Daily Papers

The Instruction Following (IF) ability measures how well Multi-modal Large Language Models (MLLMs) understand exactly what users are telling them and whether they are doing it right. Existing multimodal instruction following training data is scarce, the benchmarks are simple with atomic instructions, and the evaluation strategies are imprecise for tasks demanding exact output constraints. To address this, we present MM-IFEngine, an effective pipeline to generate high-quality image-instruction pairs. Our MM-IFEngine pipeline yields large-scale, diverse, and high-quality training data MM-IFInstruct-23k, which is suitable for Supervised Fine-Tuning (SFT) and extended as MM-IFDPO-23k for Direct Preference Optimization (DPO). We further introduce MM-IFEval, a challenging and diverse multi-modal instruction-following benchmark that includes (1) both compose-level constraints for output responses and perception-level constraints tied to the input images, and (2) a comprehensive evaluation pipeline incorporating both rule-based assessment and judge model. We conduct SFT and DPO experiments and demonstrate that fine-tuning MLLMs on MM-IFInstruct-23k and MM-IFDPO-23k achieves notable gains on various IF benchmarks, such as MM-IFEval (+10.2%), MIA (+7.6%), and IFEval (+12.3%). The full data and evaluation code will be released on https://github.com/SYuan03/MM-IFEngine.

Large language models can produce creative and diverse responses. However, to integrate them into current developer workflows, it is essential to constrain their outputs to follow specific formats or standards. In this work, we surveyed 51 experienced industry professionals to understand the range of scenarios and motivations driving the need for output constraints from a user-centered perspective. We identified 134 concrete use cases for constraints at two levels: low-level, which ensures the output adhere to a structured format and an appropriate length, and high-level, which requires the output to follow semantic and stylistic guidelines without hallucination. Critically, applying output constraints could not only streamline the currently repetitive process of developing, testing, and integrating LLM prompts for developers, but also enhance the user experience of LLM-powered features and applications. We conclude with a discussion on user preferences and needs towards articulating intended constraints for LLMs, alongside an initial design for a constraint prototyping tool.

Instruction-following made modern large language models (LLMs) helpful assistants. However, the key to taming LLMs on complex instructions remains mysterious, for that there are huge gaps between models trained by open-source community and those trained by leading companies. To bridge the gap, we propose a simple and scalable approach UltraIF for building LLMs that can follow complex instructions with open-source data. UltraIF first decomposes real-world user prompts into simpler queries, constraints, and corresponding evaluation questions for the constraints. Then, we train an UltraComposer to compose constraint-associated prompts with evaluation questions. This prompt composer allows us to synthesize complicated instructions as well as filter responses with evaluation questions. In our experiment, for the first time, we successfully align LLaMA-3.1-8B-Base to catch up with its instruct version on 5 instruction-following benchmarks without any benchmark information, using only 8B model as response generator and evaluator. The aligned model also achieved competitive scores on other benchmarks. Moreover, we also show that UltraIF could further improve LLaMA-3.1-8B-Instruct through self-alignment, motivating broader use cases for the method. Our code will be available at https://github.com/kkk-an/UltraIF.

Recent LLMs have shown remarkable success in following user instructions, yet handling instructions with multiple constraints remains a significant challenge. In this work, we introduce WildIFEval - a large-scale dataset of 12K real user instructions with diverse, multi-constraint conditions. Unlike prior datasets, our collection spans a broad lexical and topical spectrum of constraints, in natural user prompts. We categorize these constraints into eight high-level classes to capture their distribution and dynamics in real-world scenarios. Leveraging WildIFEval, we conduct extensive experiments to benchmark the instruction-following capabilities of leading LLMs. Our findings reveal that all evaluated models experience performance degradation with an increasing number of constraints. Thus, we show that all models have a large room for improvement on such tasks. Moreover, we observe that the specific type of constraint plays a critical role in model performance. We release our dataset to promote further research on instruction-following under complex, realistic conditions.

The ability to follow instructions is crucial for Large Language Models (LLMs) to handle various real-world applications. Existing benchmarks primarily focus on evaluating pure response quality, rather than assessing whether the response follows constraints stated in the instruction. To fill this research gap, in this paper, we propose FollowBench, a Multi-level Fine-grained Constraints Following Benchmark for LLMs. FollowBench comprehensively includes five different types (i.e., Content, Situation, Style, Format, and Example) of fine-grained constraints. To enable a precise constraint following estimation on diverse difficulties, we introduce a Multi-level mechanism that incrementally adds a single constraint to the initial instruction at each increased level. To assess whether LLMs' outputs have satisfied every individual constraint, we propose to prompt strong LLMs with constraint-evolution paths to handle challenging open-ended instructions. By evaluating ten closed-source and open-source popular LLMs on FollowBench, we highlight the weaknesses of LLMs in instruction following and point towards potential avenues for future work. The data and code are publicly available at https://github.com/YJiangcm/FollowBench.

Instruction following evaluates large language models (LLMs) on their ability to generate outputs that adhere to user-defined constraints. However, existing benchmarks often rely on templated constraint prompts, which lack the diversity of real-world usage and limit fine-grained performance assessment. To fill this gap, we propose a multi-dimensional constraint framework encompassing three constraint patterns, four constraint categories, and four difficulty levels. Building on this framework, we develop an automated instruction generation pipeline that performs constraint expansion, conflict detection, and instruction rewriting, yielding 1,200 code-verifiable instruction-following test samples. We evaluate 19 LLMs across seven model families and uncover substantial variation in performance across constraint forms. For instance, average performance drops from 77.67% at Level I to 32.96% at Level IV. Furthermore, we demonstrate the utility of our approach by using it to generate data for reinforcement learning, achieving substantial gains in instruction following without degrading general performance. In-depth analysis indicates that these gains stem primarily from modifications in the model's attention modules parameters, which enhance constraint recognition and adherence. Code and data are available in https://github.com/Junjie-Ye/MulDimIF.

This paper presents DWIE, the 'Deutsche Welle corpus for Information Extraction', a newly created multi-task dataset that combines four main Information Extraction (IE) annotation subtasks: (i) Named Entity Recognition (NER), (ii) Coreference Resolution, (iii) Relation Extraction (RE), and (iv) Entity Linking. DWIE is conceived as an entity-centric dataset that describes interactions and properties of conceptual entities on the level of the complete document. This contrasts with currently dominant mention-driven approaches that start from the detection and classification of named entity mentions in individual sentences. Further, DWIE presented two main challenges when building and evaluating IE models for it. First, the use of traditional mention-level evaluation metrics for NER and RE tasks on entity-centric DWIE dataset can result in measurements dominated by predictions on more frequently mentioned entities. We tackle this issue by proposing a new entity-driven metric that takes into account the number of mentions that compose each of the predicted and ground truth entities. Second, the document-level multi-task annotations require the models to transfer information between entity mentions located in different parts of the document, as well as between different tasks, in a joint learning setting. To realize this, we propose to use graph-based neural message passing techniques between document-level mention spans. Our experiments show an improvement of up to 5.5 F1 percentage points when incorporating neural graph propagation into our joint model. This demonstrates DWIE's potential to stimulate further research in graph neural networks for representation learning in multi-task IE. We make DWIE publicly available at https://github.com/klimzaporojets/DWIE.

We propose DepR, a depth-guided single-view scene reconstruction framework that integrates instance-level diffusion within a compositional paradigm. Instead of reconstructing the entire scene holistically, DepR generates individual objects and subsequently composes them into a coherent 3D layout. Unlike previous methods that use depth solely for object layout estimation during inference and therefore fail to fully exploit its rich geometric information, DepR leverages depth throughout both training and inference. Specifically, we introduce depth-guided conditioning to effectively encode shape priors into diffusion models. During inference, depth further guides DDIM sampling and layout optimization, enhancing alignment between the reconstruction and the input image. Despite being trained on limited synthetic data, DepR achieves state-of-the-art performance and demonstrates strong generalization in single-view scene reconstruction, as shown through evaluations on both synthetic and real-world datasets.

It is crucial for large language models (LLMs) to follow instructions that involve multiple constraints. However, it is an unexplored area to enhance LLMs' ability to follow soft constraints. To bridge the gap, we initially design a pipeline to construct datasets with high-quality outputs automatically. Additionally, to fully utilize the positive and negative samples generated during the data construction process, we choose Direct Preference Optimization (DPO) as the training method. Furthermore, taking into account the difficulty of soft constraints indicated by the number of constraints, we design a curriculum learning training paradigm based on the constraint quantity. We experimentally evaluate the effectiveness of our methods in improving LLMs' soft constraint following ability and analyze the factors driving the improvements.The datasets and code are publicly available at https://github.com/Rainier-rq/FollowSoftConstraint.

Large Language Models (LLMs) have demonstrated advanced capabilities in real-world agentic applications. Growing research efforts aim to develop LLM-based agents to address practical demands, introducing a new challenge: agentic scenarios often involve lengthy instructions with complex constraints, such as extended system prompts and detailed tool specifications. While adherence to such instructions is crucial for agentic applications, whether LLMs can reliably follow them remains underexplored. In this paper, we introduce AgentIF, the first benchmark for systematically evaluating LLM instruction following ability in agentic scenarios. AgentIF features three key characteristics: (1) Realistic, constructed from 50 real-world agentic applications. (2) Long, averaging 1,723 words with a maximum of 15,630 words. (3) Complex, averaging 11.9 constraints per instruction, covering diverse constraint types, such as tool specifications and condition constraints. To construct AgentIF, we collect 707 human-annotated instructions across 50 agentic tasks from industrial application agents and open-source agentic systems. For each instruction, we annotate the associated constraints and corresponding evaluation metrics, including code-based evaluation, LLM-based evaluation, and hybrid code-LLM evaluation. We use AgentIF to systematically evaluate existing advanced LLMs. We observe that current models generally perform poorly, especially in handling complex constraint structures and tool specifications. We further conduct error analysis and analytical experiments on instruction length and meta constraints, providing some findings about the failure modes of existing LLMs. We have released the code and data to facilitate future research.

Twenty-seven years ago, E. Freuder highlighted that "Constraint programming represents one of the closest approaches computer science has yet made to the Holy Grail of programming: the user states the problem, the computer solves it". Nowadays, CP users have great modeling tools available (like Minizinc and CPMpy), allowing them to formulate the problem and then let a solver do the rest of the job, getting closer to the stated goal. However, this still requires the CP user to know the formalism and respect it. Another significant challenge lies in the expertise required to effectively model combinatorial problems. All this limits the wider adoption of CP. In this position paper, we investigate a possible approach to leverage pre-trained Large Language Models to extract models from textual problem descriptions. More specifically, we take inspiration from the Natural Language Processing for Optimization (NL4OPT) challenge and present early results with a decomposition-based prompting approach to GPT Models.

Text generation under constraints have seen increasing interests in natural language processing, especially with the rapidly improving capabilities of large language models. However, existing benchmarks for constrained generation usually focus on fixed constraint types (e.g.,generate a sentence containing certain words) that have proved to be easy for state-of-the-art models like GPT-4. We present COLLIE, a grammar-based framework that allows the specification of rich, compositional constraints with diverse generation levels (word, sentence, paragraph, passage) and modeling challenges (e.g.,language understanding, logical reasoning, counting, semantic planning). We also develop tools for automatic extraction of task instances given a constraint structure and a raw text corpus. Using COLLIE, we compile the COLLIE-v1 dataset with 2080 instances comprising 13 constraint structures. We perform systematic experiments across five state-of-the-art instruction-tuned language models and analyze their performances to reveal shortcomings. COLLIE is designed to be extensible and lightweight, and we hope the community finds it useful to develop more complex constraints and evaluations in the future.

Human cognition exhibits systematic compositionality, the algebraic ability to generate infinite novel combinations from finite learned components, which is the key to understanding and reasoning about complex logic. In this work, we investigate the compositionality of large language models (LLMs) in mathematical reasoning. Specifically, we construct a new dataset MathTrap by introducing carefully designed logical traps into the problem descriptions of MATH and GSM8K. Since problems with logical flaws are quite rare in the real world, these represent "unseen" cases to LLMs. Solving these requires the models to systematically compose (1) the mathematical knowledge involved in the original problems with (2) knowledge related to the introduced traps. Our experiments show that while LLMs possess both components of requisite knowledge, they do not spontaneously combine them to handle these novel cases. We explore several methods to mitigate this deficiency, such as natural language prompts, few-shot demonstrations, and fine-tuning. Additionally, we test the recently released OpenAI o1 model and find that human-like `slow thinking' helps improve the compositionality of LLMs. Overall, systematic compositionality remains an open challenge for large language models.

Existing large language models (LLMs) face challenges of following complex instructions, especially when multiple constraints are present and organized in paralleling, chaining, and branching structures. One intuitive solution, namely chain-of-thought (CoT), is expected to universally improve capabilities of LLMs. However, we find that the vanilla CoT exerts a negative impact on performance due to its superficial reasoning pattern of simply paraphrasing the instructions. It fails to peel back the compositions of constraints for identifying their relationship across hierarchies of types and dimensions. To this end, we propose a systematic method to boost LLMs in dealing with complex instructions via incentivizing reasoning for test-time compute scaling. First, we stem from the decomposition of complex instructions under existing taxonomies and propose a reproducible data acquisition method. Second, we exploit reinforcement learning (RL) with verifiable rule-centric reward signals to cultivate reasoning specifically for instruction following. We address the shallow, non-essential nature of reasoning under complex instructions via sample-wise contrast for superior CoT enforcement. We also exploit behavior cloning of experts to facilitate steady distribution shift from fast-thinking LLMs to skillful reasoners. Extensive evaluations on seven comprehensive benchmarks confirm the validity of the proposed method, where a 1.5B LLM achieves 11.74% gains with performance comparable to a 8B LLM. Codes and data are available at https://github.com/yuleiqin/RAIF.

