Daily Papers

Recent work has shown the immense potential of synthetically generated datasets for training large language models (LLMs), especially for acquiring targeted skills. Current large-scale math instruction tuning datasets such as MetaMathQA (Yu et al., 2024) and MAmmoTH (Yue et al., 2024) are constructed using outputs from closed-source LLMs with commercially restrictive licenses. A key reason limiting the use of open-source LLMs in these data generation pipelines has been the wide gap between the mathematical skills of the best closed-source LLMs, such as GPT-4, and the best open-source LLMs. Building on the recent progress in open-source LLMs, our proposed prompting novelty, and some brute-force scaling, we construct OpenMathInstruct-1, a math instruction tuning dataset with 1.8M problem-solution pairs. The dataset is constructed by synthesizing code-interpreter solutions for GSM8K and MATH, two popular math reasoning benchmarks, using the recently released and permissively licensed Mixtral model. Our best model, OpenMath-CodeLlama-70B, trained on a subset of OpenMathInstruct-1, achieves a score of 84.6% on GSM8K and 50.7% on MATH, which is competitive with the best gpt-distilled models. We release our code, models, and the OpenMathInstruct-1 dataset under a commercially permissive license.

This paper introduces CodeGemma, a collection of specialized open code models built on top of Gemma, capable of a variety of code and natural language generation tasks. We release three model variants. CodeGemma 7B pretrained (PT) and instruction-tuned (IT) variants have remarkably resilient natural language understanding, excel in mathematical reasoning, and match code capabilities of other open models. CodeGemma 2B is a state-of-the-art code completion model designed for fast code infilling and open-ended generation in latency-sensitive settings.

Large language models (LLMs) have pushed the limits of natural language understanding and exhibited excellent problem-solving ability. Despite the great success, most existing open-source LLMs (\eg, LLaMA-2) are still far away from satisfactory for solving mathematical problem due to the complex reasoning procedures. To bridge this gap, we propose MetaMath, a fine-tuned language model that specializes in mathematical reasoning. Specifically, we start by bootstrapping mathematical questions by rewriting the question from multiple perspectives without extra knowledge, which results in a new dataset called {MetaMathQA}. Then we fine-tune the LLaMA-2 models on MetaMathQA. Experimental results on two popular benchmarks (\ie, GSM8K and MATH) for mathematical reasoning demonstrate that MetaMath outperforms a suite of open-source LLMs by a significant margin. Our MetaMath-7B model achieves 66.4% on GSM8K and 19.4% on MATH, exceeding the state-of-the-art models of the same size by 11.5% and 8.7%. Particularly, {MetaMath-70B} achieves an accuracy of 82.3% on {GSM8K}, slightly better than {GPT-3.5-Turbo}. We release the {MetaMathQA} dataset, the {MetaMath} models with different model sizes and the training code for public use.

The rapid development of large language models (LLMs) has spurred extensive research into their domain-specific capabilities, particularly mathematical reasoning. However, most open-source LLMs focus solely on mathematical reasoning, neglecting the integration with visual injection, despite the fact that many mathematical tasks rely on visual inputs such as geometric diagrams, charts, and function plots. To fill this gap, we introduce MultiMath-7B, a multimodal large language model that bridges the gap between math and vision. MultiMath-7B is trained through a four-stage process, focusing on vision-language alignment, visual and math instruction-tuning, and process-supervised reinforcement learning. We also construct a novel, diverse and comprehensive multimodal mathematical dataset, MultiMath-300K, which spans K-12 levels with image captions and step-wise solutions. MultiMath-7B achieves state-of-the-art (SOTA) performance among open-source models on existing multimodal mathematical benchmarks and also excels on text-only mathematical benchmarks. Our model and dataset are available at {blue{https://github.com/pengshuai-rin/MultiMath}}.

The tool-use Large Language Models (LLMs) that integrate with external Python interpreters have significantly enhanced mathematical reasoning capabilities for open-source LLMs, while tool-free methods chose another track: augmenting math reasoning data. However, a great method to integrate the above two research paths and combine their advantages remains to be explored. In this work, we firstly include new math questions via multi-perspective data augmenting methods and then synthesize code-nested solutions to them. The open LLMs (i.e., Llama-2) are finetuned on the augmented dataset to get the resulting models, MuMath-Code (mu-Math-Code). During the inference phase, our MuMath-Code generates code and interacts with the external python interpreter to get the execution results. Therefore, MuMath-Code leverages the advantages of both the external tool and data augmentation. To fully leverage the advantages of our augmented data, we propose a two-stage training strategy: In Stage-1, we finetune Llama-2 on pure CoT data to get an intermediate model, which then is trained on the code-nested data in Stage-2 to get the resulting MuMath-Code. Our MuMath-Code-7B achieves 83.8 on GSM8K and 52.4 on MATH, while MuMath-Code-70B model achieves new state-of-the-art performance among open methods -- achieving 90.7% on GSM8K and 55.1% on MATH. Extensive experiments validate the combination of tool use and data augmentation, as well as our two-stage training strategy. We release the proposed dataset along with the associated code for public use.

