineering, and math). Unlike existing datasets, our dataset requires the understanding of multimodal vision-language information of STEM. Our dataset features one of the largest and most comprehensive datasets for the challenge. It includes 448 skills and 1,073,146 questions spanning all STEM subjects. Compared to existing datasets that often focus on examining expert-level ability, our dataset includes fundamental skills and questions designed based on the K-12 curriculum. We also add state-of-the-art foundation models such as CLIP and GPT-3.5-Turbo to our benchmark. Results show that the recent model advances only help master a very limited number of lower grade-level skills (2.5% in the third grade) in our dataset. In fact, these models are still well below (averaging 54.7%) the performance of elementary students, not to mention near expert-level performance. To understand and increase the performance on our dataset, we teach the models on a training split of our dataset. Even though we observe improved performance, the model performance remains relatively low compared to average elementary students. To solve STEM problems, we will need novel algorithmic innovations from the community.

Solving math story problems is a complex task for students and NLP models alike, requiring them to understand the world as described in the story and reason over it to compute an answer. Recent years have seen impressive performance on automatically solving these problems with large pre-trained language models and innovative techniques to prompt them. However, it remains unclear if these models possess accurate representations of mathematical concepts. This leads to lack of interpretability and trustworthiness which impedes their usefulness in various applications. In this paper, we consolidate previous work on categorizing and representing math story problems and develop MathWorld, which is a graph-based semantic formalism specific for the domain of math story problems. With MathWorld, we can assign world models to math story problems which represent the situations and actions introduced in the text and their mathematical relationships. We combine math story problems from several existing datasets and annotate a corpus of 1,019 problems and 3,204 logical forms with MathWorld. Using this data, we demonstrate the following use cases of MathWorld: (1) prompting language models with synthetically generated question-answer pairs to probe their reasoning and world modeling abilities, and (2) generating new problems by using the world models as a design space.

Mathematical reasoning continues to be a critical challenge in large language model (LLM) development with significant interest. However, most of the cutting-edge progress in mathematical reasoning with LLMs has become closed-source due to lack of access to training data. This lack of data access limits researchers from understanding the impact of different choices for synthesizing and utilizing the data. With the goal of creating a high-quality finetuning (SFT) dataset for math reasoning, we conduct careful ablation experiments on data synthesis using the recently released Llama3.1 family of models. Our experiments show that: (a) solution format matters, with excessively verbose solutions proving detrimental to SFT performance, (b) data generated by a strong teacher outperforms on-policy data generated by a weak student model, (c) SFT is robust to low-quality solutions, allowing for imprecise data filtering, and (d) question diversity is crucial for achieving data scaling gains. Based on these insights, we create the OpenMathInstruct-2 dataset, which consists of 14M question-solution pairs (approx 600K unique questions), making it nearly eight times larger than the previous largest open-source math reasoning dataset. Finetuning the Llama-3.1-8B-Base using OpenMathInstruct-2 outperforms Llama3.1-8B-Instruct on MATH by an absolute 15.9\% (51.9\% rightarrow 67.8\%). Finally, to accelerate the open-source efforts, we release the code, the finetuned models, and the OpenMathInstruct-2 dataset under a commercially permissive license.

Recent advancements in Large Language Models (LLMs) have been reshaping Natural Language Processing (NLP) task in several domains. Their use in the field of Human Resources (HR) has still room for expansions and could be beneficial for several time consuming tasks. Examples such as time-off submissions, medical claims filing, and access requests are noteworthy, but they are by no means the sole instances. However, the aforementioned developments must grapple with the pivotal challenge of constructing a high-quality training dataset. On one hand, most conversation datasets are solving problems for customers not employees. On the other hand, gathering conversations with HR could raise privacy concerns. To solve it, we introduce HR-Multiwoz, a fully-labeled dataset of 550 conversations spanning 10 HR domains to evaluate LLM Agent. Our work has the following contributions: (1) It is the first labeled open-sourced conversation dataset in the HR domain for NLP research. (2) It provides a detailed recipe for the data generation procedure along with data analysis and human evaluations. The data generation pipeline is transferable and can be easily adapted for labeled conversation data generation in other domains. (3) The proposed data-collection pipeline is mostly based on LLMs with minimal human involvement for annotation, which is time and cost-efficient.

Chain-of-thought (CoT) prompting with large language models has proven effective in numerous natural language processing tasks, but designing prompts that generalize well to diverse problem types can be challenging, especially in the context of math word problem (MWP) solving. Additionally, it is common to have a large amount of training data that have a better diversity coverage but CoT annotations are not available, which limits the use of supervised learning techniques. To address these issues, we investigate two approaches to leverage the training data in a few-shot prompting scenario: dynamic program prompting and program distillation. Our approach is largely inspired by Gao et al., (2022), where they proposed to replace the CoT with the programs as the intermediate reasoning step. Such a prompting strategy allows us to accurately verify the answer correctness through program execution in MWP solving. Our dynamic program prompting involves annotating the training data by sampling correct programs from a large language model, while program distillation involves adapting a smaller model to the program-annotated training data. Our experiments on three standard MWP datasets demonstrate the effectiveness of these approaches, yielding significant improvements over previous baselines for prompting and fine-tuning. Our results suggest that leveraging a large amount of training data can improve the generalization ability of prompts and boost the performance of fine-tuned small models in MWP solving.

Virtually all aspects of modern life depend on space technology. Thanks to the great advancement of computer vision in general and deep learning-based techniques in particular, over the decades, the world witnessed the growing use of deep learning in solving problems for space applications, such as self-driving robot, tracers, insect-like robot on cosmos and health monitoring of spacecraft. These are just some prominent examples that has advanced space industry with the help of deep learning. However, the success of deep learning models requires a lot of training data in order to have decent performance, while on the other hand, there are very limited amount of publicly available space datasets for the training of deep learning models. Currently, there is no public datasets for space-based object detection or instance segmentation, partly because manually annotating object segmentation masks is very time consuming as they require pixel-level labelling, not to mention the challenge of obtaining images from space. In this paper, we aim to fill this gap by releasing a dataset for spacecraft detection, instance segmentation and part recognition. The main contribution of this work is the development of the dataset using images of space stations and satellites, with rich annotations including bounding boxes of spacecrafts and masks to the level of object parts, which are obtained with a mixture of automatic processes and manual efforts. We also provide evaluations with state-of-the-art methods in object detection and instance segmentation as a benchmark for the dataset. The link for downloading the proposed dataset can be found on https://github.com/Yurushia1998/SatelliteDataset.

Mathematical understanding and reasoning are crucial tasks for assessing the capabilities of artificial intelligence (AI). However, existing benchmarks either require just a few steps of reasoning, or only contain a small amount of data in one specific topic, making it hard to analyse AI's behaviour with reference to different problems within a specific topic in detail. In this work, we propose Conic10K, a challenging math problem dataset on conic sections in Chinese senior high school education. Our dataset contains various problems with different reasoning depths, while only the knowledge from conic sections is required. Since the dataset only involves a narrow range of knowledge, it is easy to separately analyse the knowledge a model possesses and the reasoning ability it has. For each problem, we provide a high-quality formal representation, the reasoning steps, and the final solution. Experiments show that existing large language models, including GPT-4, exhibit weak performance on complex reasoning. We hope that our findings could inspire more advanced techniques for precise natural language understanding and reasoning. Our dataset and codes are available at https://github.com/whyNLP/Conic10K.

Our work presents a novel angle for evaluating language models' (LMs) mathematical abilities, by investigating whether they can discern skills and concepts enabled by math content. We contribute two datasets: one consisting of 385 fine-grained descriptions of K-12 math skills and concepts, or standards, from Achieve the Core (ATC), and another of 9.9K problems labeled with these standards (MathFish). Working with experienced teachers, we find that LMs struggle to tag and verify standards linked to problems, and instead predict labels that are close to ground truth, but differ in subtle ways. We also show that LMs often generate problems that do not fully align with standards described in prompts. Finally, we categorize problems in GSM8k using math standards, allowing us to better understand why some problems are more difficult to solve for models than others.

Scientific problem-solving involves synthesizing information while applying expert knowledge. We introduce CURIE, a scientific long-Context Understanding,Reasoning and Information Extraction benchmark to measure the potential of Large Language Models (LLMs) in scientific problem-solving and assisting scientists in realistic workflows. This benchmark introduces ten challenging tasks with a total of 580 problems and solution pairs curated by experts in six disciplines - materials science, condensed matter physics, quantum computing, geospatial analysis, biodiversity, and proteins - covering both experimental and theoretical work-flows in science. We evaluate a range of closed and open LLMs on tasks in CURIE which requires domain expertise, comprehension of long in-context information,and multi-step reasoning. While Gemini Flash 2.0 and Claude-3 show consistent high comprehension across domains, the popular GPT-4o and command-R+ fail dramatically on protein sequencing tasks. With the best performance at 32% there is much room for improvement for all models. We hope that insights gained from CURIE can guide the future development of LLMs in sciences. Evaluation code and data are in https://github.com/google/curie

Real-world enterprise text-to-SQL workflows often involve complex cloud or local data across various database systems, multiple SQL queries in various dialects, and diverse operations from data transformation to analytics. We introduce Spider 2.0, an evaluation framework comprising 632 real-world text-to-SQL workflow problems derived from enterprise-level database use cases. The databases in Spider 2.0 are sourced from real data applications, often containing over 1,000 columns and stored in local or cloud database systems such as BigQuery and Snowflake. We show that solving problems in Spider 2.0 frequently requires understanding and searching through database metadata, dialect documentation, and even project-level codebases. This challenge calls for models to interact with complex SQL workflow environments, process extremely long contexts, perform intricate reasoning, and generate multiple SQL queries with diverse operations, often exceeding 100 lines, which goes far beyond traditional text-to-SQL challenges. Our evaluations indicate that based on o1-preview, our code agent framework successfully solves only 17.0% of the tasks, compared with 91.2% on Spider 1.0 and 73.0% on BIRD. Our results on Spider 2.0 show that while language models have demonstrated remarkable performance in code generation -- especially in prior text-to-SQL benchmarks -- they require significant improvement in order to achieve adequate performance for real-world enterprise usage. Progress on Spider 2.0 represents crucial steps towards developing intelligent, autonomous, code agents for real-world enterprise settings. Our code, baseline models, and data are available at https://spider2-sql.github.io.