Code generation, symbolic math reasoning, and other tasks require LLMs to produce outputs that are both syntactically and semantically correct. Constrained LLM generation is a promising direction to enforce adherence to formal grammar, but prior works have empirically observed that strict enforcement of formal constraints often diminishes the reasoning capabilities of LLMs. In this work, we first provide a theoretical explanation for why constraining LLM outputs to very restrictive grammars that only allow syntactically valid final answers reduces the reasoning capabilities of the model. Second, we demonstrate that by augmenting the output grammar with carefully designed additional rules, it is always possible to preserve the reasoning capabilities of the LLM while ensuring syntactic and semantic correctness in its outputs. Building on these theoretical insights, we propose a reasoning-augmented constrained decoding algorithm, CRANE, which effectively balances the correctness of constrained generation with the flexibility of unconstrained generation. Experiments on multiple open-source LLMs and benchmarks show that CRANE significantly outperforms both state-of-the-art constrained decoding strategies and standard unconstrained decoding, showing up to 10% points accuracy improvement over baselines on challenging symbolic reasoning benchmarks GSM-symbolic and FOLIO.

Recent progress in o1-like models has significantly enhanced the reasoning abilities of Large Language Models (LLMs), empowering them to tackle increasingly complex tasks through reflection capabilities, such as making assumptions, backtracking, and self-refinement. However, effectively evaluating such reflection capabilities remains challenging due to the lack of appropriate benchmarks. To bridge this gap, we introduce LR^2Bench, a novel benchmark designed to evaluate the Long-chain Reflective Reasoning capabilities of LLMs. LR^2Bench comprises 850 samples across six Constraint Satisfaction Problems (CSPs) where reflective reasoning is crucial for deriving solutions that meet all given constraints. Each type of task focuses on distinct constraint patterns, such as knowledge-based, logical, and spatial constraints, providing a comprehensive evaluation of diverse problem-solving scenarios. We conduct extensive evaluation on both conventional models and o1-like models. Our experimental results reveal that even the most advanced reasoning-specific models, such as DeepSeek-R1 and OpenAI o1-preview, struggle with tasks in LR^2Bench, achieving an average Exact Match score of only 20.0% and 23.6%, respectively. These findings underscore the significant room for improvement in the reflective reasoning capabilities of current LLMs. The leaderboard of our benchmark is available at https://huggingface.co/spaces/UltraRonin/LR2Bench

Generative Adversarial Networks (GANs) struggle to generate structured objects like molecules and game maps. The issue is that structured objects must satisfy hard requirements (e.g., molecules must be chemically valid) that are difficult to acquire from examples alone. As a remedy, we propose Constrained Adversarial Networks (CANs), an extension of GANs in which the constraints are embedded into the model during training. This is achieved by penalizing the generator proportionally to the mass it allocates to invalid structures. In contrast to other generative models, CANs support efficient inference of valid structures (with high probability) and allows to turn on and off the learned constraints at inference time. CANs handle arbitrary logical constraints and leverage knowledge compilation techniques to efficiently evaluate the disagreement between the model and the constraints. Our setup is further extended to hybrid logical-neural constraints for capturing very complex constraints, like graph reachability. An extensive empirical analysis shows that CANs efficiently generate valid structures that are both high-quality and novel.

Rule-based reasoning, a fundamental type of legal reasoning, enables us to draw conclusions by accurately applying a rule to a set of facts. We explore causal language models as rule-based reasoners, specifically with respect to compositional rules - rules consisting of multiple elements which form a complex logical expression. Reasoning about compositional rules is challenging because it requires multiple reasoning steps, and attending to the logical relationships between elements. We introduce a new prompting method, Chain of Logic, which elicits rule-based reasoning through decomposition (solving elements as independent threads of logic), and recomposition (recombining these sub-answers to resolve the underlying logical expression). This method was inspired by the IRAC (Issue, Rule, Application, Conclusion) framework, a sequential reasoning approach used by lawyers. We evaluate chain of logic across eight rule-based reasoning tasks involving three distinct compositional rules from the LegalBench benchmark and demonstrate it consistently outperforms other prompting methods, including chain of thought and self-ask, using open-source and commercial language models.

Deep Generative Models (DGMs) have been shown to be powerful tools for generating tabular data, as they have been increasingly able to capture the complex distributions that characterize them. However, to generate realistic synthetic data, it is often not enough to have a good approximation of their distribution, as it also requires compliance with constraints that encode essential background knowledge on the problem at hand. In this paper, we address this limitation and show how DGMs for tabular data can be transformed into Constrained Deep Generative Models (C-DGMs), whose generated samples are guaranteed to be compliant with the given constraints. This is achieved by automatically parsing the constraints and transforming them into a Constraint Layer (CL) seamlessly integrated with the DGM. Our extensive experimental analysis with various DGMs and tasks reveals that standard DGMs often violate constraints, some exceeding 95% non-compliance, while their corresponding C-DGMs are never non-compliant. Then, we quantitatively demonstrate that, at training time, C-DGMs are able to exploit the background knowledge expressed by the constraints to outperform their standard counterparts with up to 6.5% improvement in utility and detection. Further, we show how our CL does not necessarily need to be integrated at training time, as it can be also used as a guardrail at inference time, still producing some improvements in the overall performance of the models. Finally, we show that our CL does not hinder the sample generation time of the models.

Recently, multi-aspect controllable text generation that controls the generated text in multiple aspects (e.g., sentiment, topic, and keywords) has attracted increasing attention. Although methods based on parameter efficient tuning like prefix-tuning could achieve multi-aspect controlling in a plug-and-play way, the mutual interference of multiple prefixes leads to significant degeneration of constraints and limits their extensibility to training-time unseen aspect combinations. In this work, we provide a theoretical lower bound for the interference and empirically found that the interference grows with the number of layers where prefixes are inserted. Based on these analyses, we propose using trainable gates to normalize the intervention of prefixes to restrain the growing interference. As a result, controlling training-time unseen combinations of aspects can be realized by simply concatenating corresponding plugins such that new constraints can be extended at a lower cost. In addition, we propose a unified way to process both categorical and free-form constraints. Experiments on text generation and machine translation demonstrate the superiority of our approach over baselines on constraint accuracy, text quality, and extensibility.

We present a new method for large language models to solve compositional tasks. Although they have shown strong performance on traditional language understanding tasks, large language models struggle to solve compositional tasks, where the solution depends on solving smaller instances of the same problem. We propose a natural approach to solve compositional tasks recursively. Our method, Re-Tuning, tunes models to break down a problem into subproblems, solve those subproblems, and combine the results. We show that our method significantly improves model performance on three representative compositional tasks: integer addition, dynamic programming, and parity. Compared to state-of-the-art methods that keep intermediate steps towards solving the problems, Re-Tuning achieves significantly higher accuracy and is more GPU memory efficient.

The drive for predictable LLM reasoning in their integration with compound systems has popularized structured outputs, yet concerns remain about performance trade-offs compared to unconstrained natural language. At the same time, training on unconstrained Chain of Thought (CoT) traces has brought about a new class of strong reasoning models that nevertheless present novel compute budget and faithfulness challenges. This paper introduces iSelf-Discover, an instance-level adaptation of the Self-Discover framework, and using it compares dynamically generated structured JSON reasoning with its unstructured counterpart. Our empirical evaluation across diverse benchmarks using state-of-the-art open-source models supports a consistent advantage for unstructured reasoning. Notably, on the complex MATH benchmark, unstructured plans achieved relative performance improvements of up to 18.90\% over structured approaches. Zero-shot unstructured iSelf-Discover variants are also shown to outperform their five-shot structured counterparts, underscoring the significance of this gap, even when structured plans are dynamically generated to ensure reasoning precedes the final answer. We further demonstrate that the optimal granularity of plan generation (instance-level vs. task-level) is context-dependent. These findings invite re-evaluation of the reliance on structured formats for complex problem-solving and how compound systems should be organized.

We present a novel approach to formalise and solve search-based problems using large language models, which significantly improves upon previous state-of-the-art results. We demonstrate the efficacy of this approach on the logic puzzles benchmark ZebraLogicBench. Instead of letting the LLM attempt to directly solve the puzzles, our method prompts the model to formalise the problem in a logic-focused domain-specific language (DSL) called Logic.py. This formalised representation is then solved using a constraint solver, leveraging the strengths of both the language model and the solver. Our approach achieves a remarkable 65% absolute improvement over the baseline performance of Llama 3.1 70B on ZebraLogicBench, setting a new state-of-the-art with an accuracy of over 90%. This significant advancement demonstrates the potential of combining language models with domain-specific languages and auxiliary tools on traditionally challenging tasks for LLMs.

While large language models (LLMs) have exhibited impressive instruction-following capabilities, it is still unclear whether and to what extent they can respond to explicit constraints that might be entailed in various instructions. As a significant aspect of LLM alignment, it is thus important to formulate such a specialized set of instructions as well as investigate the resulting behavior of LLMs. To address this vacancy, we propose a new benchmark CoDI-Eval to systematically and comprehensively evaluate LLMs' responses to instructions with various constraints. We construct a large collection of constraints-attributed instructions as a test suite focused on both generalization and coverage. Specifically, we advocate an instruction diversification process to synthesize diverse forms of constraint expression and also deliberate the candidate task taxonomy with even finer-grained sub-categories. Finally, we automate the entire evaluation process to facilitate further developments. Different from existing studies on controllable text generation, CoDI-Eval extends the scope to the prevalent instruction-following paradigm for the first time. We provide extensive evaluations of representative LLMs (e.g., ChatGPT, Vicuna) on CoDI-Eval, revealing their limitations in following instructions with specific constraints and there is still a significant gap between open-source and commercial closed-source LLMs. We believe this benchmark will facilitate research into improving the controllability of LLMs' responses to instructions. Our data and code are available at https://github.com/Xt-cyh/CoDI-Eval.

Numerous real-world decision-making problems can be formulated and solved using Mixed-Integer Linear Programming (MILP) models. However, the transformation of these problems into MILP models heavily relies on expertise in operations research and mathematical optimization, which restricts non-experts' accessibility to MILP. To address this challenge, we propose a framework for automatically formulating MILP models from unstructured natural language descriptions of decision problems, which integrates Large Language Models (LLMs) and mathematical modeling techniques. This framework consists of three phases: i) identification of decision variables, ii) classification of objective and constraints, and iii) finally, generation of MILP models. In this study, we present a constraint classification scheme and a set of constraint templates that can guide the LLMs in synthesizing a complete MILP model. After fine-tuning LLMs, our approach can identify and synthesize logic constraints in addition to classic demand and resource constraints. The logic constraints have not been studied in existing work. To evaluate the performance of the proposed framework, we extend the NL4Opt dataset with more problem descriptions and constraint types, and with the new dataset, we compare our framework with one-step model generation methods offered by LLMs. The experimental results reveal that with respect to the accuracies of generating the correct model, objective, and constraints, our method which integrates constraint classification and templates with LLMs significantly outperforms the others. The prototype system that we developed has a great potential to capture more constraints for more complex MILPs. It opens up opportunities for developing training tools for operations research practitioners and has the potential to be a powerful tool for automatic decision problem modeling and solving in practice.

We consider the problem of eliciting compositional generalization capabilities in large language models (LLMs) with a novel type of prompting strategy. Compositional generalization empowers the LLMs to solve problems that are harder than the ones they have seen (i.e., easy-to-hard generalization), which is a critical reasoning capability of human-like intelligence. However, even the current state-of-the-art LLMs still struggle with this form of reasoning. To bridge this gap, we propose skills-in-context (SKiC) prompting, which instructs LLMs how to compose basic skills to resolve more complex problems. We find that it is crucial to demonstrate both the skills and the compositional examples within the same prompting context. With as few as two examplars, our SKiC prompting initiates strong synergies between skills and their composition capabilities. Notably, it empowers LLMs to solve unseen problems that require innovative skill compositions, achieving near-perfect generalization on a broad range of challenging compositionality tasks. Intriguingly, SKiC prompting unlocks the latent potential of LLMs, enabling them to leverage pre-existing internal skills acquired during earlier pre-training stages, even when these skills are not explicitly presented in the prompting context. This results in the capability of LLMs to solve unseen complex problems by activating and composing internal competencies. With such prominent features, SKiC prompting is able to achieve state-of-the-art performance on challenging mathematical reasoning benchmarks (e.g., MATH).

Large Language Models (LLMs) excel at generating fluent text but struggle to enforce external constraints because they generate tokens sequentially without explicit control mechanisms. GenCP addresses this limitation by combining LLM predictions with Constraint Programming (CP) reasoning, formulating text generation as a Constraint Satisfaction Problem (CSP). In this paper, we improve GenCP by integrating Masked Language Models (MLMs) for domain generation, which allows bidirectional constraint propagation that leverages both past and future tokens. This integration bridges the gap between token-level prediction and structured constraint enforcement, leading to more reliable and constraint-aware text generation. Our evaluation on COLLIE benchmarks demonstrates that incorporating domain preview via MLM calls significantly improves GenCP's performance. Although this approach incurs additional MLM calls and, in some cases, increased backtracking, the overall effect is a more efficient use of LLM inferences and an enhanced ability to generate feasible and meaningful solutions, particularly in tasks with strict content constraints.