In this paper, we introduce AceMath, a suite of frontier math models that excel in solving complex math problems, along with highly effective reward models capable of evaluating generated solutions and reliably identifying the correct ones. To develop the instruction-tuned math models, we propose a supervised fine-tuning (SFT) process that first achieves competitive performance across general domains, followed by targeted fine-tuning for the math domain using a carefully curated set of prompts and synthetically generated responses. The resulting model, AceMath-72B-Instruct greatly outperforms Qwen2.5-Math-72B-Instruct, GPT-4o and Claude-3.5 Sonnet. To develop math-specialized reward model, we first construct AceMath-RewardBench, a comprehensive and robust benchmark for evaluating math reward models across diverse problems and difficulty levels. After that, we present a systematic approach to build our math reward models. The resulting model, AceMath-72B-RM, consistently outperforms state-of-the-art reward models. Furthermore, when combining AceMath-72B-Instruct with AceMath-72B-RM, we achieve the highest average rm@8 score across the math reasoning benchmarks. We will release model weights, training data, and evaluation benchmarks at: https://research.nvidia.com/labs/adlr/acemath

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.

Mathematical reasoning is a cornerstone of artificial general intelligence and a primary benchmark for evaluating the capabilities of Large Language Models (LLMs). While state-of-the-art models show promise, they often falter when faced with complex problems that demand deep conceptual understanding and intricate, multi-step deliberation. To address this challenge, we introduce JT-Math-8B, a series of open-source models comprising base, instruct, and thinking versions, built upon a systematic, multi-stage optimization framework. Our pre-training corpus is a high-quality, 210B-token dataset curated through a dedicated data pipeline that uses model-based validation to ensure quality and diversity. The Instruct Model is optimized for direct, concise answers through Supervised Fine-Tuning (SFT) and a GRPO-based reinforcement learning (RL) method. The Thinking Model is trained for complex problem-solving using a Long Chain-of-Thought (Long CoT) approach, combining SFT with a novel, multi-stage RL curriculum that progressively increases task difficulty and context length up to 32K tokens. JT-Math-8B achieves state-of-the-art results among open-source models of similar size, surpassing prominent models like OpenAI's O1-mini and GPT-4o , and demonstrating superior performance on competition-level mathematics.

The recently released GPT-4 Code Interpreter has demonstrated remarkable proficiency in solving challenging math problems, primarily attributed to its ability to seamlessly reason with natural language, generate code, execute code, and continue reasoning based on the execution output. In this paper, we present a method to fine-tune open-source language models, enabling them to use code for modeling and deriving math equations and, consequently, enhancing their mathematical reasoning abilities. We propose a method of generating novel and high-quality datasets with math problems and their code-based solutions, referred to as MathCodeInstruct. Each solution interleaves natural language, code, and execution results. We also introduce a customized supervised fine-tuning and inference approach. This approach yields the MathCoder models, a family of models capable of generating code-based solutions for solving challenging math problems. Impressively, the MathCoder models achieve state-of-the-art scores among open-source LLMs on the MATH (45.2%) and GSM8K (83.9%) datasets, substantially outperforming other open-source alternatives. Notably, the MathCoder model not only surpasses ChatGPT-3.5 and PaLM-2 on GSM8K and MATH but also outperforms GPT-4 on the competition-level MATH dataset. The dataset and models will be released at https://github.com/mathllm/MathCoder.

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.

General-purpose large language models, despite their broad capabilities, often struggle with specialized domain knowledge, a limitation particularly pronounced in more accessible, lower-parameter versions. This gap hinders their deployment as effective agents in demanding fields such as astronomy. Building on our prior work with AstroSage-8B, this study introduces AstroSage-70B, a significantly larger and more advanced domain-specialized natural-language AI assistant. It is designed for research and education across astronomy, astrophysics, space science, astroparticle physics, cosmology, and astronomical instrumentation. Developed from the Llama-3.1-70B foundation, AstroSage-70B underwent extensive continued pre-training on a vast corpus of astronomical literature, followed by supervised fine-tuning and model merging. Beyond its 70-billion parameter scale, this model incorporates refined datasets, judiciously chosen learning hyperparameters, and improved training procedures, achieving state-of-the-art performance on complex astronomical tasks. Notably, we integrated reasoning chains into the SFT dataset, enabling AstroSage-70B to either answer the user query immediately, or first emit a human-readable thought process. Evaluated on the AstroMLab-1 benchmark -- comprising 4,425 questions from literature withheld during training -- AstroSage-70B achieves state-of-the-art performance. It surpasses all other tested open-weight and proprietary models, including leading systems like o3, Gemini-2.5-Pro, Claude-3.7-Sonnet, Deepseek-R1, and Qwen-3-235B, even those with API costs two orders of magnitude higher. This work demonstrates that domain specialization, when applied to large-scale models, can enable them to outperform generalist counterparts in specialized knowledge areas like astronomy, thereby advancing the frontier of AI capabilities in the field.