Mathematical word problem-solving has long been recognized as a complex task for small language models (SLMs). A recent study hypothesized that the smallest model size, needed to achieve over 80% accuracy on the GSM8K benchmark, is 34 billion parameters. To reach this level of performance with smaller models, researcher often train SLMs to generate Python code or use tools to help avoid calculation errors. Additionally, they employ ensembling, where outputs of up to 100 model runs are combined to arrive at a more accurate result. Result selection is done using consensus, majority vote or a separate a verifier model used in conjunction with the SLM. Ensembling provides a substantial boost in accuracy but at a significant cost increase with multiple calls to the model (e.g., Phi-GSM uses top-48 to boost the performance from 68.2 to 81.5). In this work, we present Orca-Math, a 7-billion-parameter SLM based on the Mistral-7B, which achieves 86.81% on GSM8k without the need for multiple model calls or the use of verifiers, code execution or any other external tools. Our approach has the following key elements: (1) A high quality synthetic dataset of 200K math problems created using a multi-agent setup where agents collaborate to create the data, (2) An iterative learning techniques that enables the SLM to practice solving problems, receive feedback on its solutions and learn from preference pairs incorporating the SLM solutions and the feedback. When trained with Supervised Fine-Tuning alone, Orca-Math achieves 81.50% on GSM8k pass@1 metric. With iterative preference learning, Orca-Math achieves 86.81% pass@1. Orca-Math surpasses the performance of significantly larger models such as LLAMA-2-70B, WizardMath-70B, Gemini-Pro, ChatGPT-3.5. It also significantly outperforms other smaller models while using much smaller data (hundreds of thousands vs. millions of problems).

In modern large-scale deep learning, a prevalent and effective workflow for solving low-data problems is adapting powerful pre-trained foundation models (FMs) to new tasks via parameter-efficient fine-tuning (PEFT). However, while empirically effective, the resulting solutions lack generalisation guarantees to certify their accuracy - which may be required for ethical or legal reasons prior to deployment in high-importance applications. In this paper we develop a novel transfer learning approach that is designed to facilitate non-vacuous learning theoretic generalisation guarantees for downstream tasks, even in the low-shot regime. Specifically, we first use upstream tasks to train a distribution over PEFT parameters. We then learn the downstream task by a sample-and-evaluate procedure -- sampling plausible PEFTs from the trained diffusion model and selecting the one with the highest likelihood on the downstream data. Crucially, this confines our model hypothesis to a finite set of PEFT samples. In contrast to learning in the typical continuous hypothesis spaces of neural network weights, this facilitates tighter risk certificates. We instantiate our bound and show non-trivial generalization guarantees compared to existing learning approaches which lead to vacuous bounds in the low-shot regime.

We provide here a dataset for tasks related to natural language understanding and natural language inference. The dataset contains logical puzzles in natural language from three domains: comparing puzzles, knighs and knaves, and zebra puzzles. Each puzzle is associated with the entire set of atomic questions that can be generated based on the relations and individuals occurring in the text. For each question we provide the correct answer: entailment, contradiction or ambiguity. The answer's correctness is verified against theorem provers. Good puzzles have two properties: (i) each piece of information is necessary and (ii) no unnecessary information is provided. These properties make puzzles interesting candidates for machine comprehension tasks.

Increasing interest in reasoning models has led math to become a prominent testing ground for algorithmic and methodological improvements. However, existing open math datasets either contain a small collection of high-quality, human-written problems or a large corpus of machine-generated problems of uncertain quality, forcing researchers to choose between quality and quantity. In this work, we present Big-Math, a dataset of over 250,000 high-quality math questions with verifiable answers, purposefully made for reinforcement learning (RL). To create Big-Math, we rigorously filter, clean, and curate openly available datasets, extracting questions that satisfy our three desiderata: (1) problems with uniquely verifiable solutions, (2) problems that are open-ended, (3) and problems with a closed-form solution. To ensure the quality of Big-Math, we manually verify each step in our filtering process. Based on the findings from our filtering process, we introduce 47,000 new questions with verified answers, Big-Math-Reformulated: closed-ended questions (i.e. multiple choice questions) that have been reformulated as open-ended questions through a systematic reformulation algorithm. Compared to the most commonly used existing open-source datasets for math reasoning, GSM8k and MATH, Big-Math is an order of magnitude larger, while our rigorous filtering ensures that we maintain the questions most suitable for RL. We also provide a rigorous analysis of the dataset, finding that Big-Math contains a high degree of diversity across problem domains, and incorporates a wide range of problem difficulties, enabling a wide range of downstream uses for models of varying capabilities and training requirements. By bridging the gap between data quality and quantity, Big-Math establish a robust foundation for advancing reasoning in LLMs.

We present SURE-Score: an approach for learning score-based generative models using training samples corrupted by additive Gaussian noise. When a large training set of clean samples is available, solving inverse problems via score-based (diffusion) generative models trained on the underlying fully-sampled data distribution has recently been shown to outperform end-to-end supervised deep learning. In practice, such a large collection of training data may be prohibitively expensive to acquire in the first place. In this work, we present an approach for approximately learning a score-based generative model of the clean distribution, from noisy training data. We formulate and justify a novel loss function that leverages Stein's unbiased risk estimate to jointly denoise the data and learn the score function via denoising score matching, while using only the noisy samples. We demonstrate the generality of SURE-Score by learning priors and applying posterior sampling to ill-posed inverse problems in two practical applications from different domains: compressive wireless multiple-input multiple-output channel estimation and accelerated 2D multi-coil magnetic resonance imaging reconstruction, where we demonstrate competitive reconstruction performance when learning at signal-to-noise ratio values of 0 and 10 dB, respectively.

We provide a framework for solving inverse problems with diffusion models learned from linearly corrupted data. Our method, Ambient Diffusion Posterior Sampling (A-DPS), leverages a generative model pre-trained on one type of corruption (e.g. image inpainting) to perform posterior sampling conditioned on measurements from a potentially different forward process (e.g. image blurring). We test the efficacy of our approach on standard natural image datasets (CelebA, FFHQ, and AFHQ) and we show that A-DPS can sometimes outperform models trained on clean data for several image restoration tasks in both speed and performance. We further extend the Ambient Diffusion framework to train MRI models with access only to Fourier subsampled multi-coil MRI measurements at various acceleration factors (R=2, 4, 6, 8). We again observe that models trained on highly subsampled data are better priors for solving inverse problems in the high acceleration regime than models trained on fully sampled data. We open-source our code and the trained Ambient Diffusion MRI models: https://github.com/utcsilab/ambient-diffusion-mri .

Math reasoning is becoming an ever increasing area of focus as we scale large language models. However, even the previously-toughest evals like MATH are now close to saturated by frontier models (90.0% for o1-mini and 86.5% for Gemini 1.5 Pro). We introduce HARP, Human Annotated Reasoning Problems (for Math), consisting of 5,409 problems from the US national math competitions (A(J)HSME, AMC, AIME, USA(J)MO). Of these, 4,780 have answers that are automatically check-able (with libraries such as SymPy). These problems range six difficulty levels, with frontier models performing relatively poorly on the hardest bracket of 197 problems (average accuracy 41.1% for o1-mini, and 9.6% for Gemini 1.5 Pro). Our dataset also features multiple choices (for 4,110 problems) and an average of two human-written, ground-truth solutions per problem, offering new avenues of research that we explore briefly. We report evaluations for many frontier models and share some interesting analyses, such as demonstrating that frontier models across families intrinsically scale their inference-time compute for more difficult problems. Finally, we open source all code used for dataset construction (including scraping) and all code for evaluation (including answer checking) to enable future research at: https://github.com/aadityasingh/HARP.

In this paper we look at the ability of recent large language models (LLMs) at solving mathematical problems in combinatorics. We compare models LLaMA-2, LLaMA-3.1, GPT-4, and Mixtral against each other and against human pupils and undergraduates with prior experience in mathematical olympiads. To facilitate these comparisons we introduce the Combi-Puzzles dataset, which contains 125 problem variants based on 25 combinatorial reasoning problems. Each problem is presented in one of five distinct forms, created by systematically manipulating the problem statements through adversarial additions, numeric parameter changes, and linguistic obfuscation. Our variations preserve the mathematical core and are designed to measure the generalisability of LLM problem-solving abilities, while also increasing confidence that problems are submitted to LLMs in forms that have not been seen as training instances. We found that a model based on GPT-4 outperformed all other models in producing correct responses, and performed significantly better in the mathematical variation of the problems than humans. We also found that modifications to problem statements significantly impact the LLM's performance, while human performance remains unaffected.