Program synthesis is challenging largely because of the difficulty of search in a large space of programs. Human programmers routinely tackle the task of writing complex programs by writing sub-programs and then analyzing their intermediate results to compose them in appropriate ways. Motivated by this intuition, we present a new synthesis approach that leverages learning to guide a bottom-up search over programs. In particular, we train a model to prioritize compositions of intermediate values during search conditioned on a given set of input-output examples. This is a powerful combination because of several emergent properties. First, in bottom-up search, intermediate programs can be executed, providing semantic information to the neural network. Second, given the concrete values from those executions, we can exploit rich features based on recent work on property signatures. Finally, bottom-up search allows the system substantial flexibility in what order to generate the solution, allowing the synthesizer to build up a program from multiple smaller sub-programs. Overall, our empirical evaluation finds that the combination of learning and bottom-up search is remarkably effective, even with simple supervised learning approaches. We demonstrate the effectiveness of our technique on two datasets, one from the SyGuS competition and one of our own creation.

Instruction following is one of the fundamental capabilities of large language models (LLMs). As the ability of LLMs is constantly improving, they have been increasingly applied to deal with complex human instructions in real-world scenarios. Therefore, how to evaluate the ability of complex instruction-following of LLMs has become a critical research problem. Existing benchmarks mainly focus on modeling different types of constraints in human instructions while neglecting the composition of different constraints, which is an indispensable constituent in complex instructions. To this end, we propose ComplexBench, a benchmark for comprehensively evaluating the ability of LLMs to follow complex instructions composed of multiple constraints. We propose a hierarchical taxonomy for complex instructions, including 4 constraint types, 19 constraint dimensions, and 4 composition types, and manually collect a high-quality dataset accordingly. To make the evaluation reliable, we augment LLM-based evaluators with rules to effectively verify whether generated texts can satisfy each constraint and composition. Furthermore, we obtain the final evaluation score based on the dependency structure determined by different composition types. ComplexBench identifies significant deficiencies in existing LLMs when dealing with complex instructions with multiple constraints composition.

This paper introduces an approach for learning to solve continuous constraint satisfaction problems (CCSP) in robotic reasoning and planning. Previous methods primarily rely on hand-engineering or learning generators for specific constraint types and then rejecting the value assignments when other constraints are violated. By contrast, our model, the compositional diffusion continuous constraint solver (Diffusion-CCSP) derives global solutions to CCSPs by representing them as factor graphs and combining the energies of diffusion models trained to sample for individual constraint types. Diffusion-CCSP exhibits strong generalization to novel combinations of known constraints, and it can be integrated into a task and motion planner to devise long-horizon plans that include actions with both discrete and continuous parameters. Project site: https://diffusion-ccsp.github.io/

Real-world instructions with multiple constraints pose a significant challenge to existing large language models (LLMs). An observation is that the LLMs exhibit dramatic performance fluctuation when disturbing the order of the incorporated constraints. Yet, none of the existing works has systematically investigated this position bias problem in the field of multi-constraint instruction following. To bridge this gap, we design a probing task where we quantitatively measure the difficulty distribution of the constraints by a novel Difficulty Distribution Index (CDDI). Through the experimental results, we find that LLMs are more performant when presented with the constraints in a ``hard-to-easy'' order. This preference can be generalized to LLMs with different architecture or different sizes of parameters. Additionally, we conduct an explanation study, providing an intuitive insight into the correlation between the LLM's attention and constraint orders. Our code and dataset are publicly available at https://github.com/meowpass/PBIF.

Large Language Models (LLMs) prompted to generate chain-of-thought (CoT) exhibit impressive reasoning capabilities. Recent attempts at prompt decomposition toward solving complex, multi-step reasoning problems depend on the ability of the LLM to simultaneously decompose and solve the problem. A significant disadvantage is that foundational LLMs are typically not available for fine-tuning, making adaptation computationally prohibitive. We believe (and demonstrate) that problem decomposition and solution generation are distinct capabilites, better addressed in separate modules, than by one monolithic LLM. We introduce DaSLaM, which uses a decomposition generator to decompose complex problems into subproblems that require fewer reasoning steps. These subproblems are answered by a solver. We use a relatively small (13B parameters) LM as the decomposition generator, which we train using policy gradient optimization to interact with a solver LM (regarded as black-box) and guide it through subproblems, thereby rendering our method solver-agnostic. Evaluation on multiple different reasoning datasets reveal that with our method, a 175 billion parameter LM (text-davinci-003) can produce competitive or even better performance, compared to its orders-of-magnitude larger successor, GPT-4. Additionally, we show that DaSLaM is not limited by the solver's capabilities as a function of scale; e.g., solver LMs with diverse sizes give significant performance improvement with our solver-agnostic decomposition technique. Exhaustive ablation studies evince the superiority of our modular finetuning technique over exorbitantly large decomposer LLMs, based on prompting alone.

Many complex tasks can be decomposed into simpler, independent parts. Discovering such underlying compositional structure has the potential to enable compositional generalization. Despite progress, our most powerful systems struggle to compose flexibly. It therefore seems natural to make models more modular to help capture the compositional nature of many tasks. However, it is unclear under which circumstances modular systems can discover hidden compositional structure. To shed light on this question, we study a teacher-student setting with a modular teacher where we have full control over the composition of ground truth modules. This allows us to relate the problem of compositional generalization to that of identification of the underlying modules. In particular we study modularity in hypernetworks representing a general class of multiplicative interactions. We show theoretically that identification up to linear transformation purely from demonstrations is possible without having to learn an exponential number of module combinations. We further demonstrate empirically that under the theoretically identified conditions, meta-learning from finite data can discover modular policies that generalize compositionally in a number of complex environments.

Transformer large language models (LLMs) have sparked admiration for their exceptional performance on tasks that demand intricate multi-step reasoning. Yet, these models simultaneously show failures on surprisingly trivial problems. This begs the question: Are these errors incidental, or do they signal more substantial limitations? In an attempt to demystify Transformers, we investigate the limits of these models across three representative compositional tasks -- multi-digit multiplication, logic grid puzzles, and a classic dynamic programming problem. These tasks require breaking problems down into sub-steps and synthesizing these steps into a precise answer. We formulate compositional tasks as computation graphs to systematically quantify the level of complexity, and break down reasoning steps into intermediate sub-procedures. Our empirical findings suggest that Transformers solve compositional tasks by reducing multi-step compositional reasoning into linearized subgraph matching, without necessarily developing systematic problem-solving skills. To round off our empirical study, we provide theoretical arguments on abstract multi-step reasoning problems that highlight how Transformers' performance will rapidly decay with increased task complexity.

Large Language Models are powerful tools for program synthesis and advanced auto-completion, but come with no guarantee that their output code is syntactically correct. This paper contributes an incremental parser that allows early rejection of syntactically incorrect code, as well as efficient detection of complete programs for fill-in-the-middle (FIM) tasks. We extend the Earley parsing algorithm to allow for left and right quotients of context-free grammars, and develop methods to handle quotienting of several context-sensitive features present in the grammars of many common programming languages. The result of these contributions is an efficient, general, and well-grounded method for left and right quotient parsing. To validate our theoretical contributions -- and the effectiveness of certain design decisions -- we evaluate our method on the particularly difficult case of FIM completion for Python 3, with syntax-correctness constraints. Our results demonstrate that constrained generation can significantly reduce the incidence of syntax errors in recommended code.

We automate deep step-by step reasoning in an LLM dialog thread by recursively exploring alternatives (OR-nodes) and expanding details (AND-nodes) up to a given depth. Starting from a single succinct task-specific initiator we steer the automated dialog thread to stay focussed on the task by synthesizing a prompt that summarizes the depth-first steps taken so far. Our algorithm is derived from a simple recursive descent implementation of a Horn Clause interpreter, except that we accommodate our logic engine to fit the natural language reasoning patterns LLMs have been trained on. Semantic similarity to ground-truth facts or oracle advice from another LLM instance is used to restrict the search space and validate the traces of justification steps returned as answers. At the end, the unique minimal model of a generated Horn Clause program collects the results of the reasoning process. As applications, we sketch implementations of consequence predictions, causal explanations, recommendation systems and topic-focussed exploration of scientific literature.

Recently, a large amount of work has focused on improving large language models' (LLMs') performance on reasoning benchmarks such as math and logic. However, past work has largely assumed that tasks are well-defined. In the real world, queries to LLMs are often underspecified, only solvable through acquiring missing information. We formalize this as a constraint satisfaction problem (CSP) with missing variable assignments. Using a special case of this formalism where only one necessary variable assignment is missing, we can rigorously evaluate an LLM's ability to identify the minimal necessary question to ask and quantify axes of difficulty levels for each problem. We present QuestBench, a set of underspecified reasoning tasks solvable by asking at most one question, which includes: (1) Logic-Q: Logical reasoning tasks with one missing proposition, (2) Planning-Q: PDDL planning problems with initial states that are partially-observed, (3) GSM-Q: Human-annotated grade school math problems with one missing variable assignment, and (4) GSME-Q: a version of GSM-Q where word problems are translated into equations by human annotators. The LLM is tasked with selecting the correct clarification question(s) from a list of options. While state-of-the-art models excel at GSM-Q and GSME-Q, their accuracy is only 40-50% on Logic-Q and Planning-Q. Analysis demonstrates that the ability to solve well-specified reasoning problems may not be sufficient for success on our benchmark: models have difficulty identifying the right question to ask, even when they can solve the fully specified version of the problem. Furthermore, in the Planning-Q domain, LLMs tend not to hedge, even when explicitly presented with the option to predict ``not sure.'' This highlights the need for deeper investigation into models' information acquisition capabilities.

Large Language Models (LLMs) struggle to directly generate correct plans for complex multi-constraint planning problems, even with self-verification and self-critique. For example, a U.S. domestic travel planning benchmark TravelPlanner was proposed in Xie et al. (2024), where the best LLM OpenAI o1-preview can only find viable travel plans with a 10% success rate given all needed information. In this work, we tackle this by proposing an LLM-based planning framework that formalizes and solves complex multi-constraint planning problems as constrained satisfiability problems, which are further consumed by sound and complete satisfiability solvers. We start with TravelPlanner as the primary use case and show that our framework achieves a success rate of 93.9% and is effective with diverse paraphrased prompts. More importantly, our framework has strong zero-shot generalizability, successfully handling unseen constraints in our newly created unseen international travel dataset and generalizing well to new fundamentally different domains. Moreover, when user input queries are infeasible, our framework can identify the unsatisfiable core, provide failure reasons, and offers personalized modification suggestions. We show that our framework can modify and solve for an average of 81.6% and 91.7% unsatisfiable queries from two datasets and prove with ablations that all key components of our framework are effective and necessary. Project page: https://sites.google.com/view/llm-rwplanning.

When writing programs, people have the ability to tackle a new complex task by decomposing it into smaller and more familiar subtasks. While it is difficult to measure whether neural program synthesis methods have similar capabilities, we can measure whether they compositionally generalize, that is, whether a model that has been trained on the simpler subtasks is subsequently able to solve more complex tasks. In this paper, we characterize several different forms of compositional generalization that are desirable in program synthesis, forming a meta-benchmark which we use to create generalization tasks for two popular datasets, RobustFill and DeepCoder. We then propose ExeDec, a novel decomposition-based synthesis strategy that predicts execution subgoals to solve problems step-by-step informed by program execution at each step. ExeDec has better synthesis performance and greatly improved compositional generalization ability compared to baselines.

Temporal reasoning and planning are essential capabilities for large language models (LLMs), yet most existing benchmarks evaluate them in isolation and under limited forms of complexity. To address this gap, we introduce the Temporal Constraint-based Planning (TCP) benchmark, that jointly assesses both capabilities. Each instance in TCP features a naturalistic dialogue around a collaborative project, where diverse and interdependent temporal constraints are explicitly or implicitly expressed, and models must infer an optimal schedule that satisfies all constraints. To construct TCP, we first generate abstract problem prototypes that are paired with realistic scenarios from various domains and enriched into dialogues using an LLM. A human quality check is performed on a sampled subset to confirm the reliability of our benchmark. We evaluate state-of-the-art LLMs and find that even the strongest models struggle with TCP, highlighting its difficulty and revealing limitations in LLMs' temporal constraint-based planning abilities. We analyze underlying failure cases, open source our benchmark, and hope our findings can inspire future research.

It is common in graphic design humans visually arrange various elements according to their design intent and semantics. For example, a title text almost always appears on top of other elements in a document. In this work, we generate graphic layouts that can flexibly incorporate such design semantics, either specified implicitly or explicitly by a user. We optimize using the latent space of an off-the-shelf layout generation model, allowing our approach to be complementary to and used with existing layout generation models. Our approach builds on a generative layout model based on a Transformer architecture, and formulates the layout generation as a constrained optimization problem where design constraints are used for element alignment, overlap avoidance, or any other user-specified relationship. We show in the experiments that our approach is capable of generating realistic layouts in both constrained and unconstrained generation tasks with a single model. The code is available at https://github.com/ktrk115/const_layout .