Recent progress in large language models (LLMs) like GPT-4 and PaLM-2 has brought significant advancements in addressing math reasoning problems. In particular, OpenAI's latest version of GPT-4, known as GPT-4 Code Interpreter, shows remarkable performance on challenging math datasets. In this paper, we explore the effect of code on enhancing LLMs' reasoning capability by introducing different constraints on the Code Usage Frequency of GPT-4 Code Interpreter. We found that its success can be largely attributed to its powerful skills in generating and executing code, evaluating the output of code execution, and rectifying its solution when receiving unreasonable outputs. Based on this insight, we propose a novel and effective prompting method, explicit code-based self-verification~(CSV), to further boost the mathematical reasoning potential of GPT-4 Code Interpreter. This method employs a zero-shot prompt on GPT-4 Code Interpreter to encourage it to use code to self-verify its answers. In instances where the verification state registers as ``False'', the model shall automatically amend its solution, analogous to our approach of rectifying errors during a mathematics examination. Furthermore, we recognize that the states of the verification result indicate the confidence of a solution, which can improve the effectiveness of majority voting. With GPT-4 Code Interpreter and CSV, we achieve an impressive zero-shot accuracy on MATH dataset (53.9\% to 84.3\%).

The BigCode project, an open-scientific collaboration focused on the responsible development of Large Language Models for Code (Code LLMs), introduces StarCoder2. In partnership with Software Heritage (SWH), we build The Stack v2 on top of the digital commons of their source code archive. Alongside the SWH repositories spanning 619 programming languages, we carefully select other high-quality data sources, such as GitHub pull requests, Kaggle notebooks, and code documentation. This results in a training set that is 4x larger than the first StarCoder dataset. We train StarCoder2 models with 3B, 7B, and 15B parameters on 3.3 to 4.3 trillion tokens and thoroughly evaluate them on a comprehensive set of Code LLM benchmarks. We find that our small model, StarCoder2-3B, outperforms other Code LLMs of similar size on most benchmarks, and also outperforms StarCoderBase-15B. Our large model, StarCoder2- 15B, significantly outperforms other models of comparable size. In addition, it matches or outperforms CodeLlama-34B, a model more than twice its size. Although DeepSeekCoder- 33B is the best-performing model at code completion for high-resource languages, we find that StarCoder2-15B outperforms it on math and code reasoning benchmarks, as well as several low-resource languages. We make the model weights available under an OpenRAIL license and ensure full transparency regarding the training data by releasing the SoftWare Heritage persistent IDentifiers (SWHIDs) of the source code data.

This study explores the performance of large language models (LLMs) in solving competitive programming problems from the Romanian Informatics Olympiad at the county level. Romania, a leading nation in computer science competitions, provides an ideal environment for evaluating LLM capabilities due to its rich history and stringent competition standards. We collected and analyzed a dataset comprising 304 challenges from 2002 to 2023, focusing on solutions written by LLMs in C++ and Python for these problems. Our primary goal is to understand why LLMs perform well or poorly on different tasks. We evaluated various models, including closed-source models like GPT-4 and open-weight models such as CodeLlama and RoMistral, using a standardized process involving multiple attempts and feedback rounds. The analysis revealed significant variations in LLM performance across different grades and problem types. Notably, GPT-4 showed strong performance, indicating its potential use as an educational tool for middle school students. We also observed differences in code quality and style across various LLMs

Large language models (LMs) of code have recently shown tremendous promise in completing code and synthesizing code from natural language descriptions. However, the current state-of-the-art code LMs (e.g., Codex (Chen et al., 2021)) are not publicly available, leaving many questions about their model and data design decisions. We aim to fill in some of these blanks through a systematic evaluation of the largest existing models: Codex, GPT-J, GPT-Neo, GPT-NeoX-20B, and CodeParrot, across various programming languages. Although Codex itself is not open-source, we find that existing open-source models do achieve close results in some programming languages, although targeted mainly for natural language modeling. We further identify an important missing piece in the form of a large open-source model trained exclusively on a multi-lingual corpus of code. We release a new model, PolyCoder, with 2.7B parameters based on the GPT-2 architecture, which was trained on 249GB of code across 12 programming languages on a single machine. In the C programming language, PolyCoder outperforms all models including Codex. Our trained models are open-source and publicly available at https://github.com/VHellendoorn/Code-LMs, which enables future research and application in this area.