Mathematical reasoning---a core ability within human intelligence---presents some unique challenges as a domain: we do not come to understand and solve mathematical problems primarily on the back of experience and evidence, but on the basis of inferring, learning, and exploiting laws, axioms, and symbol manipulation rules. In this paper, we present a new challenge for the evaluation (and eventually the design) of neural architectures and similar system, developing a task suite of mathematics problems involving sequential questions and answers in a free-form textual input/output format. The structured nature of the mathematics domain, covering arithmetic, algebra, probability and calculus, enables the construction of training and test splits designed to clearly illuminate the capabilities and failure-modes of different architectures, as well as evaluate their ability to compose and relate knowledge and learned processes. Having described the data generation process and its potential future expansions, we conduct a comprehensive analysis of models from two broad classes of the most powerful sequence-to-sequence architectures and find notable differences in their ability to resolve mathematical problems and generalize their knowledge.

This study focuses on improving the performance of lightweight Large Language Models (LLMs) in mathematical reasoning tasks. We introduce a novel method for measuring mathematical logic similarity and design an automatic screening mechanism to construct a set of reference problems that integrate both semantic and logical similarity. By employing carefully crafted positive and negative example prompts, we guide the model towards adopting sound reasoning logic. To the best of our knowledge, this is the first attempt to utilize retrieval-enhanced generation for mathematical problem-solving. Experimental results demonstrate that our method achieves a 15.8% improvement over the Chain of Thought approach on the SVAMP dataset and a 21.5 % improvement on the GSM8K dataset. Further application of this method to a large-scale model with 175 billion parameters yields performance comparable to the best results on both aforementioned datasets. Finally, we conduct an analysis of errors during the reasoning process, providing valuable insights and directions for future research on reasoning tasks using large language models.

Advances in Large Language Models (LLMs) have sparked interest in their ability to solve Olympiad-level math problems. However, the training and evaluation of these models are constrained by the limited size and quality of available datasets, as creating large-scale data for such advanced problems requires extensive effort from human experts. In addition, current benchmarks are prone to contamination, leading to unreliable evaluations. In this paper, we present an automated pipeline that leverages the rich resources of the Art of Problem Solving (AoPS) forum, which predominantly features Olympiad-level problems and community-driven solutions. Using open-source LLMs, we develop a method to extract question-answer pairs from the forum, resulting in AoPS-Instruct, a dataset of more than 600,000 high-quality QA pairs. Our experiments demonstrate that fine-tuning LLMs on AoPS-Instruct improves their reasoning abilities across various benchmarks. Moreover, we build an automatic pipeline that introduces LiveAoPSBench, an evolving evaluation set with timestamps, derived from the latest forum data, providing a contamination-resistant benchmark for assessing LLM performance. Notably, we observe a significant decline in LLM performance over time, suggesting their success on older examples may stem from pre-training exposure rather than true reasoning ability. Our work presents a scalable approach to creating and maintaining large-scale, high-quality datasets for advanced math reasoning, offering valuable insights into the capabilities and limitations of LLMs in this domain. Our benchmark and code is available at https://github.com/DSL-Lab/aops

The recent LLMs like GPT-4 and PaLM-2 have made tremendous progress in solving fundamental math problems like GSM8K by achieving over 90\% accuracy. However, their capabilities to solve more challenging math problems which require domain-specific knowledge (i.e. theorem) have yet to be investigated. In this paper, we introduce TheoremQA, the first theorem-driven question-answering dataset designed to evaluate AI models' capabilities to apply theorems to solve challenging science problems. \dataset is curated by domain experts containing 800 high-quality questions covering 350 theoremse.g. Taylor's theorem, Lagrange's theorem, Huffman coding, Quantum Theorem, Elasticity Theorem, etc from Math, Physics, EE\&CS, and Finance. We evaluate a wide spectrum of 16 large language and code models with different prompting strategies like Chain-of-Thoughts and Program-of-Thoughts. We found that GPT-4's capabilities to solve these problems are unparalleled, achieving an accuracy of 51\% with Program-of-Thoughts Prompting. All the existing open-sourced models are below 15\%, barely surpassing the random-guess baseline. Given the diversity and broad coverage of \dataset, we believe it can be used as a better benchmark to evaluate LLMs' capabilities to solve challenging science problems. The data and code are released in https://github.com/wenhuchen/TheoremQA.

This paper presents our winning submission to the AI Mathematical Olympiad - Progress Prize 2 (AIMO-2) competition. Our recipe for building state-of-the-art mathematical reasoning models relies on three key pillars. First, we create a large-scale dataset comprising 540K unique high-quality math problems, including olympiad-level problems, and their 3.2M long-reasoning solutions. Second, we develop a novel method to integrate code execution with long reasoning models through iterative training, generation, and quality filtering, resulting in 1.7M high-quality Tool-Integrated Reasoning solutions. Third, we create a pipeline to train models to select the most promising solution from many candidates. We show that such generative solution selection (GenSelect) can significantly improve upon majority voting baseline. Combining these ideas, we train a series of models that achieve state-of-the-art results on mathematical reasoning benchmarks. To facilitate further research, we release our code, models, and the complete OpenMathReasoning dataset under a commercially permissive license.

We present ASDiv (Academia Sinica Diverse MWP Dataset), a diverse (in terms of both language patterns and problem types) English math word problem (MWP) corpus for evaluating the capability of various MWP solvers. Existing MWP corpora for studying AI progress remain limited either in language usage patterns or in problem types. We thus present a new English MWP corpus with 2,305 MWPs that cover more text patterns and most problem types taught in elementary school. Each MWP is annotated with its problem type and grade level (for indicating the level of difficulty). Furthermore, we propose a metric to measure the lexicon usage diversity of a given MWP corpus, and demonstrate that ASDiv is more diverse than existing corpora. Experiments show that our proposed corpus reflects the true capability of MWP solvers more faithfully.

We introduce a high-quality dataset that contains 3,397 samples comprising (i) multiple choice questions, (ii) answers (including distractors), and (iii) their source documents, from the educational domain. Each question is phrased in two forms, normal and close. Correct answers are linked to source documents with sentence-level annotations. Thus, our versatile dataset can be used for both question and distractor generation, as well as to explore new challenges such as question format conversion. Furthermore, 903 questions are accompanied by their cognitive complexity level as per Bloom's taxonomy. All questions have been generated by educational experts rather than crowd workers to ensure they are maintaining educational and learning standards. Our analysis and experiments suggest distinguishable differences between our dataset and commonly used ones for question generation for educational purposes. We believe this new dataset can serve as a valuable resource for research and evaluation in the educational domain. The dataset and baselines will be released to support further research in question generation.

We present Archer, a challenging bilingual text-to-SQL dataset specific to complex reasoning, including arithmetic, commonsense and hypothetical reasoning. It contains 1,042 English questions and 1,042 Chinese questions, along with 521 unique SQL queries, covering 20 English databases across 20 domains. Notably, this dataset demonstrates a significantly higher level of complexity compared to existing publicly available datasets. Our evaluation shows that Archer challenges the capabilities of current state-of-the-art models, with a high-ranked model on the Spider leaderboard achieving only 6.73% execution accuracy on Archer test set. Thus, Archer presents a significant challenge for future research in this field.

Flow-based latent generative models such as Stable Diffusion 3 are able to generate images with remarkable quality, even enabling photorealistic text-to-image generation. Their impressive performance suggests that these models should also constitute powerful priors for inverse imaging problems, but that approach has not yet led to comparable fidelity. There are several key obstacles: (i) the encoding into a lower-dimensional latent space makes the underlying (forward) mapping non-linear; (ii) the data likelihood term is usually intractable; and (iii) learned generative models struggle to recover rare, atypical data modes during inference. We present FLAIR, a novel training free variational framework that leverages flow-based generative models as a prior for inverse problems. To that end, we introduce a variational objective for flow matching that is agnostic to the type of degradation, and combine it with deterministic trajectory adjustments to recover atypical modes. To enforce exact consistency with the observed data, we decouple the optimization of the data fidelity and regularization terms. Moreover, we introduce a time-dependent calibration scheme in which the strength of the regularization is modulated according to off-line accuracy estimates. Results on standard imaging benchmarks demonstrate that FLAIR consistently outperforms existing diffusion- and flow-based methods in terms of reconstruction quality and sample diversity.

Large language models (LLMs) have demonstrated significant capabilities in mathematical reasoning, particularly with text-based mathematical problems. However, current multi-modal large language models (MLLMs), especially those specialized in mathematics, tend to focus predominantly on solving geometric problems but ignore the diversity of visual information available in other areas of mathematics. Moreover, the geometric information for these specialized mathematical MLLMs is derived from several public datasets, which are typically limited in diversity and complexity. To address these limitations, we aim to construct a fine-tuning dataset named MathVL, and develop a series of specialized mathematical MLLMs termed MathGLM-Vision by conducting Supervised Fine-Tuning (SFT) on MathVL with various parameter-scale backbones. To extensively evaluate the effectiveness of MathGLM-Vision, we conduct experiments on several public benchmarks and our curated MathVL-test consisting of 2,000 problems. Experimental results demonstrate that MathGLM-Vision achieves significant improvements compared with some existing models, including backbone models and open-source mathematical MLLMs. These findings indicate the importance of diversity dataset in enhancing the mathematical reasoning abilities of MLLMs.

Large Language Models (LLMs) have exhibited exceptional performance across a broad range of tasks and domains. However, they still encounter difficulties in solving mathematical problems due to the rigorous and logical nature of mathematics. Previous studies have employed techniques such as supervised fine-tuning (SFT), prompt engineering, and search-based methods to improve the mathematical problem-solving abilities of LLMs. Despite these efforts, their performance remains suboptimal and demands substantial computational resources. To address this issue, we propose a novel approach, BEATS, to enhance mathematical problem-solving abilities. Our method leverages newly designed prompts that guide the model to iteratively rewrite, advance by one step, and generate answers based on previous steps. Additionally, we introduce a new back-verification technique that uses LLMs to validate the correctness of the generated answers. Furthermore, we employ a pruning tree search to optimize search time while achieving strong performance. Notably, our method improves Qwen2-7b-Instruct's score from 36.94 to 61.52, outperforming GPT4's 42.5 on the MATH benchmark.