Instruction following is a key capability for LLMs. However, recent studies have shown that LLMs often struggle with instructions containing multiple constraints (e.g. a request to create a social media post "in a funny tone" with "no hashtag"). Despite this, most evaluations focus solely on synthetic data. To address this, we introduce RealInstruct, the first benchmark designed to evaluate LLMs' ability to follow real-world multi-constrained instructions by leveraging queries real users asked AI assistants. We also investigate model-based evaluation as a cost-effective alternative to human annotation for this task. Our findings reveal that even the proprietary GPT-4 model fails to meet at least one constraint on over 21% of instructions, highlighting the limitations of state-of-the-art models. To address the performance gap between open-source and proprietary models, we propose the Decompose, Critique and Refine (DeCRIM) self-correction pipeline, which enhances LLMs' ability to follow constraints. DeCRIM works by decomposing the original instruction into a list of constraints and using a Critic model to decide when and where the LLM's response needs refinement. Our results show that DeCRIM improves Mistral's performance by 7.3% on RealInstruct and 8.0% on IFEval even with weak feedback. Moreover, we demonstrate that with strong feedback, open-source LLMs with DeCRIM can outperform GPT-4 on both benchmarks.

Statutory reasoning is the task of determining whether a legal statute, stated in natural language, applies to the text description of a case. Prior work introduced a resource that approached statutory reasoning as a monolithic textual entailment problem, with neural baselines performing nearly at-chance. To address this challenge, we decompose statutory reasoning into four types of language-understanding challenge problems, through the introduction of concepts and structure found in Prolog programs. Augmenting an existing benchmark, we provide annotations for the four tasks, and baselines for three of them. Models for statutory reasoning are shown to benefit from the additional structure, improving on prior baselines. Further, the decomposition into subtasks facilitates finer-grained model diagnostics and clearer incremental progress.

Foundational models with billions of parameters which have been trained on large corpora of data have demonstrated non-trivial skills in a variety of domains. However, due to their monolithic structure, it is challenging and expensive to augment them or impart new skills. On the other hand, due to their adaptation abilities, several new instances of these models are being trained towards new domains and tasks. In this work, we study the problem of efficient and practical composition of existing foundation models with more specific models to enable newer capabilities. To this end, we propose CALM -- Composition to Augment Language Models -- which introduces cross-attention between models to compose their representations and enable new capabilities. Salient features of CALM are: (i) Scales up LLMs on new tasks by 're-using' existing LLMs along with a few additional parameters and data, (ii) Existing model weights are kept intact, and hence preserves existing capabilities, and (iii) Applies to diverse domains and settings. We illustrate that augmenting PaLM2-S with a smaller model trained on low-resource languages results in an absolute improvement of up to 13\% on tasks like translation into English and arithmetic reasoning for low-resource languages. Similarly, when PaLM2-S is augmented with a code-specific model, we see a relative improvement of 40\% over the base model for code generation and explanation tasks -- on-par with fully fine-tuned counterparts.

Reasoning-enhanced large language models (RLLMs), whether explicitly trained for reasoning or prompted via chain-of-thought (CoT), have achieved state-of-the-art performance on many complex reasoning tasks. However, we uncover a surprising and previously overlooked phenomenon: explicit CoT reasoning can significantly degrade instruction-following accuracy. Evaluating 15 models on two benchmarks: IFEval (with simple, rule-verifiable constraints) and ComplexBench (with complex, compositional constraints), we consistently observe performance drops when CoT prompting is applied. Through large-scale case studies and an attention-based analysis, we identify common patterns where reasoning either helps (e.g., with formatting or lexical precision) or hurts (e.g., by neglecting simple constraints or introducing unnecessary content). We propose a metric, constraint attention, to quantify model focus during generation and show that CoT reasoning often diverts attention away from instruction-relevant tokens. To mitigate these effects, we introduce and evaluate four strategies: in-context learning, self-reflection, self-selective reasoning, and classifier-selective reasoning. Our results demonstrate that selective reasoning strategies, particularly classifier-selective reasoning, can substantially recover lost performance. To our knowledge, this is the first work to systematically expose reasoning-induced failures in instruction-following and offer practical mitigation strategies.

LLMs have demonstrated commendable performance across diverse domains. Nevertheless, formulating high-quality prompts to assist them in their work poses a challenge for non-AI experts. Existing research in prompt engineering suggests somewhat scattered optimization principles and designs empirically dependent prompt optimizers. Unfortunately, these endeavors lack a structural design, incurring high learning costs and it is not conducive to the iterative updating of prompts, especially for non-AI experts. Inspired by structured reusable programming languages, we propose LangGPT, a structural prompt design framework. Furthermore, we introduce Minstrel, a multi-generative agent system with reflection to automate the generation of structural prompts. Experiments and the case study illustrate that structural prompts generated by Minstrel or written manually significantly enhance the performance of LLMs. Furthermore, we analyze the ease of use of structural prompts through a user survey in our online community.

User alignment is crucial for adapting general-purpose language models (LMs) to downstream tasks, but human annotations are often not available for all types of instructions, especially those with customized constraints. We observe that user instructions typically contain constraints. While assessing response quality in terms of the whole instruction is often costly, efficiently evaluating the satisfaction rate of constraints is feasible. We investigate common constraints in NLP tasks, categorize them into three classes based on the types of their arguments, and propose a unified framework, ACT (Aligning to ConsTraints), to automatically produce supervision signals for user alignment with constraints. Specifically, ACT uses constraint verifiers, which are typically easy to implement in practice, to compute constraint satisfaction rate (CSR) of each response. It samples multiple responses for each prompt and collect preference labels based on their CSR automatically. Subsequently, ACT adapts the LM to the target task through a ranking-based learning process. Experiments on fine-grained entity typing, abstractive summarization, and temporal question answering show that ACT is able to enhance LMs' capability to adhere to different classes of constraints, thereby improving task performance. Further experiments show that the constraint-following capabilities are transferable.

While large language models (LLMs) have recently demonstrated strong potential in solving planning problems, there is a trade-off between flexibility and complexity. LLMs, as zero-shot planners themselves, are still not capable of directly generating valid plans for complex planning problems such as multi-constraint or long-horizon tasks. On the other hand, many frameworks aiming to solve complex planning problems often rely on task-specific preparatory efforts, such as task-specific in-context examples and pre-defined critics/verifiers, which limits their cross-task generalization capability. In this paper, we tackle these challenges by observing that the core of many planning problems lies in optimization problems: searching for the optimal solution (best plan) with goals subject to constraints (preconditions and effects of decisions). With LLMs' commonsense, reasoning, and programming capabilities, this opens up the possibilities of a universal LLM-based approach to planning problems. Inspired by this observation, we propose LLMFP, a general-purpose framework that leverages LLMs to capture key information from planning problems and formally formulate and solve them as optimization problems from scratch, with no task-specific examples needed. We apply LLMFP to 9 planning problems, ranging from multi-constraint decision making to multi-step planning problems, and demonstrate that LLMFP achieves on average 83.7% and 86.8% optimal rate across 9 tasks for GPT-4o and Claude 3.5 Sonnet, significantly outperforming the best baseline (direct planning with OpenAI o1-preview) with 37.6% and 40.7% improvements. We also validate components of LLMFP with ablation experiments and analyzed the underlying success and failure reasons.

A common approach for teaching large language models (LLMs) to reason is to train on chain-of-thought (CoT) traces of in-distribution reasoning problems, but such annotated data is costly to obtain for every problem of interest. We want reasoning models to generalize beyond their training distribution, and ideally to generalize compositionally: combine atomic reasoning skills to solve harder, unseen reasoning tasks. We take a step towards compositional generalization of reasoning skills when addressing a target compositional task that has no labeled CoT data. We find that simply training models on CoT data of atomic tasks leads to limited generalization, but minimally modifying CoT formats of constituent atomic tasks to be composable can lead to improvements. We can train "atomic CoT" models on the atomic tasks with Composable CoT data and combine them with multitask learning or model merging for better zero-shot performance on the target compositional task. Such a combined model can be further bootstrapped on a small amount of compositional data using rejection sampling fine-tuning (RFT). Results on string operations and natural language skill compositions show that training LLMs on Composable CoT outperforms multitask learning and continued fine-tuning baselines within a given training data budget.

Chain-of-Thought (CoT) prompting enhances the reasoning of large language models (LLMs) by decomposing problems into sequential steps, mimicking human logic and reducing errors. However, complex tasks with vast solution spaces and vague constraints often exceed the capacity of a single reasoning chain. Inspired by Minimal Free Resolution (MFR) in commutative algebra and algebraic geometry, we propose Syzygy of Thoughts (SoT)-a novel framework that extends CoT by introducing auxiliary, interrelated reasoning paths. SoT captures deeper logical dependencies, enabling more robust and structured problem-solving. MFR decomposes a module into a sequence of free modules with minimal rank, providing a structured analytical approach to complex systems. This method introduces the concepts of "Module", "Betti numbers","Freeness", "Mapping", "Exactness" and "Minimality", enabling the systematic decomposition of the original complex problem into logically complete minimal subproblems while preserving key problem features and reducing reasoning length. We tested SoT across diverse datasets (e.g., GSM8K, MATH) and models (e.g., GPT-4o-mini, Qwen2.5), achieving inference accuracy that matches or surpasses mainstream CoTs standards. Additionally, by aligning the sampling process with algebraic constraints, our approach enhances the scalability of inference time in LLMs, ensuring both transparent reasoning and high performance. Our code will be publicly available at https://github.com/dlMARiA/Syzygy-of-thoughts.

Recent video question answering benchmarks indicate that state-of-the-art models struggle to answer compositional questions. However, it remains unclear which types of compositional reasoning cause models to mispredict. Furthermore, it is difficult to discern whether models arrive at answers using compositional reasoning or by leveraging data biases. In this paper, we develop a question decomposition engine that programmatically deconstructs a compositional question into a directed acyclic graph of sub-questions. The graph is designed such that each parent question is a composition of its children. We present AGQA-Decomp, a benchmark containing 2.3M question graphs, with an average of 11.49 sub-questions per graph, and 4.55M total new sub-questions. Using question graphs, we evaluate three state-of-the-art models with a suite of novel compositional consistency metrics. We find that models either cannot reason correctly through most compositions or are reliant on incorrect reasoning to reach answers, frequently contradicting themselves or achieving high accuracies when failing at intermediate reasoning steps.

There is growing interest in utilizing large language models (LLMs) as co-pilots for combinatorial optimization and constraint programming tasks across various problems. This paper aims to advance this line of research by introducing Text2Zinc}, a cross-domain dataset for capturing optimization and satisfaction problems specified in natural language text. Our work is distinguished from previous attempts by integrating both satisfaction and optimization problems within a unified dataset using a solver-agnostic modeling language. To achieve this, we leverage MiniZinc's solver-and-paradigm-agnostic modeling capabilities to formulate these problems. Using the Text2Zinc dataset, we conduct comprehensive baseline experiments to compare execution and solution accuracy across several methods, including off-the-shelf prompting strategies, chain-of-thought reasoning, and a compositional approach. Additionally, we explore the effectiveness of intermediary representations, specifically knowledge graphs. Our findings indicate that LLMs are not yet a push-button technology to model combinatorial problems from text. We hope that Text2Zinc serves as a valuable resource for researchers and practitioners to advance the field further.

We present our position on the elusive quest for a general-purpose framework for specifying and studying deep learning architectures. Our opinion is that the key attempts made so far lack a coherent bridge between specifying constraints which models must satisfy and specifying their implementations. Focusing on building a such a bridge, we propose to apply category theory -- precisely, the universal algebra of monads valued in a 2-category of parametric maps -- as a single theory elegantly subsuming both of these flavours of neural network design. To defend our position, we show how this theory recovers constraints induced by geometric deep learning, as well as implementations of many architectures drawn from the diverse landscape of neural networks, such as RNNs. We also illustrate how the theory naturally encodes many standard constructs in computer science and automata theory.

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.

We introduce a pattern mining framework that operates on semi-structured datasets and exploits the dichotomy between outcomes. Our approach takes advantage of constraint reasoning to find sequential patterns that occur frequently and exhibit desired properties. This allows the creation of novel pattern embeddings that are useful for knowledge extraction and predictive modeling. Finally, we present an application on customer intent prediction from digital clickstream data. Overall, we show that pattern embeddings play an integrator role between semi-structured data and machine learning models, improve the performance of the downstream task and retain interpretability.

Interpretability or explainability is an emerging research field in NLP. From a user-centric point of view, the goal is to build models that provide proper justification for their decisions, similar to those of humans, by requiring the models to satisfy additional constraints. To this end, we introduce a new application on legal text where, contrary to mainstream literature targeting word-level rationales, we conceive rationales as selected paragraphs in multi-paragraph structured court cases. We also release a new dataset comprising European Court of Human Rights cases, including annotations for paragraph-level rationales. We use this dataset to study the effect of already proposed rationale constraints, i.e., sparsity, continuity, and comprehensiveness, formulated as regularizers. Our findings indicate that some of these constraints are not beneficial in paragraph-level rationale extraction, while others need re-formulation to better handle the multi-label nature of the task we consider. We also introduce a new constraint, singularity, which further improves the quality of rationales, even compared with noisy rationale supervision. Experimental results indicate that the newly introduced task is very challenging and there is a large scope for further research.