We introduce Magicoder, a series of fully open-source (code, weights, and data) Large Language Models (LLMs) for code that significantly closes the gap with top code models while having no more than 7B parameters. Magicoder models are trained on 75K synthetic instruction data using OSS-Instruct, a novel approach to enlightening LLMs with open-source code snippets to generate high-quality instruction data for code. Our main motivation is to mitigate the inherent bias of the synthetic data generated by LLMs by empowering them with a wealth of open-source references for the production of more diverse, realistic, and controllable data. The orthogonality of OSS-Instruct and other data generation methods like Evol-Instruct further enables us to build an enhanced MagicoderS. Both Magicoder and MagicoderS substantially outperform state-of-the-art code models with similar or even larger sizes on a wide range of coding benchmarks, including Python text-to-code generation, multilingual coding, and data-science program completion. Notably, MagicoderS-CL-7B based on CodeLlama even surpasses the prominent ChatGPT on HumanEval+ (66.5 vs. 65.9 in pass@1). Overall, OSS-Instruct opens a new direction for low-bias and high-quality instruction tuning using abundant open-source references.

Preference optimization techniques, such as Direct Preference Optimization (DPO), are frequently employed to enhance the reasoning capabilities of large language models (LLMs) in domains like mathematical reasoning and coding, typically following supervised fine-tuning. These methods rely on high-quality labels for reasoning tasks to generate preference pairs; however, the availability of reasoning datasets with human-verified labels is limited. In this study, we introduce a novel approach to generate pseudo feedback for reasoning tasks by framing the labeling of solutions to reason problems as an evaluation against associated test cases. We explore two forms of pseudo feedback based on test cases: one generated by frontier LLMs and the other by extending self-consistency to multi-test-case. We conduct experiments on both mathematical reasoning and coding tasks using pseudo feedback for preference optimization, and observe improvements across both tasks. Specifically, using Mathstral-7B as our base model, we improve MATH results from 58.3 to 68.6, surpassing both NuminaMath-72B and GPT-4-Turbo-1106-preview. In GSM8K and College Math, our scores increase from 85.6 to 90.3 and from 34.3 to 42.3, respectively. Building on Deepseek-coder-7B-v1.5, we achieve a score of 24.6 on LiveCodeBench (from 21.1), surpassing Claude-3-Haiku.

Large Language Models (LLMs) have shown strong performance in solving mathematical problems, with code-based solutions proving particularly effective. However, the best practice to leverage coding instruction data to enhance mathematical reasoning remains underexplored. This study investigates three key questions: (1) How do different coding styles of mathematical code-based rationales impact LLMs' learning performance? (2) Can general-domain coding instructions improve performance? (3) How does integrating textual rationales with code-based ones during training enhance mathematical reasoning abilities? Our findings reveal that code-based rationales with concise comments, descriptive naming, and hardcoded solutions are beneficial, while improvements from general-domain coding instructions and textual rationales are relatively minor. Based on these insights, we propose CoinMath, a learning strategy designed to enhance mathematical reasoning by diversifying the coding styles of code-based rationales. CoinMath generates a variety of code-based rationales incorporating concise comments, descriptive naming conventions, and hardcoded solutions. Experimental results demonstrate that CoinMath significantly outperforms its baseline model, MAmmoTH, one of the SOTA math LLMs.

The introduction of large language models has significantly advanced code generation. However, open-source models often lack the execution capabilities and iterative refinement of advanced systems like the GPT-4 Code Interpreter. To address this, we introduce OpenCodeInterpreter, a family of open-source code systems designed for generating, executing, and iteratively refining code. Supported by Code-Feedback, a dataset featuring 68K multi-turn interactions, OpenCodeInterpreter integrates execution and human feedback for dynamic code refinement. Our comprehensive evaluation of OpenCodeInterpreter across key benchmarks such as HumanEval, MBPP, and their enhanced versions from EvalPlus reveals its exceptional performance. Notably, OpenCodeInterpreter-33B achieves an accuracy of 83.2 (76.4) on the average (and plus versions) of HumanEval and MBPP, closely rivaling GPT-4's 84.2 (76.2) and further elevates to 91.6 (84.6) with synthesized human feedback from GPT-4. OpenCodeInterpreter brings the gap between open-source code generation models and proprietary systems like GPT-4 Code Interpreter.