Diffusion models have emerged as a key pillar of foundation models in visual domains. One of their critical applications is to universally solve different downstream inverse tasks via a single diffusion prior without re-training for each task. Most inverse tasks can be formulated as inferring a posterior distribution over data (e.g., a full image) given a measurement (e.g., a masked image). This is however challenging in diffusion models since the nonlinear and iterative nature of the diffusion process renders the posterior intractable. To cope with this challenge, we propose a variational approach that by design seeks to approximate the true posterior distribution. We show that our approach naturally leads to regularization by denoising diffusion process (RED-Diff) where denoisers at different timesteps concurrently impose different structural constraints over the image. To gauge the contribution of denoisers from different timesteps, we propose a weighting mechanism based on signal-to-noise-ratio (SNR). Our approach provides a new variational perspective for solving inverse problems with diffusion models, allowing us to formulate sampling as stochastic optimization, where one can simply apply off-the-shelf solvers with lightweight iterates. Our experiments for image restoration tasks such as inpainting and superresolution demonstrate the strengths of our method compared with state-of-the-art sampling-based diffusion models.

Reconstructing medical images from partial measurements is an important inverse problem in Computed Tomography (CT) and Magnetic Resonance Imaging (MRI). Existing solutions based on machine learning typically train a model to directly map measurements to medical images, leveraging a training dataset of paired images and measurements. These measurements are typically synthesized from images using a fixed physical model of the measurement process, which hinders the generalization capability of models to unknown measurement processes. To address this issue, we propose a fully unsupervised technique for inverse problem solving, leveraging the recently introduced score-based generative models. Specifically, we first train a score-based generative model on medical images to capture their prior distribution. Given measurements and a physical model of the measurement process at test time, we introduce a sampling method to reconstruct an image consistent with both the prior and the observed measurements. Our method does not assume a fixed measurement process during training, and can thus be flexibly adapted to different measurement processes at test time. Empirically, we observe comparable or better performance to supervised learning techniques in several medical imaging tasks in CT and MRI, while demonstrating significantly better generalization to unknown measurement processes.

Data visualizations are powerful tools for communicating patterns in quantitative data. Yet understanding any data visualization is no small feat -- succeeding requires jointly making sense of visual, numerical, and linguistic inputs arranged in a conventionalized format one has previously learned to parse. Recently developed vision-language models are, in principle, promising candidates for developing computational models of these cognitive operations. However, it is currently unclear to what degree these models emulate human behavior on tasks that involve reasoning about data visualizations. This gap reflects limitations in prior work that has evaluated data visualization understanding in artificial systems using measures that differ from those typically used to assess these abilities in humans. Here we evaluated eight vision-language models on six data visualization literacy assessments designed for humans and compared model responses to those of human participants. We found that these models performed worse than human participants on average, and this performance gap persisted even when using relatively lenient criteria to assess model performance. Moreover, while relative performance across items was somewhat correlated between models and humans, all models produced patterns of errors that were reliably distinct from those produced by human participants. Taken together, these findings suggest significant opportunities for further development of artificial systems that might serve as useful models of how humans reason about data visualizations. All code and data needed to reproduce these results are available at: https://osf.io/e25mu/?view_only=399daff5a14d4b16b09473cf19043f18.

While large language models (LLMs) have demonstrated impressive performance in question-answering tasks, their performance is limited when the questions require knowledge that is not included in the model's training data and can only be acquired through direct observation or interaction with the real world. Existing methods decompose reasoning tasks through the use of modules invoked sequentially, limiting their ability to answer deep reasoning tasks. We introduce a method, Recursion based extensible LLM (REBEL), which handles open-world, deep reasoning tasks by employing automated reasoning techniques like dynamic planning and forward-chaining strategies. REBEL allows LLMs to reason via recursive problem decomposition and utilization of external tools. The tools that REBEL uses are specified only by natural language description. We further demonstrate REBEL capabilities on a set of problems that require a deeply nested use of external tools in a compositional and conversational setting.

The way in which data are shared can affect their utility and reusability. Here, we demonstrate how data that we had previously shared in bulk can be mobilized further through a knowledge graph that allows for much more granular exploration and interrogation. The original dataset is about the computational reproducibility of GitHub-hosted Jupyter notebooks associated with biomedical publications. It contains rich metadata about the publications, associated GitHub repositories and Jupyter notebooks, and the notebooks' reproducibility. We took this dataset, converted it into semantic triples and loaded these into a triple store to create a knowledge graph, FAIR Jupyter, that we made accessible via a web service. This enables granular data exploration and analysis through queries that can be tailored to specific use cases. Such queries may provide details about any of the variables from the original dataset, highlight relationships between them or combine some of the graph's content with materials from corresponding external resources. We provide a collection of example queries addressing a range of use cases in research and education. We also outline how sets of such queries can be used to profile specific content types, either individually or by class. We conclude by discussing how such a semantically enhanced sharing of complex datasets can both enhance their FAIRness, i.e., their findability, accessibility, interoperability, and reusability, and help identify and communicate best practices, particularly with regards to data quality, standardization, automation and reproducibility.

Quantum computing holds great potential for advancing the limitations of machine learning algorithms to handle higher dimensions of data and reduce overall training parameters in deep learning (DL) models. This study uses a trainable variational quantum circuit (VQC) on a gate-based quantum computing model to investigate the potential for quantum benefit in a model-free reinforcement learning problem. Through a comprehensive investigation and evaluation of the current model and capabilities of quantum computers, we designed and trained a novel hybrid quantum neural network based on the latest Qiskit and PyTorch framework. We compared its performance with a full-classical CNN with and without an incorporated VQC. Our research provides insights into the potential of deep quantum learning to solve a maze problem and, potentially, other reinforcement learning problems. We conclude that reinforcement learning problems can be practical with reasonable training epochs. Moreover, a comparative study of full-classical and hybrid quantum neural networks is discussed to understand these two approaches' performance, advantages, and disadvantages to deep-Q learning problems, especially on larger-scale maze problems larger than 4x4.

Large Language Models have achieved remarkable success in natural language processing tasks, with Reinforcement Learning playing a key role in adapting them to specific applications. However, obtaining ground truth answers for training LLMs in mathematical problem-solving is often challenging, costly, and sometimes unfeasible. This research delves into the utilization of format and length as surrogate signals to train LLMs for mathematical problem-solving, bypassing the need for traditional ground truth answers.Our study shows that a reward function centered on format correctness alone can yield performance improvements comparable to the standard GRPO algorithm in early phases. Recognizing the limitations of format-only rewards in the later phases, we incorporate length-based rewards. The resulting GRPO approach, leveraging format-length surrogate signals, not only matches but surpasses the performance of the standard GRPO algorithm relying on ground truth answers in certain scenarios, achieving 40.0\% accuracy on AIME2024 with a 7B base model. Through systematic exploration and experimentation, this research not only offers a practical solution for training LLMs to solve mathematical problems and reducing the dependence on extensive ground truth data collection, but also reveals the essence of why our label-free approach succeeds: base model is like an excellent student who has already mastered mathematical and logical reasoning skills, but performs poorly on the test paper, it simply needs to develop good answering habits to achieve outstanding results in exams , in other words, to unlock the capabilities it already possesses.

With the rapid advancement of mathematical reasoning capabilities in Large Language Models (LLMs), AI systems are increasingly being adopted in educational settings to support students' comprehension of problem-solving processes. However, a critical component remains underexplored in current LLM-generated explanations: visual explanation. In real-world instructional contexts, human tutors routinely employ visual aids - such as diagrams, markings, and highlights - to enhance conceptual clarity. To bridge this gap, we introduce a novel task of visual solution explanation, which requires generating explanations that incorporate newly introduced visual elements essential for understanding (e.g., auxiliary lines, annotations, or geometric constructions). To evaluate model performance on this task, we propose MathExplain, a multimodal benchmark consisting of 997 math problems annotated with visual keypoints and corresponding explanatory text that references those elements. Our empirical results show that while some closed-source models demonstrate promising capabilities on visual solution-explaining, current open-source general-purpose models perform inconsistently, particularly in identifying relevant visual components and producing coherent keypoint-based explanations. We expect that visual solution-explaining and the MathExplain dataset will catalyze further research on multimodal LLMs in education and advance their deployment as effective, explanation-oriented AI tutors. Code and data will be released publicly.

Machine learning is now used in many applications thanks to its ability to predict, generate, or discover patterns from large quantities of data. However, the process of collecting and transforming data for practical use is intricate. Even in today's digital era, where substantial data is generated daily, it is uncommon for it to be readily usable; most often, it necessitates meticulous manual data preparation. The haste in developing new models can frequently result in various shortcomings, potentially posing risks when deployed in real-world scenarios (eg social discrimination, critical failures), leading to the failure or substantial escalation of costs in AI-based projects. This chapter provides a comprehensive overview of established methodological tools, enriched by our practical experience, in the development of datasets for machine learning. Initially, we develop the tasks involved in dataset development and offer insights into their effective management (including requirements, design, implementation, evaluation, distribution, and maintenance). Then, we provide more details about the implementation process which includes data collection, transformation, and quality evaluation. Finally, we address practical considerations regarding dataset distribution and maintenance.