We investigate the ability of language models to perform compositional reasoning tasks where the overall solution depends on correctly composing the answers to sub-problems. We measure how often models can correctly answer all sub-problems but not generate the overall solution, a ratio we call the compositionality gap. We evaluate this ratio by asking multi-hop questions with answers that require composing multiple facts unlikely to have been observed together during pretraining. In the GPT-3 family of models, as model size increases we show that the single-hop question answering performance improves faster than the multi-hop performance does, therefore the compositionality gap does not decrease. This surprising result suggests that while more powerful models memorize and recall more factual knowledge, they show no corresponding improvement in their ability to perform this kind of compositional reasoning. We then demonstrate how elicitive prompting (such as chain of thought) narrows the compositionality gap by reasoning explicitly instead of implicitly. We present a new method, self-ask, that further improves on chain of thought. In our method, the model explicitly asks itself (and then answers) follow-up questions before answering the initial question. We finally show that self-ask's structured prompting lets us easily plug in a search engine to answer the follow-up questions, which additionally improves accuracy.

Large language models have demonstrated outstanding performance on a wide range of tasks such as question answering and code generation. On a high level, given an input, a language model can be used to automatically complete the sequence in a statistically-likely way. Based on this, users prompt these models with language instructions or examples, to implement a variety of downstream tasks. Advanced prompting methods can even imply interaction between the language model, a user, and external tools such as calculators. However, to obtain state-of-the-art performance or adapt language models for specific tasks, complex task- and model-specific programs have to be implemented, which may still require ad-hoc interaction. Based on this, we present the novel idea of Language Model Programming (LMP). LMP generalizes language model prompting from pure text prompts to an intuitive combination of text prompting and scripting. Additionally, LMP allows constraints to be specified over the language model output. This enables easy adaption to many tasks while abstracting language model internals and providing high-level semantics. To enable LMP, we implement LMQL(short for Language Model Query Language), which leverages the constraints and control flow from an LMP prompt to generate an efficient inference procedure that minimizes the number of expensive calls to the underlying language model. We show that LMQL can capture a wide range of state-of-the-art prompting methods in an intuitive way, especially facilitating interactive flows that are challenging to implement with existing high-level APIs. Our evaluation shows that we retain or increase the accuracy on several downstream tasks, while also significantly reducing the required amount of computation or cost in the case of pay-to-use APIs (26-85% cost savings).

Large language models (LLMs) can perform complex reasoning in few- and zero-shot settings by generating intermediate chain of thought (CoT) reasoning steps. Further, each reasoning step can rely on external tools to support computation beyond the core LLM capabilities (e.g. search/running code). Prior work on CoT prompting and tool use typically requires hand-crafting task-specific demonstrations and carefully scripted interleaving of model generations with tool use. We introduce Automatic Reasoning and Tool-use (ART), a framework that uses frozen LLMs to automatically generate intermediate reasoning steps as a program. Given a new task to solve, ART selects demonstrations of multi-step reasoning and tool use from a task library. At test time, ART seamlessly pauses generation whenever external tools are called, and integrates their output before resuming generation. ART achieves a substantial improvement over few-shot prompting and automatic CoT on unseen tasks in the BigBench and MMLU benchmarks, and matches performance of hand-crafted CoT prompts on a majority of these tasks. ART is also extensible, and makes it easy for humans to improve performance by correcting errors in task-specific programs or incorporating new tools, which we demonstrate by drastically improving performance on select tasks with minimal human intervention.

Recent advances in language model (LM) agents and function calling have enabled autonomous, feedback-driven systems to solve problems across various digital domains. To better understand the unique limitations of LM agents, we introduce RefactorBench, a benchmark consisting of 100 large handcrafted multi-file refactoring tasks in popular open-source repositories. Solving tasks within RefactorBench requires thorough exploration of dependencies across multiple files and strong adherence to relevant instructions. Every task is defined by 3 natural language instructions of varying specificity and is mutually exclusive, allowing for the creation of longer combined tasks on the same repository. Baselines on RefactorBench reveal that current LM agents struggle with simple compositional tasks, solving only 22% of tasks with base instructions, in contrast to a human developer with short time constraints solving 87%. Through trajectory analysis, we identify various unique failure modes of LM agents, and further explore the failure mode of tracking past actions. By adapting a baseline agent to condition on representations of state, we achieve a 43.9% improvement in solving RefactorBench tasks. We further extend our state-aware approach to encompass entire digital environments and outline potential directions for future research. RefactorBench aims to support the study of LM agents by providing a set of real-world, multi-hop tasks within the realm of code.

Circuits based on sum-product structure have become a ubiquitous representation to compactly encode knowledge, from Boolean functions to probability distributions. By imposing constraints on the structure of such circuits, certain inference queries become tractable, such as model counting and most probable configuration. Recent works have explored analyzing probabilistic and causal inference queries as compositions of basic operators to derive tractability conditions. In this paper, we take an algebraic perspective for compositional inference, and show that a large class of queries - including marginal MAP, probabilistic answer set programming inference, and causal backdoor adjustment - correspond to a combination of basic operators over semirings: aggregation, product, and elementwise mapping. Using this framework, we uncover simple and general sufficient conditions for tractable composition of these operators, in terms of circuit properties (e.g., marginal determinism, compatibility) and conditions on the elementwise mappings. Applying our analysis, we derive novel tractability conditions for many such compositional queries. Our results unify tractability conditions for existing problems on circuits, while providing a blueprint for analysing novel compositional inference queries.

We enhance the calculus of string diagrams for monoidal categories with hierarchical features in order to capture closed monoidal (and cartesian closed) structure. Using this new syntax we formulate an automatic differentiation algorithm for (applied) simply typed lambda calculus in the style of [Pearlmutter and Siskind 2008] and we prove for the first time its soundness. To give an efficient yet principled implementation of the AD algorithm we define a sound and complete representation of hierarchical string diagrams as a class of hierarchical hypergraphs we call hypernets.

Large Language Models (LLMs) have demonstrated remarkable general capabilities, but enhancing skills such as reasoning often demands substantial computational resources and may compromise their generalization. While Parameter-Efficient Fine-Tuning (PEFT) methods offer a more resource-conscious alternative, they typically requires retraining for each LLM backbone due to architectural dependencies. To address these challenges, here we propose Universal Reasoner (UniR) - a single, lightweight, composable, and plug-and-play reasoning module that can be used with any frozen LLM to endow it with specialized reasoning capabilities. Specifically, UniR decomposes the reward into a standalone reasoning module that is trained independently using predefined rewards, effectively translating trajectory-level signals into token-level guidance. Once trained, UniR can be combined with any frozen LLM at inference time by simply adding its output logits to those of the LLM backbone. This additive structure naturally enables modular composition: multiple UniR modules trained for different tasks can be jointly applied by summing their logits, enabling complex reasoning via composition. Experimental results on mathematical reasoning and machine translation tasks show that UniR significantly outperforms existing baseline fine-tuning methods using the Llama3.2 model. Furthermore, UniR demonstrates strong weak-to-strong generalization: reasoning modules trained on smaller models effectively guide much larger LLMs. This makes UniR a cost-efficient, adaptable, and robust solution for enhancing reasoning in LLMs without compromising their core capabilities. Code is open-sourced at https://github.com/hangeol/UniR

Solving complex mathematical problems via system-2 reasoning is a natural human skill, yet it remains a significant challenge for current large language models (LLMs). We identify the scarcity of deliberate multi-step reasoning data as a primary limiting factor. To this end, we introduce Enriched Instruction Tuning (EIT), a method that enriches existing human-annotated mathematical datasets by synergizing human and AI feedback to create fine-grained reasoning trajectories. These datasets are then used to fine-tune open-source LLMs, enhancing their mathematical reasoning abilities without reliance on any symbolic verification program. Concretely, EIT is composed of two critical steps: Enriching with Reasoning Plan (ERP) and Enriching with Reasoning Step (ERS). The former generates a high-level plan that breaks down complex instructions into a sequence of simpler objectives, while ERS fills in reasoning contexts often overlooked by human annotators, creating a smoother reasoning trajectory for LLM fine-tuning. Unlike existing CoT prompting methods that generate reasoning chains only depending on LLM's internal knowledge, our method leverages human-annotated initial answers as ``meta-knowledge'' to help LLMs generate more detailed and precise reasoning processes, leading to a more trustworthy LLM expert for complex mathematical problems. In experiments, EIT achieves an accuracy of 84.1% on GSM8K and 32.5% on MATH, surpassing state-of-the-art fine-tuning and prompting methods, and even matching the performance of tool-augmented methods.

Causal reasoning and compositional reasoning are two core aspirations in generative AI. Measuring the extent of these behaviors requires principled evaluation methods. We explore a unified perspective that considers both behaviors simultaneously, termed compositional causal reasoning (CCR): the ability to infer how causal measures compose and, equivalently, how causal quantities propagate through graphs. We instantiate a framework for the systematic evaluation of CCR for the average treatment effect and the probability of necessity and sufficiency. As proof of concept, we demonstrate the design of CCR tasks for language models in the LLama, Phi, and GPT families. On a math word problem, our framework revealed a range of taxonomically distinct error patterns. Additionally, CCR errors increased with the complexity of causal paths for all models except o1.

Among the most important properties of algorithms investigated in computer science are soundness, completeness, and complexity. These properties, however, are rarely analyzed for the vast collection of recently proposed methods for planning with large language models. In this work, we alleviate this gap. We analyse these properties of using LLMs for planning and highlight that recent trends abandon both soundness and completeness for the sake of inefficiency. We propose a significantly more efficient approach that can, at the same time, maintain both soundness and completeness. We exemplify on four representative search problems, comparing to the LLM-based solutions from the literature that attempt to solve these problems. We show that by using LLMs to produce the code for the search components we can solve the entire datasets with 100\% accuracy with only a few calls to the LLM. We argue for a responsible use of compute resources; urging research community to investigate sound and complete LLM-based approaches that uphold efficiency.

Language models (LMs) can perform complex reasoning either end-to-end, with hidden latent state, or compositionally, with transparent intermediate state. Composition offers benefits for interpretability and safety, but may need workflow support and infrastructure to remain competitive. We describe iterated decomposition, a human-in-the-loop workflow for developing and refining compositional LM programs. We improve the performance of compositions by zooming in on failing components and refining them through decomposition, additional context, chain of thought, etc. To support this workflow, we develop ICE, an open-source tool for visualizing the execution traces of LM programs. We apply iterated decomposition to three real-world tasks and improve the accuracy of LM programs over less compositional baselines: describing the placebo used in a randomized controlled trial (25% to 65%), evaluating participant adherence to a medical intervention (53% to 70%), and answering NLP questions on the Qasper dataset (38% to 69%). These applications serve as case studies for a workflow that, if automated, could keep ML systems interpretable and safe even as they scale to increasingly complex tasks.

Large Language Models (LLMs) are nowadays expected to generate content aligned with human preferences. Current work focuses on alignment at model training time, through techniques such as Reinforcement Learning with Human Feedback (RLHF). However, it is unclear if such methods are an effective choice to teach alignment objectives to the model. First, the inability to incorporate multiple, custom rewards and reliance on a model developer's view of universal and static principles are key limitations. Second, the residual gaps in model training and the reliability of such approaches are also questionable (e.g. susceptibility to jail-breaking even after safety training). To address these, we propose DeAL, a framework that allows the user to customize reward functions and enables Decoding-time Alignment of LLMs (DeAL). At its core, we view decoding as a heuristic-guided search process and facilitate the use of a wide variety of alignment objectives. Our experiments with programmatic constraints such as keyword and length constraints (studied widely in the pre-LLM era) and abstract objectives such as harmlessness and helpfulness (proposed in the post-LLM era) show that we can DeAL with fine-grained trade-offs, improve adherence to alignment objectives, and address residual gaps in LLMs. Lastly, while DeAL can be effectively paired with RLHF and prompting techniques, its generality makes decoding slower, an optimization we leave for future work.

Recent advances in artificial intelligence (AI) have produced highly capable and controllable systems. This creates unprecedented opportunities for structured reasoning as well as collaboration among multiple AI systems and humans. To fully realize this potential, it is essential to develop a principled way of designing and studying such structured interactions. For this purpose, we introduce the conceptual framework of Flows: a systematic approach to modeling complex interactions. Flows are self-contained building blocks of computation, with an isolated state, communicating through a standardized message-based interface. This modular design allows Flows to be recursively composed into arbitrarily nested interactions, with a substantial reduction of complexity. Crucially, any interaction can be implemented using this framework, including prior work on AI--AI and human--AI interactions, prompt engineering schemes, and tool augmentation. We demonstrate the potential of Flows on the task of competitive coding, a challenging task on which even GPT-4 struggles. Our results suggest that structured reasoning and collaboration substantially improve generalization, with AI-only Flows adding +21 and human--AI Flows adding +54 absolute points in terms of solve rate. To support rapid and rigorous research, we introduce the aiFlows library. The library comes with a repository of Flows that can be easily used, extended, and composed into novel, more complex Flows. The aiFlows library is available at https://github.com/epfl-dlab/aiflows. Data and Flows for reproducing our experiments are available at https://github.com/epfl-dlab/cc_flows.