Evaluating the alignment of large language models (LLMs) with user-defined coding preferences is a challenging endeavour that requires a deep assessment of LLMs' outputs. Existing methods and benchmarks rely primarily on automated metrics and static analysis tools, which often fail to capture the nuances of user instructions and LLM outputs. To address this gap, we propose using the LLM-as-a-Judge methodology to evaluate the alignment of LLMs with coding preferences. Based on this approach, we present CodeUltraFeedback, a comprehensive dataset designed to facilitate the evaluation and improvement of LLM alignment. CodeUltraFeedback consists of 10,000 coding instructions, each annotated with four responses generated from a diverse pool of 14 LLMs. These responses are ranked based on five distinct coding preferences using GPT-3.5 as a judge, providing both numerical scores and detailed textual feedback. Our analysis of CodeUltraFeedback reveals that responses from GPT-3.5 and GPT-4 are generally preferred over those from open-weight LLMs, highlighting significant differences in alignment between closed and open-weight models. In turn, we explore the usage of CodeUltraFeedback as feedback data to fine-tune and align CodeLlama-7B-Instruct using supervised fine-tuning (SFT) and reinforcement learning from AI feedback (RLAIF) with direct preference optimization (DPO). The resulting aligned CodeLlama-7B-Instruct model outperforms larger LLMs in terms of alignment with coding preferences and shows improved functional correctness on the HumanEval+ benchmark compared to the original instruct model. Therefore, our contributions bridge the gap in preference tuning of LLMs for code and set the stage for further advancements in model alignment and RLAIF in automated software engineering.

OpenAI's Codex, a GPT-3 like model trained on a large code corpus, has made headlines in and outside of academia. Given a short user-provided description, it is capable of synthesizing code snippets that are syntactically and semantically valid in most cases. In this work, we want to investigate whether Codex is able to localize and fix bugs, a task of central interest in the field of automated program repair. Our initial evaluation uses the multi-language QuixBugs benchmark (40 bugs in both Python and Java). We find that, despite not being trained for APR, Codex is surprisingly effective, and competitive with recent state of the art techniques. Our results also show that Codex is slightly more successful at repairing Python than Java.

Large language models (LLMs) have exhibited great potential in mathematical reasoning. However, there remains a performance gap in this area between existing open-source models and closed-source models such as GPT-4. In this paper, we introduce MathGenie, a novel method for generating diverse and reliable math problems from a small-scale problem-solution dataset (denoted as seed data). We augment the ground-truth solutions of our seed data and train a back-translation model to translate the augmented solutions back into new questions. Subsequently, we generate code-integrated solutions for the new questions. To ensure the correctness of the code-integrated solutions, we employ rationale-based strategy for solution verification. Various pretrained models, ranging from 7B to 70B, are trained on the newly curated data to test the effectiveness of the proposed augmentation technique, resulting in a family of models known as MathGenieLM. These models consistently outperform previous open-source models across five representative mathematical reasoning datasets, achieving state-of-the-art performance. In particular, MathGenieLM-InternLM2 achieves an accuracy of 87.7% on GSM8K and 55.7% on MATH, securing the best overall score among open-source language models.

Accurate mathematical reasoning with Large Language Models (LLMs) is crucial in revolutionizing domains that heavily rely on such reasoning. However, LLMs often encounter difficulties in certain aspects of mathematical reasoning, leading to flawed reasoning and erroneous results. To mitigate these issues, we introduce a novel mechanism, the Chain of Self-Correction (CoSC), specifically designed to embed self-correction as an inherent ability in LLMs, enabling them to validate and rectify their own results. The CoSC mechanism operates through a sequence of self-correction stages. In each stage, the LLMs generate a program to address a given problem, execute this program using program-based tools to obtain an output, subsequently verify this output. Based on the verification, the LLMs either proceed to the next correction stage or finalize the answer. This iterative self-correction process allows the LLMs to refine their reasoning steps and improve the accuracy of their mathematical reasoning. To enable the CoSC mechanism at a low cost, we employ a two-phase finetuning approach. In the first phase, the LLMs are trained with a relatively small volume of seeding data generated from GPT-4, establishing an initial CoSC capability. In the second phase, the CoSC capability is further enhanced by training with a larger volume of self-generated data using the trained model in the first phase, without relying on the paid GPT-4. Our comprehensive experiments demonstrate that CoSC significantly improves performance on traditional mathematical datasets among existing open-source LLMs. Notably, our CoSC-Code-34B model achieved a 53.5% score on MATH, the most challenging mathematical reasoning dataset in the public domain, surpassing the performance of well-established models such as ChatGPT, GPT-4, and even multi-modal LLMs like GPT-4V, Gemini-1.0 Pro, and Gemini-1.0 Ultra.