The availability of high-quality data is one of the most important factors in improving the reasoning capability of LLMs. Existing works have demonstrated the effectiveness of creating more instruction data from seed questions or knowledge bases. Recent research indicates that continually scaling up data synthesis from strong models (e.g., GPT-4) can further elicit reasoning performance. Though promising, the open-sourced community still lacks high-quality data at scale and scalable data synthesis methods with affordable costs. To address this, we introduce ScaleQuest, a scalable and novel data synthesis method that utilizes "small-size" (e.g., 7B) open-source models to generate questions from scratch without the need for seed data with complex augmentation constraints. With the efficient ScaleQuest, we automatically constructed a mathematical reasoning dataset consisting of 1 million problem-solution pairs, which are more effective than existing open-sourced datasets. It can universally increase the performance of mainstream open-source models (i.e., Mistral, Llama3, DeepSeekMath, and Qwen2-Math) by achieving 29.2% to 46.4% gains on MATH. Notably, simply fine-tuning the Qwen2-Math-7B-Base model with our dataset can even surpass Qwen2-Math-7B-Instruct, a strong and well-aligned model on closed-source data, and proprietary models such as GPT-4-Turbo and Claude-3.5 Sonnet.

Modern machine learning relies on datasets to develop and validate research ideas. Given the growth of publicly available data, finding the right dataset to use is increasingly difficult. Any research question imposes explicit and implicit constraints on how well a given dataset will enable researchers to answer this question, such as dataset size, modality, and domain. We operationalize the task of recommending datasets given a short natural language description of a research idea, to help people find relevant datasets for their needs. Dataset recommendation poses unique challenges as an information retrieval problem; datasets are hard to directly index for search and there are no corpora readily available for this task. To facilitate this task, we build the DataFinder Dataset which consists of a larger automatically-constructed training set (17.5K queries) and a smaller expert-annotated evaluation set (392 queries). Using this data, we compare various information retrieval algorithms on our test set and present a superior bi-encoder retriever for text-based dataset recommendation. This system, trained on the DataFinder Dataset, finds more relevant search results than existing third-party dataset search engines. To encourage progress on dataset recommendation, we release our dataset and models to the public.

We introduce a benchmark to evaluate the capability of AI to solve problems in theoretical physics, focusing on high-energy theory and cosmology. The first iteration of our benchmark consists of 57 problems of varying difficulty, from undergraduate to research level. These problems are novel in the sense that they do not come from public problem collections. We evaluate our data set on various open and closed language models, including o3-mini, o1, DeepSeek-R1, GPT-4o and versions of Llama and Qwen. While we find impressive progress in model performance with the most recent models, our research-level difficulty problems are mostly unsolved. We address challenges of auto-verifiability and grading, and discuss common failure modes. While currently state-of-the art models are still of limited use for researchers, our results show that AI assisted theoretical physics research may become possible in the near future. We discuss the main obstacles towards this goal and possible strategies to overcome them. The public problems and solutions, results for various models, and updates to the data set and score distribution, are available on the website of the dataset tpbench.org.

Crossword puzzles are popular linguistic games often used as tools to engage students in learning. Educational crosswords are characterized by less cryptic and more factual clues that distinguish them from traditional crossword puzzles. Despite there exist several publicly available clue-answer pair databases for traditional crosswords, educational clue-answer pairs datasets are missing. In this article, we propose a methodology to build educational clue generation datasets that can be used to instruct Large Language Models (LLMs). By gathering from Wikipedia pages informative content associated with relevant keywords, we use Large Language Models to automatically generate pedagogical clues related to the given input keyword and its context. With such an approach, we created clue-instruct, a dataset containing 44,075 unique examples with text-keyword pairs associated with three distinct crossword clues. We used clue-instruct to instruct different LLMs to generate educational clues from a given input content and keyword. Both human and automatic evaluations confirmed the quality of the generated clues, thus validating the effectiveness of our approach.

In recent years, Large language models (LLMs) have garnered significant attention due to their superior performance in complex reasoning tasks. However, recent studies may diminish their reasoning capabilities markedly when problem descriptions contain irrelevant information, even with the use of advanced prompting techniques. To further investigate this issue, a dataset of primary school mathematics problems containing irrelevant information, named GSMIR, was constructed. Testing prominent LLMs and prompting techniques on this dataset revealed that while LLMs can identify irrelevant information, they do not effectively mitigate the interference it causes once identified. A novel automatic construction method, ATF, which enhances the ability of LLMs to identify and self-mitigate the influence of irrelevant information, is proposed to address this shortcoming. This method operates in two steps: first, analysis of irrelevant information, followed by its filtering. The ATF method, as demonstrated by experimental results, significantly improves the reasoning performance of LLMs and prompting techniques, even in the presence of irrelevant information on the GSMIR dataset.

Artificial Intelligence (AI) is making a profound impact in almost every domain. A vital enabler of its great success is the availability of abundant and high-quality data for building machine learning models. Recently, the role of data in AI has been significantly magnified, giving rise to the emerging concept of data-centric AI. The attention of researchers and practitioners has gradually shifted from advancing model design to enhancing the quality and quantity of the data. In this survey, we discuss the necessity of data-centric AI, followed by a holistic view of three general data-centric goals (training data development, inference data development, and data maintenance) and the representative methods. We also organize the existing literature from automation and collaboration perspectives, discuss the challenges, and tabulate the benchmarks for various tasks. We believe this is the first comprehensive survey that provides a global view of a spectrum of tasks across various stages of the data lifecycle. We hope it can help the readers efficiently grasp a broad picture of this field, and equip them with the techniques and further research ideas to systematically engineer data for building AI systems. A companion list of data-centric AI resources will be regularly updated on https://github.com/daochenzha/data-centric-AI

Graphs are widely used for modeling relational data in real-world scenarios, such as social networks and urban computing. Existing LLM-based graph analysis approaches either integrate graph neural networks (GNNs) for specific machine learning tasks, limiting their transferability, or rely solely on LLMs' internal reasoning ability, resulting in suboptimal performance. To address these limitations, we take advantage of recent advances in LLM-based agents, which have shown capabilities of utilizing external knowledge or tools for problem solving. By simulating human problem-solving strategies such as analogy and collaboration, we propose a multi-agent system based on LLMs named GraphTeam, for graph analysis. GraphTeam consists of five LLM-based agents from three modules, and the agents with different specialities can collaborate with each other to address complex problems. Specifically, (1) input-output normalization module: the question agent extracts and refines four key arguments from the original question, facilitating the problem understanding, and the answer agent organizes the results to meet the output requirement; (2) external knowledge retrieval module: we first build a knowledge base consisting of relevant documentation and experience information, and then the search agent retrieves the most relevant entries for each question. (3) problem-solving module: given the retrieved information from search agent, the coding agent uses established algorithms via programming to generate solutions, and in case the coding agent does not work, the reasoning agent will directly compute the results without programming. Extensive experiments on six graph analysis benchmarks demonstrate that GraphTeam achieves state-of-the-art performance with an average 25.85% improvement over the best baseline in terms of accuracy. The code and data are available at https://github.com/BUPT-GAMMA/GraphTeam.

While automatic dialogue tutors hold great potential in making education personalized and more accessible, research on such systems has been hampered by a lack of sufficiently large and high-quality datasets. Collecting such datasets remains challenging, as recording tutoring sessions raises privacy concerns and crowdsourcing leads to insufficient data quality. To address this, we propose a framework to generate such dialogues by pairing human teachers with a Large Language Model (LLM) prompted to represent common student errors. We describe how we use this framework to collect MathDial, a dataset of 3k one-to-one teacher-student tutoring dialogues grounded in multi-step math reasoning problems. While models like GPT-3 are good problem solvers, they fail at tutoring because they generate factually incorrect feedback or are prone to revealing solutions to students too early. To overcome this, we let teachers provide learning opportunities to students by guiding them using various scaffolding questions according to a taxonomy of teacher moves. We demonstrate MathDial and its extensive annotations can be used to finetune models to be more effective tutors (and not just solvers). We confirm this by automatic and human evaluation, notably in an interactive setting that measures the trade-off between student solving success and telling solutions. The dataset is released publicly.

Teachers and students are increasingly relying on online learning resources to supplement the ones provided in school. This increase in the breadth and depth of available resources is a great thing for students, but only provided they are able to find answers to their queries. Question-answering and information retrieval systems have benefited from public datasets to train and evaluate their algorithms, but most of these datasets have been in English text written by and for adults. We introduce a new public French question-answering dataset collected from Alloprof, a Quebec-based primary and high-school help website, containing 29 349 questions and their explanations in a variety of school subjects from 10 368 students, with more than half of the explanations containing links to other questions or some of the 2 596 reference pages on the website. We also present a case study of this dataset in an information retrieval task. This dataset was collected on the Alloprof public forum, with all questions verified for their appropriateness and the explanations verified both for their appropriateness and their relevance to the question. To predict relevant documents, architectures using pre-trained BERT models were fine-tuned and evaluated. This dataset will allow researchers to develop question-answering, information retrieval and other algorithms specifically for the French speaking education context. Furthermore, the range of language proficiency, images, mathematical symbols and spelling mistakes will necessitate algorithms based on a multimodal comprehension. The case study we present as a baseline shows an approach that relies on recent techniques provides an acceptable performance level, but more work is necessary before it can reliably be used and trusted in a production setting.