We investigate the logical reasoning capabilities of large language models (LLMs) and their scalability in complex non-monotonic reasoning. To this end, we introduce ZebraLogic, a comprehensive evaluation framework for assessing LLM reasoning performance on logic grid puzzles derived from constraint satisfaction problems (CSPs). ZebraLogic enables the generation of puzzles with controllable and quantifiable complexity, facilitating a systematic study of the scaling limits of models such as Llama, o1 models, and DeepSeek-R1. By encompassing a broad range of search space complexities and diverse logical constraints, ZebraLogic provides a structured environment to evaluate reasoning under increasing difficulty. Our results reveal a significant decline in accuracy as problem complexity grows -- a phenomenon we term the curse of complexity. This limitation persists even with larger models and increased inference-time computation, suggesting inherent constraints in current LLM reasoning capabilities. Additionally, we explore strategies to enhance logical reasoning, including Best-of-N sampling, backtracking mechanisms, and self-verification prompts. Our findings offer critical insights into the scalability of LLM reasoning, highlight fundamental limitations, and outline potential directions for improvement.

The ability of large language models to solve complex mathematical problems has progressed significantly, particularly for tasks requiring advanced reasoning. However, the scarcity of sufficiently challenging problems, particularly at the Olympiad level, hinders further advancements. In this work, we introduce PromptCoT, a novel approach for automatically generating high-quality Olympiad-level math problems. The proposed method synthesizes complex problems based on mathematical concepts and the rationale behind problem construction, emulating the thought processes of experienced problem designers. We provide a theoretical analysis demonstrating that an optimal rationale should maximize both the likelihood of rationale generation given the associated concepts and the likelihood of problem generation conditioned on both the rationale and the concepts. Our method is evaluated on standard benchmarks including GSM8K, MATH-500, and AIME2024, where it consistently outperforms existing problem generation methods. Furthermore, we demonstrate that PromptCoT exhibits superior data scalability, consistently maintaining high performance as the dataset size increases, outperforming the baselines. The implementation is available at https://github.com/zhaoxlpku/PromptCoT.

With advances in foundational and vision-language models, and effective fine-tuning techniques, a large number of both general and special-purpose models have been developed for a variety of visual tasks. Despite the flexibility and accessibility of these models, no single model is able to handle all tasks and/or applications that may be envisioned by potential users. Recent approaches, such as visual programming and multimodal LLMs with integrated tools aim to tackle complex visual tasks, by way of program synthesis. However, such approaches overlook user constraints (e.g., performance / computational needs), produce test-time sample-specific solutions that are difficult to deploy, and, sometimes, require low-level instructions that maybe beyond the abilities of a naive user. To address these limitations, we introduce MMFactory, a universal framework that includes model and metrics routing components, acting like a solution search engine across various available models. Based on a task description and few sample input-output pairs and (optionally) resource and/or performance constraints, MMFactory can suggest a diverse pool of programmatic solutions by instantiating and combining visio-lingual tools from its model repository. In addition to synthesizing these solutions, MMFactory also proposes metrics and benchmarks performance / resource characteristics, allowing users to pick a solution that meets their unique design constraints. From the technical perspective, we also introduced a committee-based solution proposer that leverages multi-agent LLM conversation to generate executable, diverse, universal, and robust solutions for the user. Experimental results show that MMFactory outperforms existing methods by delivering state-of-the-art solutions tailored to user problem specifications. Project page is available at https://davidhalladay.github.io/mmfactory_demo.

Exploiting large language models (LLMs) to tackle deductive reasoning has garnered growing attention. It still remains highly challenging to achieve satisfactory results in complex deductive problems, characterized by plenty of premises (i.e., facts or rules) entailing intricate relationships among entities and requiring multi-hop reasoning. One intuitive solution is to decompose the original task into smaller sub-tasks, and then chain the multiple casual reasoning steps together in a forward (e.g., Selection-Inference) or backward (e.g., LAMBADA) direction. However, these techniques inevitably necessitate a large number of overall stages, leading to computationally expensive operations and a higher possibility of making misleading steps. In addition to stage-by-stage decomposition, we draw inspiration from another aspect of human problem-solving. Humans tend to distill the most relevant information and organize their thoughts systematically (e.g., creating mind maps), which assists them in answering questions or drawing conclusions precisely and quickly. In light of this, we propose a novel reasoning approach named Concise and Organized Perception (COP). COP carefully analyzes the given statements to efficiently identify the most pertinent information while eliminating redundancy. It then prompts the LLMs in a more organized form that adapts to the model's inference process. By perceiving concise and organized proofs, the deductive reasoning abilities of LLMs can be better elicited, and the risk of acquiring errors caused by excessive reasoning stages is mitigated. Furthermore, our approach can be combined with the aforementioned ones to further boost their performance. Extensive experimental results on three popular deductive benchmarks (i.e., ProofWriter, PrOntoQA and PrOntoQA-OOD) show that COP significantly outperforms previous state-of-the-art methods.

The derivation of mathematical results in specialised fields using Large Language Models (LLMs) is an emerging research direction that can help identify models' limitations, and potentially support mathematical discovery. In this paper, we leverage a symbolic engine to generate derivations of equations at scale, and investigate the capabilities of LLMs when deriving goal equations from premises. Specifically, we employ in-context learning for GPT and fine-tune a range of T5 models to compare the robustness and generalisation of pre-training strategies to specialised models. Empirical results show that fine-tuned FLAN-T5-large (MathT5) outperforms GPT models on all static and out-of-distribution test sets in terms of absolute performance. However, an in-depth analysis reveals that the fine-tuned models are more sensitive to perturbations involving unseen symbols and (to a lesser extent) changes to equation structure. In addition, we analyse 1.7K equations and over 200 derivations to highlight common reasoning errors such as the inclusion of incorrect, irrelevant, and redundant equations, along with the tendency to skip derivation steps. Finally, we explore the suitability of existing metrics for evaluating mathematical derivations finding evidence that, while they capture general properties such as sensitivity to perturbations, they fail to highlight fine-grained reasoning errors and essential differences between models. Overall, this work demonstrates that training models on synthetic data can improve their mathematical capabilities beyond larger architectures.

Constraint Programming (CP) is a declarative programming paradigm that allows for modeling and solving combinatorial optimization problems, such as the Job-Shop Scheduling Problem (JSSP). While CP solvers manage to find optimal or near-optimal solutions for small instances, they do not scale well to large ones, i.e., they require long computation times or yield low-quality solutions. Therefore, real-world scheduling applications often resort to fast, handcrafted, priority-based dispatching heuristics to find a good initial solution and then refine it using optimization methods. This paper proposes a novel end-to-end approach to solving scheduling problems by means of CP and Reinforcement Learning (RL). In contrast to previous RL methods, tailored for a given problem by including procedural simulation algorithms, complex feature engineering, or handcrafted reward functions, our neural-network architecture and training algorithm merely require a generic CP encoding of some scheduling problem along with a set of small instances. Our approach leverages existing CP solvers to train an agent learning a Priority Dispatching Rule (PDR) that generalizes well to large instances, even from separate datasets. We evaluate our method on seven JSSP datasets from the literature, showing its ability to find higher-quality solutions for very large instances than obtained by static PDRs and by a CP solver within the same time limit.

Compositional Reasoning (CR) entails grasping the significance of attributes, relations, and word order. Recent Vision-Language Models (VLMs), comprising a visual encoder and a Large Language Model (LLM) decoder, have demonstrated remarkable proficiency in such reasoning tasks. This prompts a crucial question: have VLMs effectively tackled the CR challenge? We conjecture that existing CR benchmarks may not adequately push the boundaries of modern VLMs due to the reliance on an LLM-only negative text generation pipeline. Consequently, the negatives produced either appear as outliers from the natural language distribution learned by VLMs' LLM decoders or as improbable within the corresponding image context. To address these limitations, we introduce ConMe -- a compositional reasoning benchmark and a novel data generation pipeline leveraging VLMs to produce `hard CR Q&A'. Through a new concept of VLMs conversing with each other to collaboratively expose their weaknesses, our pipeline autonomously generates, evaluates, and selects challenging compositional reasoning questions, establishing a robust CR benchmark, also subsequently validated manually. Our benchmark provokes a noteworthy, up to 33%, decrease in CR performance compared to preceding benchmarks, reinstating the CR challenge even for state-of-the-art VLMs.

Large Language Models (LLMs) have demonstrated remarkable performance in solving math problems, a hallmark of human intelligence. Despite high success rates on current benchmarks; however, these often feature simple problems with only one or two unknowns, which do not sufficiently challenge their reasoning capacities. This paper introduces a novel benchmark, BeyondX, designed to address these limitations by incorporating problems with multiple unknowns. Recognizing the challenges in proposing multi-unknown problems from scratch, we developed BeyondX using an innovative automated pipeline that progressively increases complexity by expanding the number of unknowns in simpler problems. Empirical study on BeyondX reveals that the performance of existing LLMs, even those fine-tuned specifically on math tasks, significantly decreases as the number of unknowns increases - with a performance drop of up to 70\% observed in GPT-4. To tackle these challenges, we propose the Formulate-and-Solve strategy, a generalized prompting approach that effectively handles problems with an arbitrary number of unknowns. Our findings reveal that this strategy not only enhances LLM performance on the BeyondX benchmark but also provides deeper insights into the computational limits of LLMs when faced with more complex mathematical challenges.

Large language models excel at pattern matching, yet often fall short in systematic compositional generalization. We propose the coverage principle: a data-centric framework showing that models relying primarily on pattern matching for compositional tasks cannot reliably generalize beyond substituting fragments that yield identical results when used in the same contexts. We demonstrate that this framework has a strong predictive power for the generalization capabilities of Transformers. First, we derive and empirically confirm that the training data required for two-hop generalization grows at least quadratically with the token set size, and the training data efficiency does not improve with 20x parameter scaling. Second, for compositional tasks with path ambiguity where one variable affects the output through multiple computational paths, we show that Transformers learn context-dependent state representations that undermine both performance and interoperability. Third, Chain-of-Thought supervision improves training data efficiency for multi-hop tasks but still struggles with path ambiguity. Finally, we outline a mechanism-based taxonomy that distinguishes three ways neural networks can generalize: structure-based (bounded by coverage), property-based (leveraging algebraic invariances), and shared-operator (through function reuse). This conceptual lens contextualizes our results and highlights where new architectural ideas are needed to achieve systematic compositionally. Overall, the coverage principle provides a unified lens for understanding compositional reasoning, and underscores the need for fundamental architectural or training innovations to achieve truly systematic compositionality.

Robotic agents performing domestic chores by natural language directives are required to master the complex job of navigating environment and interacting with objects in the environments. The tasks given to the agents are often composite thus are challenging as completing them require to reason about multiple subtasks, e.g., bring a cup of coffee. To address the challenge, we propose to divide and conquer it by breaking the task into multiple subgoals and attend to them individually for better navigation and interaction. We call it Multi-level Compositional Reasoning Agent (MCR-Agent). Specifically, we learn a three-level action policy. At the highest level, we infer a sequence of human-interpretable subgoals to be executed based on language instructions by a high-level policy composition controller. At the middle level, we discriminatively control the agent's navigation by a master policy by alternating between a navigation policy and various independent interaction policies. Finally, at the lowest level, we infer manipulation actions with the corresponding object masks using the appropriate interaction policy. Our approach not only generates human interpretable subgoals but also achieves 2.03% absolute gain to comparable state of the arts in the efficiency metric (PLWSR in unseen set) without using rule-based planning or a semantic spatial memory.

Complex reasoning tasks often rely on the ability to consistently and accurately apply simple rules across incremental steps, a foundational capability which we term "level-0" reasoning. To systematically evaluate this capability, we introduce L0-Bench, a language model benchmark for testing procedural correctness -- the ability to generate correct reasoning processes, complementing existing benchmarks that primarily focus on outcome correctness. Given synthetic Python functions with simple operations, L0-Bench grades models on their ability to generate step-by-step, error-free execution traces. The synthetic nature of L0-Bench enables systematic and scalable generation of test programs along various axes (e.g., number of trace steps). We evaluate a diverse array of recent closed-source and open-weight models on a baseline test set. All models exhibit degradation as the number of target trace steps increases, while larger models and reasoning-enhanced models better maintain correctness over multiple steps. Additionally, we use L0-Bench to explore test-time scaling along three dimensions: input context length, number of solutions for majority voting, and inference steps. Our results suggest substantial room to improve "level-0" reasoning and potential directions to build more reliable reasoning systems.

Constraints are critical in text generation as LLM outputs are often unreliable when it comes to ensuring generated outputs adhere to user defined instruction or general safety guidelines. To address this gap, we present Constrained Discrete Diffusion (CDD), a novel method for enforcing constraints on natural language by integrating discrete diffusion models with differentiable optimization. Unlike conventional text generators, which often rely on post-hoc filtering or model retraining for controllable generation, we propose imposing constraints directly into the discrete diffusion sampling process. We illustrate how this technique can be applied to satisfy a variety of natural language constraints, including (i) toxicity mitigation by preventing harmful content from emerging, (ii) character and sequence level lexical constraints, and (iii) novel molecule sequence generation with specific property adherence. Experimental results show that our constraint-aware procedure achieves high fidelity in meeting these requirements while preserving fluency and semantic coherence, outperforming auto-regressive and existing discrete diffusion approaches.