We introduce the latest series of TeleChat models: TeleChat2, TeleChat2.5, and T1, offering a significant upgrade over their predecessor, TeleChat. Despite minimal changes to the model architecture, the new series achieves substantial performance gains through enhanced training strategies in both pre-training and post-training stages. The series begins with TeleChat2, which undergoes pretraining on 10 trillion high-quality and diverse tokens. This is followed by Supervised Fine-Tuning (SFT) and Direct Preference Optimization (DPO) to further enhance its capabilities. TeleChat2.5 and T1 expand the pipeline by incorporating a continual pretraining phase with domain-specific datasets, combined with reinforcement learning (RL) to improve performance in code generation and mathematical reasoning tasks. The T1 variant is designed for complex reasoning, supporting long Chain-of-Thought (CoT) reasoning and demonstrating substantial improvements in mathematics and coding. In contrast, TeleChat2.5 prioritizes speed, delivering rapid inference. Both flagship models of T1 and TeleChat2.5 are dense Transformer-based architectures with 115B parameters, showcasing significant advancements in reasoning and general task performance compared to the original TeleChat. Notably, T1-115B outperform proprietary models such as OpenAI's o1-mini and GPT-4o. We publicly release TeleChat2, TeleChat2.5 and T1, including post-trained versions with 35B and 115B parameters, to empower developers and researchers with state-of-the-art language models tailored for diverse applications.

MM-Vet, with open-ended vision-language questions targeting at evaluating integrated capabilities, has become one of the most popular benchmarks for large multimodal model evaluation. MM-Vet assesses six core vision-language (VL) capabilities: recognition, knowledge, spatial awareness, language generation, OCR, and math. However, its question format is restricted to single image-text pairs, lacking the interleaved image and text sequences prevalent in real-world scenarios. To address this limitation, we introduce MM-Vet v2, which includes a new VL capability called "image-text sequence understanding", evaluating models' ability to process VL sequences. Furthermore, we maintain the high quality of evaluation samples while further expanding the evaluation set size. Using MM-Vet v2 to benchmark large multimodal models, we found that Claude 3.5 Sonnet is the best model with a score of 71.8, slightly outperforming GPT-4o which scored 71.0. Among open-weight models, InternVL2-Llama3-76B leads with a score of 68.4.

With the increasing code reasoning capabilities of existing large language models (LLMs) and breakthroughs in reasoning models like OpenAI o1 and o3, there is a growing need to develop more challenging and comprehensive benchmarks that effectively test their sophisticated competition-level coding abilities. Existing benchmarks, like LiveCodeBench and USACO, fall short due to the unavailability of private test cases, lack of support for special judges, and misaligned execution environments. To bridge this gap, we introduce CodeElo, a standardized competition-level code generation benchmark that effectively addresses all these challenges for the first time. CodeElo benchmark is mainly based on the official CodeForces platform and tries to align with the platform as much as possible. We compile the recent six months of contest problems on CodeForces with detailed information such as contest divisions, problem difficulty ratings, and problem algorithm tags. We introduce a unique judging method in which problems are submitted directly to the platform and develop a reliable Elo rating calculation system that aligns with the platform and is comparable with human participants but has lower variance. By testing on our CodeElo, we provide the Elo ratings of 30 existing popular open-source and 3 proprietary LLMs for the first time. The results show that o1-mini and QwQ-32B-Preview stand out significantly, achieving Elo ratings of 1578 and 1261, respectively, while other models struggle even with the easiest problems, placing in the lowest 20 percent among all human participants. Detailed analysis experiments are also conducted to provide insights into performance across algorithms and comparisons between using C++ and Python, which can suggest directions for future studies.

Large Language Models (LLMs) have made significant strides in code generation and problem solving. Current approaches employ external tool-based iterative debuggers that use compiler or other tool-based runtime feedback to refine coarse programs generated by various methods. However, the effectiveness of these approaches heavily relies on the quality of the initial code generation, which remains an open challenge. In this paper, we introduce CodeSim, a novel multi-agent code generation framework that comprehensively addresses the stages of program synthesis-planning, coding, and debugging-through a human-like perception approach. As human verifies their understanding of any algorithms through visual simulation, CodeSim uniquely features a method of plan verification and internal debugging through the step-by-step simulation of input/output. Extensive experiments across seven challenging competitive problem-solving and program synthesis benchmarks demonstrate CodeSim's remarkable code generation capabilities. Our framework achieves new state-of-the-art (pass@1) results-(HumanEval 95.1%, MBPP 90.7%, APPS 22%, and CodeContests 29.1%). Furthermore, our method shows potential for even greater enhancement when cascaded with external debuggers. To facilitate further research and development in this area, we have open-sourced our framework in this link (https://kagnlp.github.io/codesim.github.io/).