Recent breakthroughs in large language modeling have facilitated rigorous exploration of their application in diverse tasks related to tabular data modeling, such as prediction, tabular data synthesis, question answering, and table understanding. Each task presents unique challenges and opportunities. However, there is currently a lack of comprehensive review that summarizes and compares the key techniques, metrics, datasets, models, and optimization approaches in this research domain. This survey aims to address this gap by consolidating recent progress in these areas, offering a thorough survey and taxonomy of the datasets, metrics, and methodologies utilized. It identifies strengths, limitations, unexplored territories, and gaps in the existing literature, while providing some insights for future research directions in this vital and rapidly evolving field. It also provides relevant code and datasets references. Through this comprehensive review, we hope to provide interested readers with pertinent references and insightful perspectives, empowering them with the necessary tools and knowledge to effectively navigate and address the prevailing challenges in the field.

We present the Chinese Elementary School Math Word Problems (CMATH) dataset, comprising 1.7k elementary school-level math word problems with detailed annotations, source from actual Chinese workbooks and exams. This dataset aims to provide a benchmark tool for assessing the following question: to what grade level of elementary school math do the abilities of popular large language models (LLMs) correspond? We evaluate a variety of popular LLMs, including both commercial and open-source options, and discover that only GPT-4 achieves success (accuracy geq 60\%) across all six elementary school grades, while other models falter at different grade levels. Furthermore, we assess the robustness of several top-performing LLMs by augmenting the original problems in the CMATH dataset with distracting information. Our findings reveal that GPT-4 is able to maintains robustness, while other model fail. We anticipate that our study will expose limitations in LLMs' arithmetic and reasoning capabilities, and promote their ongoing development and advancement.

We introduce a large scale MAchine Reading COmprehension dataset, which we name MS MARCO. The dataset comprises of 1,010,916 anonymized questions---sampled from Bing's search query logs---each with a human generated answer and 182,669 completely human rewritten generated answers. In addition, the dataset contains 8,841,823 passages---extracted from 3,563,535 web documents retrieved by Bing---that provide the information necessary for curating the natural language answers. A question in the MS MARCO dataset may have multiple answers or no answers at all. Using this dataset, we propose three different tasks with varying levels of difficulty: (i) predict if a question is answerable given a set of context passages, and extract and synthesize the answer as a human would (ii) generate a well-formed answer (if possible) based on the context passages that can be understood with the question and passage context, and finally (iii) rank a set of retrieved passages given a question. The size of the dataset and the fact that the questions are derived from real user search queries distinguishes MS MARCO from other well-known publicly available datasets for machine reading comprehension and question-answering. We believe that the scale and the real-world nature of this dataset makes it attractive for benchmarking machine reading comprehension and question-answering models.

Mathematical reasoning, a core ability of human intelligence, presents unique challenges for machines in abstract thinking and logical reasoning. Recent large pre-trained language models such as GPT-3 have achieved remarkable progress on mathematical reasoning tasks written in text form, such as math word problems (MWP). However, it is unknown if the models can handle more complex problems that involve math reasoning over heterogeneous information, such as tabular data. To fill the gap, we present Tabular Math Word Problems (TabMWP), a new dataset containing 38,431 open-domain grade-level problems that require mathematical reasoning on both textual and tabular data. Each question in TabMWP is aligned with a tabular context, which is presented as an image, semi-structured text, and a structured table. There are two types of questions: free-text and multi-choice, and each problem is annotated with gold solutions to reveal the multi-step reasoning process. We evaluate different pre-trained models on TabMWP, including the GPT-3 model in a few-shot setting. As earlier studies suggest, since few-shot GPT-3 relies on the selection of in-context examples, its performance is unstable and can degrade to near chance. The unstable issue is more severe when handling complex problems like TabMWP. To mitigate this, we further propose a novel approach, PromptPG, which utilizes policy gradient to learn to select in-context examples from a small amount of training data and then constructs the corresponding prompt for the test example. Experimental results show that our method outperforms the best baseline by 5.31% on the accuracy metric and reduces the prediction variance significantly compared to random selection, which verifies its effectiveness in selecting in-context examples.

A key element in solving real-life data science problems is selecting the types of models to use. Tree ensemble models (such as XGBoost) are usually recommended for classification and regression problems with tabular data. However, several deep learning models for tabular data have recently been proposed, claiming to outperform XGBoost for some use cases. This paper explores whether these deep models should be a recommended option for tabular data by rigorously comparing the new deep models to XGBoost on various datasets. In addition to systematically comparing their performance, we consider the tuning and computation they require. Our study shows that XGBoost outperforms these deep models across the datasets, including the datasets used in the papers that proposed the deep models. We also demonstrate that XGBoost requires much less tuning. On the positive side, we show that an ensemble of deep models and XGBoost performs better on these datasets than XGBoost alone.

Tabular data underpins numerous high-impact applications of machine learning from fraud detection to genomics and healthcare. Classical approaches to solving tabular problems, such as gradient boosting and random forests, are widely used by practitioners. However, recent deep learning methods have achieved a degree of performance competitive with popular techniques. We devise a hybrid deep learning approach to solving tabular data problems. Our method, SAINT, performs attention over both rows and columns, and it includes an enhanced embedding method. We also study a new contrastive self-supervised pre-training method for use when labels are scarce. SAINT consistently improves performance over previous deep learning methods, and it even outperforms gradient boosting methods, including XGBoost, CatBoost, and LightGBM, on average over a variety of benchmark tasks.

This paper introduces a new suite of question answering datasets for Norwegian; NorOpenBookQA, NorCommonSenseQA, NorTruthfulQA, and NRK-Quiz-QA. The data covers a wide range of skills and knowledge domains, including world knowledge, commonsense reasoning, truthfulness, and knowledge about Norway. Covering both of the written standards of Norwegian - Bokm{\aa}l and Nynorsk - our datasets comprise over 10k question-answer pairs, created by native speakers. We detail our dataset creation approach and present the results of evaluating 11 language models (LMs) in zero- and few-shot regimes. Most LMs perform better in Bokm{\aa}l than Nynorsk, struggle most with commonsense reasoning, and are often untruthful in generating answers to questions. All our datasets and annotation materials are publicly available.

We investigate the mathematical capabilities of ChatGPT by testing it on publicly available datasets, as well as hand-crafted ones, and measuring its performance against other models trained on a mathematical corpus, such as Minerva. We also test whether ChatGPT can be a useful assistant to professional mathematicians by emulating various use cases that come up in the daily professional activities of mathematicians (question answering, theorem searching). In contrast to formal mathematics, where large databases of formal proofs are available (e.g., the Lean Mathematical Library), current datasets of natural-language mathematics, used to benchmark language models, only cover elementary mathematics. We address this issue by introducing a new dataset: GHOSTS. It is the first natural-language dataset made and curated by working researchers in mathematics that (1) aims to cover graduate-level mathematics and (2) provides a holistic overview of the mathematical capabilities of language models. We benchmark ChatGPT on GHOSTS and evaluate performance against fine-grained criteria. We make this new dataset publicly available to assist a community-driven comparison of ChatGPT with (future) large language models in terms of advanced mathematical comprehension. We conclude that contrary to many positive reports in the media (a potential case of selection bias), ChatGPT's mathematical abilities are significantly below those of an average mathematics graduate student. Our results show that ChatGPT often understands the question but fails to provide correct solutions. Hence, if your goal is to use it to pass a university exam, you would be better off copying from your average peer!

Large language models (LLMs) have demonstrated impressive performance on reasoning tasks, including mathematical reasoning. However, the current evaluation mostly focuses on carefully constructed benchmarks and neglects the consideration of real-world reasoning problems that present missing or contradictory conditions, known as ill-defined problems. To further study this problem, we develop a largescale benchmark called Problems with Missing and Contradictory conditions ( PMC) containing over 5,000 validated ill-defined mathematical problems. Our preliminary experiments through PMC reveal two challenges about existing methods: (1) traditional methods exhibit a trade-off between solving accuracy and rejection capabilities, and (2) formal methods struggle with modeling complex problems. To address these challenges, We develop Variable-Constraint Search (VCSEARCH), a trainingfree framework that leverages formal language to detect ill-defined problems, where a variableconstraint pair search strategy is incorporated to improve the modeling capability of formal language. Extensive experiments demonstrate that VCSEARCH improves the accuracy of identifying unsolvable problems by at least 12% across different LLMs, thus achieving stronger robust mathematical reasoning ability.

Large Language Models (LLMs) have emerged as powerful tools for Text-to-SQL tasks, exhibiting remarkable reasoning capabilities. Different from tasks such as math word problems and commonsense reasoning, SQL solutions have a relatively fixed pattern. This facilitates the investigation of whether LLMs can benefit from categorical thinking, mirroring how humans acquire knowledge through inductive reasoning based on comparable examples. In this study, we propose that employing query group partitioning allows LLMs to focus on learning the thought processes specific to a single problem type, consequently enhancing their reasoning abilities across diverse difficulty levels and problem categories. Our experiments reveal that multiple advanced LLMs, when equipped with PTD-SQL, can either surpass or match previous state-of-the-art (SOTA) methods on the Spider and BIRD datasets. Intriguingly, models with varying initial performances have exhibited significant improvements, mainly at the boundary of their capabilities after targeted drilling, suggesting a parallel with human progress. Code is available at https://github.com/lrlbbzl/PTD-SQL.

Existing combinatorial search methods are often complex and require some level of expertise. This work introduces a simple and efficient deep learning method for solving combinatorial problems with a predefined goal, represented by Rubik's Cube. We demonstrate that, for such problems, training a deep neural network on random scrambles branching from the goal state is sufficient to achieve near-optimal solutions. When tested on Rubik's Cube, 15 Puzzle, and 7times7 Lights Out, our method outperformed the previous state-of-the-art method DeepCubeA, improving the trade-off between solution optimality and computational cost, despite significantly less training data. Furthermore, we investigate the scaling law of our Rubik's Cube solver with respect to model size and training data volume.