The meaning of complex phrases in natural language is composed of their individual components. The task of compositional generalization evaluates a model's ability to understand new combinations of components. Previous studies trained smaller, task-specific models, which exhibited poor generalization. While large language models (LLMs) exhibit impressive generalization abilities on many tasks through in-context learning (ICL), their potential for compositional generalization remains unexplored. In this paper, we first empirically investigate prevailing ICL methods in compositional generalization. We find that they struggle with complex compositional questions due to cumulative errors in long reasoning steps and intricate logic required for tool-making. Consequently, we propose a human-guided tool manipulation framework (HTM) that generates tools for sub-questions and integrates multiple tools. Our method enhances the effectiveness of tool creation and usage with minimal human effort. Experiments show that our method achieves state-of-the-art performance on two compositional generalization benchmarks and outperforms existing methods on the most challenging test split by 70%.

Mathematical reasoning presents a significant challenge for Large Language Models (LLMs) due to the extensive and precise chain of reasoning required for accuracy. Ensuring the correctness of each reasoning step is critical. To address this, we aim to enhance the robustness and factuality of LLMs by learning from human feedback. However, Direct Preference Optimization (DPO) has shown limited benefits for long-chain mathematical reasoning, as models employing DPO struggle to identify detailed errors in incorrect answers. This limitation stems from a lack of fine-grained process supervision. We propose a simple, effective, and data-efficient method called Step-DPO, which treats individual reasoning steps as units for preference optimization rather than evaluating answers holistically. Additionally, we have developed a data construction pipeline for Step-DPO, enabling the creation of a high-quality dataset containing 10K step-wise preference pairs. We also observe that in DPO, self-generated data is more effective than data generated by humans or GPT-4, due to the latter's out-of-distribution nature. Our findings demonstrate that as few as 10K preference data pairs and fewer than 500 Step-DPO training steps can yield a nearly 3% gain in accuracy on MATH for models with over 70B parameters. Notably, Step-DPO, when applied to Qwen2-72B-Instruct, achieves scores of 70.8% and 94.0% on the test sets of MATH and GSM8K, respectively, surpassing a series of closed-source models, including GPT-4-1106, Claude-3-Opus, and Gemini-1.5-Pro. Our code, data, and models are available at https://github.com/dvlab-research/Step-DPO.

While advancements in the reasoning abilities of LLMs have significantly enhanced their performance in solving mathematical problems, coding tasks, and general puzzles, their effectiveness in accurately adhering to instructions remains inconsistent, particularly with more complex directives. Our investigation identifies lazy reasoning during the thinking stage as the primary factor contributing to poor instruction adherence. To mitigate this issue, we propose a comprehensive framework designed to enable rigorous reasoning processes involving preview and self-checking, essential for satisfying strict instruction constraints. Specifically, we first generate instructions with complex constraints and apply a filtering process to obtain valid prompts, resulting in three distinct prompt datasets categorized as hard, easy, and pass. Then, we employ rejection sampling on the pass prompts to curate a small yet high-quality dataset, enabling a cold-start initialization of the model and facilitating its adaptation to effective reasoning patterns. Subsequently, we employ an entropy-preserving supervised fine-tuning (Entropy-SFT) strategy coupled with token-wise entropy-adaptive (TEA-RL) reinforcement learning guided by rule-based dense rewards. This approach encourages the model to transform its reasoning mechanism, ultimately fostering generalizable reasoning abilities that encompass preview and self-checking. Extensive experiments conducted on instruction-following benchmarks demonstrate remarkable performance improvements across various model scales. Notably, our Light-IF-32B model surpasses both larger open-source models such as DeepSeek-R1 and closed-source models like Doubao-1.6.

This paper presents a novel framework for enhancing reasoning capabilities in large language models (LLMs) by leveraging iterative reasoning and feedback-driven methodologies. Building on the limitations identified in the SimpleBench benchmark, a dataset designed to evaluate logical coherence and real-world reasoning, we propose a multi-step prompting strategy coupled with global consistency checks to improve model accuracy and robustness. Through comparative analysis of state-of-the-art models, including Claude 3 Opus, Claude 3.5, GPT- 4o, and o1-preview, we demonstrate that iterative reasoning significantly enhances model performance, with improvements observed in both standard accuracy metrics (AVG@5) and a newly introduced metric, Extreme Averaging (EAG@5). Our results reveal model-specific strengths: Claude excels in maintaining logical consistency, while GPT-4o exhibits exploratory creativity but struggles with ambiguous prompts. By analyzing case studies and identifying gaps in spatial and temporal reasoning, we highlight areas for further refinement. The findings underscore the potential of structured reasoning frameworks to address inherent model limitations, irrespective of pretraining methodologies. This study lays the groundwork for integrating dynamic feedback mechanisms, adaptive restart strategies, and diverse evaluation metrics to advance LLM reasoning capabilities across complex and multi-domain problem spaces.

Given the intractably large size of the space of proofs, any model that is capable of general deductive reasoning must generalize to proofs of greater complexity. Recent studies have shown that large language models (LLMs) possess some abstract deductive reasoning ability given chain-of-thought prompts. However, they have primarily been tested on proofs using modus ponens or of a specific size, and from the same distribution as the in-context examples. To measure the general deductive reasoning ability of LLMs, we test on a broad set of deduction rules and measure their ability to generalize to more complex proofs from simpler demonstrations from multiple angles: depth-, width-, and compositional generalization. To facilitate systematic exploration, we construct a new synthetic and programmable reasoning dataset that enables control over deduction rules and proof complexity. Our experiments on four LLMs of various sizes and training objectives show that they are able to generalize to longer and compositional proofs. However, they require explicit demonstrations to produce hypothetical subproofs, specifically in proof by cases and proof by contradiction.

Recent advancements in prompt engineering strategies, such as Chain-of-Thought (CoT) and Self-Discover, have demonstrated significant potential in improving the reasoning abilities of Large Language Models (LLMs). However, these state-of-the-art (SOTA) prompting strategies rely on single or fixed set of static seed reasoning modules like "think step by step" or "break down this problem" intended to simulate human approach to problem-solving. This constraint limits the flexibility of models in tackling diverse problems effectively. In this paper, we introduce Auto-Evolve, a novel framework that enables LLMs to self-create dynamic reasoning modules and downstream action plan, resulting in significant improvements over current SOTA methods. We evaluate Auto-Evolve on the challenging BigBench-Hard (BBH) dataset with Claude 2.0, Claude 3 Sonnet, Mistral Large, and GPT 4, where it consistently outperforms the SOTA prompt strategies. Auto-Evolve outperforms CoT by up to 10.4% and on an average by 7% across these four models. Our framework introduces two innovations: a) Auto-Evolve dynamically generates reasoning modules for each task while aligning with human reasoning paradigm, thus eliminating the need for predefined templates. b) We introduce an iterative refinement component, that incrementally refines instruction guidance for LLMs and helps boost performance by average 2.8% compared to doing it in a single step.

Automated software engineering has been greatly empowered by the recent advances in Large Language Models (LLMs) for programming. While current benchmarks have shown that LLMs can perform various software engineering tasks like human developers, the majority of their evaluations are limited to short and self-contained algorithmic tasks. Solving challenging and practical programming tasks requires the capability of utilizing diverse function calls as tools to efficiently implement functionalities like data analysis and web development. In addition, using multiple tools to solve a task needs compositional reasoning by accurately understanding complex instructions. Fulfilling both of these characteristics can pose a great challenge for LLMs. To assess how well LLMs can solve challenging and practical programming tasks, we introduce Bench, a benchmark that challenges LLMs to invoke multiple function calls as tools from 139 libraries and 7 domains for 1,140 fine-grained programming tasks. To evaluate LLMs rigorously, each programming task encompasses 5.6 test cases with an average branch coverage of 99%. In addition, we propose a natural-language-oriented variant of Bench, Benchi, that automatically transforms the original docstrings into short instructions only with essential information. Our extensive evaluation of 60 LLMs shows that LLMs are not yet capable of following complex instructions to use function calls precisely, with scores up to 60%, significantly lower than the human performance of 97%. The results underscore the need for further advancements in this area.

Large language models (LLMs) such as GPT-4 sometimes appear to be creative, solving novel tasks often with a few demonstrations in the prompt. These tasks require the models to generalize on distributions different from those from training data -- which is known as out-of-distribution (OOD) generalization. Despite the tremendous success of LLMs, how they approach OOD generalization remains an open and underexplored question. We examine OOD generalization in settings where instances are generated according to hidden rules, including in-context learning with symbolic reasoning. Models are required to infer the hidden rules behind input prompts without any fine-tuning. We empirically examined the training dynamics of Transformers on a synthetic example and conducted extensive experiments on a variety of pretrained LLMs, focusing on a type of components known as induction heads. We found that OOD generalization and composition are tied together -- models can learn rules by composing two self-attention layers, thereby achieving OOD generalization. Furthermore, a shared latent subspace in the embedding (or feature) space acts as a bridge for composition by aligning early layers and later layers, which we refer to as the common bridge representation hypothesis.

LLMs have demonstrated commendable performance across diverse domains. Nevertheless, formulating high-quality prompts to instruct LLMs proficiently poses a challenge for non-AI experts. Existing research in prompt engineering suggests somewhat scattered optimization principles and designs empirically dependent prompt optimizers. Unfortunately, these endeavors lack a structured design template, incurring high learning costs and resulting in low reusability. In addition, it is not conducive to the iterative updating of prompts. Inspired by structured reusable programming languages, we propose LangGPT, a dual-layer prompt design framework as the programming language for LLMs. LangGPT has an easy-to-learn normative structure and provides an extended structure for migration and reuse. Experiments illustrate that LangGPT significantly enhances the performance of LLMs. Moreover, the case study shows that LangGPT leads LLMs to generate higher-quality responses. Furthermore, we analyzed the ease of use and reusability of LangGPT through a user survey in our online community.

Input constraints are useful for many software development tasks. For example, input constraints of a function enable the generation of valid inputs, i.e., inputs that follow these constraints, to test the function deeper. API functions of deep learning (DL) libraries have DL specific input constraints, which are described informally in the free form API documentation. Existing constraint extraction techniques are ineffective for extracting DL specific input constraints. To fill this gap, we design and implement a new technique, DocTer, to analyze API documentation to extract DL specific input constraints for DL API functions. DocTer features a novel algorithm that automatically constructs rules to extract API parameter constraints from syntactic patterns in the form of dependency parse trees of API descriptions. These rules are then applied to a large volume of API documents in popular DL libraries to extract their input parameter constraints. To demonstrate the effectiveness of the extracted constraints, DocTer uses the constraints to enable the automatic generation of valid and invalid inputs to test DL API functions. Our evaluation on three popular DL libraries (TensorFlow, PyTorch, and MXNet) shows that the precision of DocTer in extracting input constraints is 85.4%. DocTer detects 94 bugs from 174 API functions, including one previously unknown security vulnerability that is now documented in the CVE database, while a baseline technique without input constraints detects only 59 bugs. Most (63) of the 94 bugs are previously unknown, 54 of which have been fixed or confirmed by developers after we report them. In addition, DocTer detects 43 inconsistencies in documents, 39 of which are fixed or confirmed.

Compositional visual reasoning methods, which translate a complex query into a structured composition of feasible visual tasks, have exhibited a strong potential in complicated multi-modal tasks. Empowered by recent advances in large language models (LLMs), this multi-modal challenge has been brought to a new stage by treating LLMs as few-shot/zero-shot planners, i.e., vision-language (VL) programming. Such methods, despite their numerous merits, suffer from challenges due to LLM planning mistakes or inaccuracy of visual execution modules, lagging behind the non-compositional models. In this work, we devise a "plug-and-play" method, ExoViP, to correct errors in both the planning and execution stages through introspective verification. We employ verification modules as "exoskeletons" to enhance current VL programming schemes. Specifically, our proposed verification module utilizes a mixture of three sub-verifiers to validate predictions after each reasoning step, subsequently calibrating the visual module predictions and refining the reasoning trace planned by LLMs. Experimental results on two representative VL programming methods showcase consistent improvements on five compositional reasoning tasks on standard benchmarks. In light of this, we believe that ExoViP can foster better performance and generalization on open-domain multi-modal challenges.

Despite recent success in large language model (LLM) reasoning, LLMs struggle with hierarchical multi-step reasoning tasks like generating complex programs. For these tasks, humans often start with a high-level algorithmic design and implement each part gradually. We introduce Parsel, a framework enabling automatic implementation and validation of complex algorithms with code LLMs. With Parsel, we automatically decompose algorithmic tasks into hierarchical natural language function descriptions and then search over combinations of possible function implementations using tests. We show that Parsel can be used across domains requiring hierarchical reasoning, including program synthesis and robotic planning. We find that, using Parsel, LLMs solve more competition-level problems in the APPS dataset, resulting in pass rates over 75\% higher than prior results from directly sampling AlphaCode and Codex, while often using a smaller sample budget. Moreover, with automatically generated tests, we find that Parsel can improve the state-of-the-art pass@1 performance on HumanEval from 67\% to 85\%. We also find that LLM-generated robotic plans using Parsel are more than twice as likely to be considered accurate than directly generated plans. Lastly, we explore how Parsel addresses LLM limitations and discuss how Parsel may be useful for human programmers. We release our code at https://github.com/ezelikman/parsel

A crucial factor for successful human and AI interaction is the ability of language models or chatbots to follow human instructions precisely. A common feature of instructions are output constraints like ``only answer with yes or no" or ``mention the word `abrakadabra' at least 3 times" that the user adds to craft a more useful answer. Even today's strongest models struggle with fulfilling such constraints. We find that most models strongly overfit on a small set of verifiable constraints from the benchmarks that test these abilities, a skill called precise instruction following, and are not able to generalize well to unseen output constraints. We introduce a new benchmark, IFBench, to evaluate precise instruction following generalization on 58 new, diverse, and challenging verifiable out-of-domain constraints. In addition, we perform an extensive analysis of how and on what data models can be trained to improve precise instruction following generalization. Specifically, we carefully design constraint verification modules and show that reinforcement learning with verifiable rewards (RLVR) significantly improves instruction following. In addition to IFBench, we release 29 additional new hand-annotated training constraints and verification functions, RLVR training prompts, and code.