Recently, Large Language Models (LLMs) have undergone a significant transformation, marked by a rapid rise in both their popularity and capabilities. Leading this evolution are proprietary LLMs like GPT-4 and GPT-o1, which have captured widespread attention in the AI community due to their remarkable performance and versatility. Simultaneously, open-source LLMs, such as LLaMA and Mistral, have made great contributions to the ever-increasing popularity of LLMs due to the ease to customize and deploy the models across diverse applications. Although open-source LLMs present unprecedented opportunities for innovation and research, the commercialization of LLMs has raised concerns about transparency, reproducibility, and safety. Many open-source LLMs fail to meet fundamental transparency requirements by withholding essential components like training code and data, and some use restrictive licenses whilst claiming to be "open-source," which may hinder further innovations on LLMs. To mitigate this issue, we introduce Moxin 7B, a fully open-source LLM developed in accordance with the Model Openness Framework (MOF), a ranked classification system that evaluates AI models based on model completeness and openness, adhering to principles of open science, open source, open data, and open access. Our model achieves the highest MOF classification level of "open science" through the comprehensive release of pre-training code and configurations, training and fine-tuning datasets, and intermediate and final checkpoints. Experiments show that our model achieves superior performance in zero-shot evaluation compared with popular 7B models and performs competitively in few-shot evaluation.

Large language models (LLMs) have demonstrated impressive reasoning capabilities, particularly in textual mathematical problem-solving. However, existing open-source image instruction fine-tuning datasets, containing limited question-answer pairs per image, do not fully exploit visual information to enhance the multimodal mathematical reasoning capabilities of Multimodal LLMs (MLLMs). To bridge this gap, we address the lack of high-quality, diverse multimodal mathematical datasets by collecting 40K high-quality images with question-answer pairs from 24 existing datasets and synthesizing 320K new pairs, creating the MathV360K dataset, which enhances both the breadth and depth of multimodal mathematical questions. We introduce Math-LLaVA, a LLaVA-1.5-based model fine-tuned with MathV360K. This novel approach significantly improves the multimodal mathematical reasoning capabilities of LLaVA-1.5, achieving a 19-point increase and comparable performance to GPT-4V on MathVista's minitest split. Furthermore, Math-LLaVA demonstrates enhanced generalizability, showing substantial improvements on the MMMU benchmark. Our research highlights the importance of dataset diversity and synthesis in advancing MLLMs' mathematical reasoning abilities. The code and data are available at: https://github.com/HZQ950419/Math-LLaVA.

Large Language Models (LLMs) are widely adopted for assisting in software development tasks, yet their performance evaluations have narrowly focused on the functional correctness of generated code. Human programmers, however, require LLM-generated code to be not only correct but also optimally efficient. We propose PerfCodeGen, a training-free framework that enhances the performance of LLM-generated code by incorporating feedback based on runtime during test case execution into the self-refinement iterations. With PerfCodeGen, we achieve speedups for a significantly higher proportion of problems compared to using the base LLM with sophisticated prompting techniques. Applied to open language models like Phi-3-mini, PerfCodeGen achieves runtime efficiency comparable to prompting powerful closed models like GPT-4. We achieve state-of-the-art runtime efficiency on benchmarks such as HumanEval, MBPP, and APPS, frequently surpassing the ground truth reference solutions with PerfCodeGen using GPT-3.5 and GPT-4. Additionally, we demonstrate the effectiveness of our approach in enhancing code quality across a range of open LLMs of varying sizes including Phi-3-mini, Llama 3 8B, Mixtral 8x7B, Command R, and Llama 3 70B.

Effective communication, specifically through documentation, is the beating heart of collaboration among contributors in software development. Recent advancements in language models (LMs) have enabled the introduction of a new type of actor in that ecosystem: LM-powered assistants capable of code generation, optimization, and maintenance. Our study investigates the efficacy of small language models (SLMs) for generating high-quality docstrings by assessing accuracy, conciseness, and clarity, benchmarking performance quantitatively through mathematical formulas and qualitatively through human evaluation using Likert scale. Further, we introduce DocuMint, as a large-scale supervised fine-tuning dataset with 100,000 samples. In quantitative experiments, Llama 3 8B achieved the best performance across all metrics, with conciseness and clarity scores of 0.605 and 64.88, respectively. However, under human evaluation, CodeGemma 7B achieved the highest overall score with an average of 8.3 out of 10 across all metrics. Fine-tuning the CodeGemma 2B model using the DocuMint dataset led to significant improvements in performance across all metrics, with gains of up to 22.5% in conciseness. The fine-tuned model and the dataset can be found in HuggingFace and the code can be found in the repository.