We curate a comprehensive dataset of 4,550 questions and solutions from problem sets, midterm exams, and final exams across all MIT Mathematics and Electrical Engineering and Computer Science (EECS) courses required for obtaining a degree. We evaluate the ability of large language models to fulfill the graduation requirements for any MIT major in Mathematics and EECS. Our results demonstrate that GPT-3.5 successfully solves a third of the entire MIT curriculum, while GPT-4, with prompt engineering, achieves a perfect solve rate on a test set excluding questions based on images. We fine-tune an open-source large language model on this dataset. We employ GPT-4 to automatically grade model responses, providing a detailed performance breakdown by course, question, and answer type. By embedding questions in a low-dimensional space, we explore the relationships between questions, topics, and classes and discover which questions and classes are required for solving other questions and classes through few-shot learning. Our analysis offers valuable insights into course prerequisites and curriculum design, highlighting language models' potential for learning and improving Mathematics and EECS education.

Existing neural operator architectures face challenges when solving multiphysics problems with coupled partial differential equations (PDEs) due to complex geometries, interactions between physical variables, and the limited amounts of high-resolution training data. To address these issues, we propose Codomain Attention Neural Operator (CoDA-NO), which tokenizes functions along the codomain or channel space, enabling self-supervised learning or pretraining of multiple PDE systems. Specifically, we extend positional encoding, self-attention, and normalization layers to function spaces. CoDA-NO can learn representations of different PDE systems with a single model. We evaluate CoDA-NO's potential as a backbone for learning multiphysics PDEs over multiple systems by considering few-shot learning settings. On complex downstream tasks with limited data, such as fluid flow simulations, fluid-structure interactions, and Rayleigh-B\'enard convection, we found CoDA-NO to outperform existing methods by over 36%.

We introduce Goedel-Prover-V2, a series of open-source language models that set a new state-of-the-art in automated theorem proving. Built on the standard expert iteration and reinforcement learning pipeline, our approach incorporates three key innovations: (1) Scaffolded data synthesis: We generate synthetic tasks of increasing difficulty to train the model to master increasingly complex theorems; (2) Verifier-guided self-correction: We enable the model to iteratively revise its proofs by leveraging feedback from the Lean compiler; (3) Model averaging: We merge model checkpoints to mitigate the decrease in model output diversity in later stages of training. Our small model, Goedel-Prover-V2-8B, reaches 84.6% pass@32 on MiniF2F and outperforms DeepSeek-Prover-V2-671B under the same metric, despite being 80X smaller. Our flagship model, Goedel-Prover-V2-32B, achieves 88.1% on MiniF2F at pass@32 in standard mode and 90.4% in self-correction mode, outperforming prior SOTA by a large margin. Additionally, our flagship model solves 86 problems on PutnamBench at pass@184, securing the first place among open-source models on the leaderboard, surpassing DeepSeek-Prover-V2-671B's record of solving 47 problems by pass@1024 with a significantly smaller model size and compute budget. At the time of its release (July-August 2025), Goedel-Prover-V2 achieves the strongest overall performance among all open-source theorem provers. It also ranks among the top-performing models--including closed-source systems with publicly reported performance--under a constrained test-time compute budget. Our models, code, and data are released at https://github.com/Goedel-LM/Goedel-Prover-V2.

Representing a manifold of very high-dimensional data with generative models has been shown to be computationally efficient in practice. However, this requires that the data manifold admits a global parameterization. In order to represent manifolds of arbitrary topology, we propose to learn a mixture model of variational autoencoders. Here, every encoder-decoder pair represents one chart of a manifold. We propose a loss function for maximum likelihood estimation of the model weights and choose an architecture that provides us the analytical expression of the charts and of their inverses. Once the manifold is learned, we use it for solving inverse problems by minimizing a data fidelity term restricted to the learned manifold. To solve the arising minimization problem we propose a Riemannian gradient descent algorithm on the learned manifold. We demonstrate the performance of our method for low-dimensional toy examples as well as for deblurring and electrical impedance tomography on certain image manifolds.

MRI is an inherently slow process, which leads to long scan time for high-resolution imaging. The speed of acquisition can be increased by ignoring parts of the data (undersampling). Consequently, this leads to the degradation of image quality, such as loss of resolution or introduction of image artefacts. This work aims to reconstruct highly undersampled Cartesian or radial MR acquisitions, with better resolution and with less to no artefact compared to conventional techniques like compressed sensing. In recent times, deep learning has emerged as a very important area of research and has shown immense potential in solving inverse problems, e.g. MR image reconstruction. In this paper, a deep learning based MR image reconstruction framework is proposed, which includes a modified regularised version of ResNet as the network backbone to remove artefacts from the undersampled image, followed by data consistency steps that fusions the network output with the data already available from undersampled k-space in order to further improve reconstruction quality. The performance of this framework for various undersampling patterns has also been tested, and it has been observed that the framework is robust to deal with various sampling patterns, even when mixed together while training, and results in very high quality reconstruction, in terms of high SSIM (highest being 0.990pm0.006 for acceleration factor of 3.5), while being compared with the fully sampled reconstruction. It has been shown that the proposed framework can successfully reconstruct even for an acceleration factor of 20 for Cartesian (0.968pm0.005) and 17 for radially (0.962pm0.012) sampled data. Furthermore, it has been shown that the framework preserves brain pathology during reconstruction while being trained on healthy subjects.

We advocate for a strong integration of Computational Creativity (CC) with research in large language and vision models (LLVMs) to address a key limitation of these models, i.e., creative problem solving. We present preliminary experiments showing how CC principles can be applied to address this limitation. Our goal is to foster discussions on creative problem solving in LLVMs and CC at prestigious ML venues. Our code is available at: https://github.com/lnairGT/creative-problem-solving-LLMs

Open domain question answering (OpenQA) tasks have been recently attracting more and more attention from the natural language processing (NLP) community. In this work, we present the first free-form multiple-choice OpenQA dataset for solving medical problems, MedQA, collected from the professional medical board exams. It covers three languages: English, simplified Chinese, and traditional Chinese, and contains 12,723, 34,251, and 14,123 questions for the three languages, respectively. We implement both rule-based and popular neural methods by sequentially combining a document retriever and a machine comprehension model. Through experiments, we find that even the current best method can only achieve 36.7\%, 42.0\%, and 70.1\% of test accuracy on the English, traditional Chinese, and simplified Chinese questions, respectively. We expect MedQA to present great challenges to existing OpenQA systems and hope that it can serve as a platform to promote much stronger OpenQA models from the NLP community in the future.

We introduce FigureQA, a visual reasoning corpus of over one million question-answer pairs grounded in over 100,000 images. The images are synthetic, scientific-style figures from five classes: line plots, dot-line plots, vertical and horizontal bar graphs, and pie charts. We formulate our reasoning task by generating questions from 15 templates; questions concern various relationships between plot elements and examine characteristics like the maximum, the minimum, area-under-the-curve, smoothness, and intersection. To resolve, such questions often require reference to multiple plot elements and synthesis of information distributed spatially throughout a figure. To facilitate the training of machine learning systems, the corpus also includes side data that can be used to formulate auxiliary objectives. In particular, we provide the numerical data used to generate each figure as well as bounding-box annotations for all plot elements. We study the proposed visual reasoning task by training several models, including the recently proposed Relation Network as a strong baseline. Preliminary results indicate that the task poses a significant machine learning challenge. We envision FigureQA as a first step towards developing models that can intuitively recognize patterns from visual representations of data.

Given the dominance of dense retrievers that do not generalize well beyond their training dataset distributions, domain-specific test sets are essential in evaluating retrieval. There are few test datasets for retrieval systems intended for use by healthcare providers in a point-of-care setting. To fill this gap we have collaborated with medical professionals to create CURE, an ad-hoc retrieval test dataset for passage ranking with 2000 queries spanning 10 medical domains with a monolingual (English) and two cross-lingual (French/Spanish -> English) conditions. In this paper, we describe how CURE was constructed and provide baseline results to showcase its effectiveness as an evaluation tool. CURE is published with a Creative Commons Attribution Non Commercial 4.0 license and can be accessed on Hugging Face.