We present MiMo-7B, a large language model born for reasoning tasks, with optimization across both pre-training and post-training stages. During pre-training, we enhance the data preprocessing pipeline and employ a three-stage data mixing strategy to strengthen the base model's reasoning potential. MiMo-7B-Base is pre-trained on 25 trillion tokens, with additional Multi-Token Prediction objective for enhanced performance and accelerated inference speed. During post-training, we curate a dataset of 130K verifiable mathematics and programming problems for reinforcement learning, integrating a test-difficulty-driven code-reward scheme to alleviate sparse-reward issues and employing strategic data resampling to stabilize training. Extensive evaluations show that MiMo-7B-Base possesses exceptional reasoning potential, outperforming even much larger 32B models. The final RL-tuned model, MiMo-7B-RL, achieves superior performance on mathematics, code and general reasoning tasks, surpassing the performance of OpenAI o1-mini. The model checkpoints are available at https://github.com/xiaomimimo/MiMo.

We introduce Confucius3-Math, an open-source large language model with 14B parameters that (1) runs efficiently on a single consumer-grade GPU; (2) achieves SOTA performances on a range of mathematical reasoning tasks, outperforming many models with significantly larger sizes. In particular, as part of our mission to enhancing education and knowledge dissemination with AI, Confucius3-Math is specifically committed to mathematics learning for Chinese K-12 students and educators. Built via post-training with large-scale reinforcement learning (RL), Confucius3-Math aligns with national curriculum and excels at solving main-stream Chinese K-12 mathematical problems with low cost. In this report we share our development recipe, the challenges we encounter and the techniques we develop to overcome them. In particular, we introduce three technical innovations: Targeted Entropy Regularization, Recent Sample Recovery and Policy-Specific Hardness Weighting. These innovations encompass a new entropy regularization, a novel data scheduling policy, and an improved group-relative advantage estimator. Collectively, they significantly stabilize the RL training, improve data efficiency, and boost performance. Our work demonstrates the feasibility of building strong reasoning models in a particular domain at low cost. We open-source our model and code at https://github.com/netease-youdao/Confucius3-Math.

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.

Recent advancements in Chain-of-Thoughts (CoT) and Program-of-Thoughts (PoT) methods have greatly enhanced language models' mathematical reasoning capabilities, facilitating their integration into instruction tuning datasets with LLMs. However, existing methods for large-scale dataset creation require substantial seed data and high computational costs for data synthesis, posing significant challenges for scalability. We introduce InfinityMATH, a scalable instruction tuning dataset for programmatic mathematical reasoning. The construction pipeline emphasizes decoupling numbers from mathematical problems to synthesize number-independent programs, enabling efficient and flexible scaling while minimizing dependency on specific numerical values. Fine-tuning experiments with open-source language and code models, such as Llama2 and CodeLlama, demonstrate the practical benefits of InfinityMATH. These fine-tuned models, showed significant relative improvements on both in-domain and out-of-domain benchmarks, ranging from 184.7% to 514.3% on average. Additionally, these models exhibited high robustness on the GSM8K+ and MATH+ benchmarks, which are enhanced version of test sets with simply the number variations. InfinityMATH ensures that models are more versatile and effective across a broader range of mathematical problems. The data is available at https://huggingface.co/datasets/flagopen/InfinityMATH.

Mathematical reasoning is a cornerstone of human intelligence and a key benchmark for advanced capabilities in large language models (LLMs). However, the research community still lacks an open, large-scale, high-quality corpus tailored to the demands of math-centric LLM pre-training. We present MegaMath, an open dataset curated from diverse, math-focused sources through following practices: (1) Revisiting web data: We re-extracted mathematical documents from Common Crawl with math-oriented HTML optimizations, fasttext-based filtering and deduplication, all for acquiring higher-quality data on the Internet. (2) Recalling Math-related code data: We identified high quality math-related code from large code training corpus, Stack-V2, further enhancing data diversity. (3) Exploring Synthetic data: We synthesized QA-style text, math-related code, and interleaved text-code blocks from web data or code data. By integrating these strategies and validating their effectiveness through extensive ablations, MegaMath delivers 371B tokens with the largest quantity and top quality among existing open math pre-training datasets.