We present the Stanford Question Answering Dataset (SQuAD), a new reading comprehension dataset consisting of 100,000+ questions posed by crowdworkers on a set of Wikipedia articles, where the answer to each question is a segment of text from the corresponding reading passage. We analyze the dataset to understand the types of reasoning required to answer the questions, leaning heavily on dependency and constituency trees. We build a strong logistic regression model, which achieves an F1 score of 51.0%, a significant improvement over a simple baseline (20%). However, human performance (86.8%) is much higher, indicating that the dataset presents a good challenge problem for future research. The dataset is freely available at https://stanford-qa.com

Many methods now exist for conditioning model outputs on task instructions, retrieved documents, and user-provided explanations and feedback. Rather than relying solely on examples of task inputs and outputs, these approaches use valuable additional data for improving model correctness and aligning learned models with human priors. Meanwhile, a growing body of evidence suggests that some language models can (1) store a large amount of knowledge in their parameters, and (2) perform inference over tasks in textual inputs at test time. These results raise the possibility that, for some tasks, humans cannot explain to a model any more about the task than it already knows or could infer on its own. In this paper, we study the circumstances under which explanations of individual data points can (or cannot) improve modeling performance. In order to carefully control important properties of the data and explanations, we introduce a synthetic dataset for experiments, and we also make use of three existing datasets with explanations: e-SNLI, TACRED, and SemEval. We first give a formal framework for the available modeling approaches, in which explanation data can be used as model inputs, as targets, or as a prior. After arguing that the most promising role for explanation data is as model inputs, we propose to use a retrieval-based method and show that it solves our synthetic task with accuracies upwards of 95%, while baselines without explanation data achieve below 65% accuracy. We then identify properties of datasets for which retrieval-based modeling fails. With the three existing datasets, we find no improvements from explanation retrieval. Drawing on findings from our synthetic task, we suggest that at least one of six preconditions for successful modeling fails to hold with these datasets. Our code is publicly available at https://github.com/peterbhase/ExplanationRoles

Scientific reasoning is critical for developing AI scientists and supporting human researchers in advancing the frontiers of natural science discovery. However, the open-source community has primarily focused on mathematics and coding while neglecting the scientific domain, largely due to the absence of open, large-scale, high-quality, verifiable scientific reasoning datasets. To bridge this gap, we first present TextbookReasoning, an open dataset featuring truthful reference answers extracted from 12k university-level scientific textbooks, comprising 650k reasoning questions spanning 7 scientific disciplines. We further introduce MegaScience, a large-scale mixture of high-quality open-source datasets totaling 1.25 million instances, developed through systematic ablation studies that evaluate various data selection methodologies to identify the optimal subset for each publicly available scientific dataset. Meanwhile, we build a comprehensive evaluation system covering diverse subjects and question types across 15 benchmarks, incorporating comprehensive answer extraction strategies to ensure accurate evaluation metrics. Our experiments demonstrate that our datasets achieve superior performance and training efficiency with more concise response lengths compared to existing open-source scientific datasets. Furthermore, we train Llama3.1, Qwen2.5, and Qwen3 series base models on MegaScience, which significantly outperform the corresponding official instruct models in average performance. In addition, MegaScience exhibits greater effectiveness for larger and stronger models, suggesting a scaling benefit for scientific tuning. We release our data curation pipeline, evaluation system, datasets, and seven trained models to the community to advance scientific reasoning research.

Language models have demonstrated remarkable performance in solving reasoning tasks; however, even the strongest models still occasionally make reasoning mistakes. Recently, there has been active research aimed at improving reasoning accuracy, particularly by using pretrained language models to "self-correct" their mistakes via multi-round prompting. In this paper, we follow this line of work but focus on understanding the usefulness of incorporating "error-correction" data directly into the pretraining stage. This data consists of erroneous solution steps immediately followed by their corrections. Using a synthetic math dataset, we show promising results: this type of pretrain data can help language models achieve higher reasoning accuracy directly (i.e., through simple auto-regression, without multi-round prompting) compared to pretraining on the same amount of error-free data. We also delve into many details, such as (1) how this approach differs from beam search, (2) how such data can be prepared, (3) whether masking is needed on the erroneous tokens, (4) the amount of error required, (5) whether such data can be deferred to the fine-tuning stage, and many others.

Expert problem-solving is driven by powerful languages for thinking about problems and their solutions. Acquiring expertise means learning these languages -- systems of concepts, alongside the skills to use them. We present DreamCoder, a system that learns to solve problems by writing programs. It builds expertise by creating programming languages for expressing domain concepts, together with neural networks to guide the search for programs within these languages. A ``wake-sleep'' learning algorithm alternately extends the language with new symbolic abstractions and trains the neural network on imagined and replayed problems. DreamCoder solves both classic inductive programming tasks and creative tasks such as drawing pictures and building scenes. It rediscovers the basics of modern functional programming, vector algebra and classical physics, including Newton's and Coulomb's laws. Concepts are built compositionally from those learned earlier, yielding multi-layered symbolic representations that are interpretable and transferrable to new tasks, while still growing scalably and flexibly with experience.

We introduce a framework for automatically defining and learning deep generative models with problem-specific structure. We tackle problem domains that are more traditionally solved by algorithms such as sorting, constraint satisfaction for Sudoku, and matrix factorization. Concretely, we train diffusion models with an architecture tailored to the problem specification. This problem specification should contain a graphical model describing relationships between variables, and often benefits from explicit representation of subcomputations. Permutation invariances can also be exploited. Across a diverse set of experiments we improve the scaling relationship between problem dimension and our model's performance, in terms of both training time and final accuracy. Our code can be found at https://github.com/plai-group/gsdm.

Recent breakthroughs in large language models (LLMs) exemplified by the impressive mathematical and scientific reasoning capabilities of the o1 model have spotlighted the critical importance of high-quality training data in advancing LLM performance across STEM disciplines. While the mathematics community has benefited from a growing body of curated datasets, the scientific domain at the higher education level has long suffered from a scarcity of comparable resources. To address this gap, we present SCP-116K, a new large-scale dataset of 116,756 high-quality problem-solution pairs, automatically extracted from heterogeneous sources using a streamlined and highly generalizable pipeline. Our approach involves stringent filtering to ensure the scientific rigor and educational level of the extracted materials, while maintaining adaptability for future expansions or domain transfers. By openly releasing both the dataset and the extraction pipeline, we seek to foster research on scientific reasoning, enable comprehensive performance evaluations of new LLMs, and lower the barrier to replicating the successes of advanced models like o1 in the broader science community. We believe SCP-116K will serve as a critical resource, catalyzing progress in high-level scientific reasoning tasks and promoting further innovations in LLM development. The dataset and code are publicly available at https://github.com/AQA6666/SCP-116K-open.

Although previous research on large language models (LLMs) and large multi-modal models (LMMs) has systematically explored mathematical problem-solving (MPS) within visual contexts, the analysis of how these models process visual information during problem-solving remains insufficient. To address this gap, we present VisAidMath, a benchmark for evaluating the MPS process related to visual information. We follow a rigorous data curation pipeline involving both automated processes and manual annotations to ensure data quality and reliability. Consequently, this benchmark includes 1,200 challenging problems from various mathematical branches, vision-aid formulations, and difficulty levels, collected from diverse sources such as textbooks, examination papers, and Olympiad problems. Based on the proposed benchmark, we conduct comprehensive evaluations on ten mainstream LLMs and LMMs, highlighting deficiencies in the visual-aided reasoning process. For example, GPT-4V only achieves 45.33% accuracy in the visual-aided reasoning task, even with a drop of 2 points when provided with golden visual aids. In-depth analysis reveals that the main cause of deficiencies lies in hallucination regarding the implicit visual reasoning process, shedding light on future research directions in the visual-aided MPS process.

Scientists often infer abstract procedures from specific instances of problems and use the abstractions to generate new, related instances. For example, programs encoding the formal rules and properties of a system have been useful in fields ranging from RL (procedural environments) to physics (simulation engines). These programs can be seen as functions which execute to different outputs based on their parameterizations (e.g., gridworld configuration or initial physical conditions). We introduce the term EFA (Executable Functional Abstraction) to denote such programs for math problems. EFA-like constructs have been shown to be useful for math reasoning as problem generators for stress-testing models. However, prior work has been limited to abstractions for grade-school math (whose simple rules are easy to encode in programs), while generating EFAs for advanced math has thus far required human engineering. We explore the automatic construction of EFAs for advanced math problems. We operationalize the task of automatically constructing EFAs as a program synthesis task, and develop EFAGen, which conditions an LLM on a seed math problem and its step-by-step solution to generate candidate EFA programs that are faithful to the generalized problem and solution class underlying the seed problem. Furthermore, we formalize properties any valid EFA must possess in terms of executable unit tests, and show how the tests can be used as verifiable rewards to train LLMs to become better writers of EFAs. We demonstrate that EFAs constructed by EFAGen behave rationally by remaining faithful to seed problems, produce learnable problem variations, and that EFAGen can infer EFAs across multiple diverse sources of competition-level math problems. Finally, we show downstream uses of model-written EFAs e.g. finding problem variations that are harder or easier for a learner to solve, as well as data generation.

Although demonstrating remarkable performance on reasoning tasks, Large Language Models (LLMs) still tend to fabricate unreliable responses when confronted with problems that are unsolvable or beyond their capability, severely undermining the reliability. Prior studies of LLM reliability have primarily focused on knowledge tasks to identify unanswerable questions, while mathematical reasoning tasks have remained unexplored due to the dearth of unsolvable math problems. To systematically investigate LLM reliability in mathematical reasoning tasks, we formulate the reliability evaluation for both solvable and unsolvable problems. We then develop a ReliableMath dataset which incorporates open-source solvable problems and high-quality unsolvable problems synthesized by our proposed construction workflow with human evaluations. Experiments are conducted on various LLMs with several key findings uncovered. LLMs fail to directly identify unsolvable problems and always generate fabricated responses. When instructing LLMs to indicate unsolvability using a reliable prompt, the reliability of larger-sized LLMs remains on solvable problems, but notably improves on unsolvable problems yet still falls short of solvable problems. However, small LLMs rarely show any progress despite employing reliable prompts. Therefore, we further propose an alignment strategy to enhance small LLMs' reliability, which can significantly improve LLM reliability performances on both in-domain and out-of-domain tasks.

The machine learning community currently has no standardized process for documenting datasets, which can lead to severe consequences in high-stakes domains. To address this gap, we propose datasheets for datasets. In the electronics industry, every component, no matter how simple or complex, is accompanied with a datasheet that describes its operating characteristics, test results, recommended uses, and other information. By analogy, we propose that every dataset be accompanied with a datasheet that documents its motivation, composition, collection process, recommended uses, and so on. Datasheets for datasets will facilitate better communication between dataset creators and dataset consumers, and encourage the machine learning community to prioritize transparency and accountability.