Large Language Models (LLMs) have demonstrated impressive reasoning capabilities, yet their direct application to NP-hard combinatorial problems (CPs) remains underexplored. In this work, we systematically investigate the reasoning abilities of LLMs on a variety of NP-hard combinatorial optimization tasks and introduce ACCORD: Autoregressive Constraint-satisfying generation for COmbinatorial optimization with Routing and Dynamic attention. ACCORD features a novel dataset representation and model architecture that leverage the autoregressive nature of LLMs to dynamically enforce feasibility constraints, coupled with attention-based routing to activate problem-specific LoRA modules. We also present the ACCORD-90k supervised dataset, covering six NP-hard combinatorial problems: TSP, VRP, Knapsack, FlowShop, JSSP, and BinPacking. Extensive experiments demonstrate that our ACCORD model, built on an 8B-parameter Llama backbone, consistently outperforms standard prompting and input-output methods, even when compared to much larger LLMs, such as gpt-4. Ablation studies further show that our output structure enhances solution feasibility. To the best of our knowledge, this is the first large-scale, end-to-end framework for exploring the applications of LLMs to a broad spectrum of combinatorial optimization problems. The codes are publicly available at https://github.com/starjob42/ACCORD

Music composition represents the creative side of humanity, and itself is a complex task that requires abilities to understand and generate information with long dependency and harmony constraints. While demonstrating impressive capabilities in STEM subjects, current LLMs easily fail in this task, generating ill-written music even when equipped with modern techniques like In-Context-Learning and Chain-of-Thoughts. To further explore and enhance LLMs' potential in music composition by leveraging their reasoning ability and the large knowledge base in music history and theory, we propose ComposerX, an agent-based symbolic music generation framework. We find that applying a multi-agent approach significantly improves the music composition quality of GPT-4. The results demonstrate that ComposerX is capable of producing coherent polyphonic music compositions with captivating melodies, while adhering to user instructions.

Reasoning is a cognitive process of using evidence to reach a sound conclusion. The reasoning capability is essential for large language models (LLMs) to serve as the brain of the artificial general intelligence agent. Recent studies reveal that fine-tuning LLMs on data with the chain of thought (COT) reasoning process can significantly enhance their reasoning capabilities. However, we find that the fine-tuned LLMs suffer from an Assessment Misalignment problem, i.e., they frequently assign higher scores to subpar COTs, leading to potential limitations in their reasoning abilities. To address this problem, we introduce an Alignment Fine-Tuning (AFT) paradigm, which involves three steps: 1) fine-tuning LLMs with COT training data; 2) generating multiple COT responses for each question, and categorizing them into positive and negative ones based on whether they achieve the correct answer; 3) calibrating the scores of positive and negative responses given by LLMs with a novel constraint alignment loss. Specifically, the constraint alignment loss has two objectives: a) Alignment, which guarantees that positive scores surpass negative scores to encourage answers with high-quality COTs; b) Constraint, which keeps the negative scores confined to a reasonable range to prevent the model degradation. Beyond just the binary positive and negative feedback, the constraint alignment loss can be seamlessly adapted to the ranking situations when ranking feedback is accessible. Furthermore, we also delve deeply into recent ranking-based alignment methods, such as DPO, RRHF, and PRO, and discover that the constraint, which has been overlooked by these approaches, is also crucial for their performance. Extensive experiments on four reasoning benchmarks with both binary and ranking feedback demonstrate the effectiveness of AFT.

Chaining language model (LM) calls as composable modules is fueling a new powerful way of programming. However, ensuring that LMs adhere to important constraints remains a key challenge, one often addressed with heuristic "prompt engineering". We introduce LM Assertions, a new programming construct for expressing computational constraints that LMs should satisfy. We integrate our constructs into the recent DSPy programming model for LMs, and present new strategies that allow DSPy to compile programs with arbitrary LM Assertions into systems that are more reliable and more accurate. In DSPy, LM Assertions can be integrated at compile time, via automatic prompt optimization, and/or at inference time, via automatic selfrefinement and backtracking. We report on two early case studies for complex question answering (QA), in which the LM program must iteratively retrieve information in multiple hops and synthesize a long-form answer with citations. We find that LM Assertions improve not only compliance with imposed rules and guidelines but also enhance downstream task performance, delivering intrinsic and extrinsic gains up to 35.7% and 13.3%, respectively. Our reference implementation of LM Assertions is integrated into DSPy at https://github.com/stanfordnlp/dspy

In this paper, we present Smart Compose, a novel system for generating interactive, real-time suggestions in Gmail that assists users in writing mails by reducing repetitive typing. In the design and deployment of such a large-scale and complicated system, we faced several challenges including model selection, performance evaluation, serving and other practical issues. At the core of Smart Compose is a large-scale neural language model. We leveraged state-of-the-art machine learning techniques for language model training which enabled high-quality suggestion prediction, and constructed novel serving infrastructure for high-throughput and real-time inference. Experimental results show the effectiveness of our proposed system design and deployment approach. This system is currently being served in Gmail.

Recent generations of language models have introduced Large Reasoning Models (LRMs) that generate detailed thinking processes before providing answers. While these models demonstrate improved performance on reasoning benchmarks, their fundamental capabilities, scaling properties, and limitations remain insufficiently understood. Current evaluations primarily focus on established math and coding benchmarks, emphasizing final answer accuracy. However, this evaluation paradigm often suffers from contamination and does not provide insights into the reasoning traces. In this work, we systematically investigate these gaps with the help of controllable puzzle environments that allow precise manipulation of complexity while maintaining consistent logical structures. This setup enables the analysis of not only final answers but also the internal reasoning traces, offering insights into how LRMs think. Through extensive experiments, we show that LRMs face a complete accuracy collapse beyond certain complexities. Moreover, they exhibit a counterintuitive scaling limit: their reasoning effort increases with problem complexity up to a point, then declines despite having remaining token budget. By comparing LRMs with their standard LLM counterparts under same inference compute, we identify three performance regimes: (1) low-complexity tasks where standard models outperform LRMs, (2) medium-complexity tasks where LRMs demonstrates advantage, and (3) high-complexity tasks where both models face complete collapse. We found that LRMs have limitations in exact computation: they fail to use explicit algorithms and reason inconsistently across scales. We also investigate the reasoning traces in more depth, studying the patterns of explored solutions and analyzing the models' computational behavior, shedding light on their strengths, limitations, and raising questions about their reasoning capabilities.

Many challenging reasoning tasks require not just rapid, intuitive responses, but a more deliberate, multi-step approach. Recent progress in large language models (LLMs) highlights an important shift from the "System 1" way of quick reactions to the "System 2" style of reflection-and-correction problem solving. However, current benchmarks heavily rely on the final-answer accuracy, leaving much of a model's intermediate reasoning steps unexamined. This fails to assess the model's ability to reflect and rectify mistakes within the reasoning process. To bridge this gap, we introduce FINEREASON, a logic-puzzle benchmark for fine-grained evaluation of LLMs' reasoning capabilities. Each puzzle can be decomposed into atomic steps, making it ideal for rigorous validation of intermediate correctness. Building on this, we introduce two tasks: state checking, and state transition, for a comprehensive evaluation of how models assess the current situation and plan the next move. To support broader research, we also provide a puzzle training set aimed at enhancing performance on general mathematical tasks. We show that models trained on our state checking and transition data demonstrate gains in math reasoning by up to 5.1% on GSM8K.

Learning compositional representation is a key aspect of object-centric learning as it enables flexible systematic generalization and supports complex visual reasoning. However, most of the existing approaches rely on auto-encoding objective, while the compositionality is implicitly imposed by the architectural or algorithmic bias in the encoder. This misalignment between auto-encoding objective and learning compositionality often results in failure of capturing meaningful object representations. In this study, we propose a novel objective that explicitly encourages compositionality of the representations. Built upon the existing object-centric learning framework (e.g., slot attention), our method incorporates additional constraints that an arbitrary mixture of object representations from two images should be valid by maximizing the likelihood of the composite data. We demonstrate that incorporating our objective to the existing framework consistently improves the objective-centric learning and enhances the robustness to the architectural choices.

In this study, we introduced a new benchmark consisting of a curated dataset and a defined evaluation process to assess the compositional reasoning capabilities of large language models within the chemistry domain. We designed and validated a fully automated pipeline, verified by subject matter experts, to facilitate this task. Our approach integrates OpenAI reasoning models with named entity recognition (NER) systems to extract chemical entities from recent literature, which are then augmented with external knowledge bases to form a comprehensive knowledge graph. By generating multi-hop questions across these graphs, we assess LLM performance in both context-augmented and non-context augmented settings. Our experiments reveal that even state-of-the-art models face significant challenges in multi-hop compositional reasoning. The results reflect the importance of augmenting LLMs with document retrieval, which can have a substantial impact on improving their performance. However, even perfect retrieval accuracy with full context does not eliminate reasoning errors, underscoring the complexity of compositional reasoning. This work not only benchmarks and highlights the limitations of current LLMs but also presents a novel data generation pipeline capable of producing challenging reasoning datasets across various domains. Overall, this research advances our understanding of reasoning in computational linguistics.

In this paper, we present a novel approach, called LogicPro, to enhance Large Language Models (LLMs) complex Logical reasoning through Program Examples. We do this effectively by simply utilizing widely available algorithmic problems and their code solutions. First, we constructed diverse test samples input based on algorithmic questions and code solutions. Then, we designed different complex reasoning questions based on algorithmic problems and test samples. Finally, combining the intermediate variable outputs of the code solutions and the complex reasoning questions, we derived the reasoning process and the final answer. With this approach, we can construct a dataset that is sufficiently difficult (all models are ineffective), diverse (synthesized from 2,360 different algorithmic questions), and scalable (building different test samples and collecting more algorithmic questions). In addition, we obtain a high-quality reasoning process guided by the values of intermediate variables. As a result, our approach achieves significant improvements in multiple models for the BBH^{27}, GSM8K, HellSwag, Logicqa, Reclor, and RTE datasets, outperforming a wide range of existing reasoning datasets.

Reliably generating structured outputs has become a critical capability for modern language model (LM) applications. Constrained decoding has emerged as the dominant technology across sectors for enforcing structured outputs during generation. Despite its growing adoption, little has been done with the systematic evaluation of the behaviors and performance of constrained decoding. Constrained decoding frameworks have standardized around JSON Schema as a structured data format, with most uses guaranteeing constraint compliance given a schema. However, there is poor understanding of the effectiveness of the methods in practice. We present an evaluation framework to assess constrained decoding approaches across three critical dimensions: efficiency in generating constraint-compliant outputs, coverage of diverse constraint types, and quality of the generated outputs. To facilitate this evaluation, we introduce JSONSchemaBench, a benchmark for constrained decoding comprising 10K real-world JSON schemas that encompass a wide range of constraints with varying complexity. We pair the benchmark with the existing official JSON Schema Test Suite and evaluate six state-of-the-art constrained decoding frameworks, including Guidance, Outlines, Llamacpp, XGrammar, OpenAI, and Gemini. Through extensive experiments, we gain insights into the capabilities and limitations of constrained decoding on structured generation with real-world JSON schemas. Our work provides actionable insights for improving constrained decoding frameworks and structured generation tasks, setting a new standard for evaluating constrained decoding and structured generation. We release JSONSchemaBench at https://github.com/guidance-ai/jsonschemabench

Remarkable performance of large language models (LLMs) in a variety of tasks brings forth many opportunities as well as challenges of utilizing them in production settings. Towards practical adoption of LLMs, multi-agent systems hold great promise to augment, integrate, and orchestrate LLMs in the larger context of enterprise platforms that use existing proprietary data and models to tackle complex real-world tasks. Despite the tremendous success of these systems, current approaches rely on narrow, single-focus objectives for optimization and evaluation, often overlooking potential constraints in real-world scenarios, including restricted budgets, resources and time. Furthermore, interpreting, analyzing, and debugging these systems requires different components to be evaluated in relation to one another. This demand is currently not feasible with existing methodologies. In this postion paper, we introduce the concept of reasoning capacity as a unifying criterion to enable integration of constraints during optimization and establish connections among different components within the system, which also enable a more holistic and comprehensive approach to evaluation. We present a formal definition of reasoning capacity and illustrate its utility in identifying limitations within each component of the system. We then argue how these limitations can be addressed with a self-reflective process wherein human-feedback is used to alleviate shortcomings in reasoning and enhance overall consistency of the system.

Task-oriented dialogues must maintain consistency both within the dialogue itself, ensuring logical coherence across turns, and with the conversational domain, accurately reflecting external knowledge. We propose to conceptualize dialogue consistency as a Constraint Satisfaction Problem (CSP), wherein variables represent segments of the dialogue referencing the conversational domain, and constraints among variables reflect dialogue properties, including linguistic, conversational, and domain-based aspects. To demonstrate the feasibility of the approach, we utilize a CSP solver to detect inconsistencies in dialogues re-lexicalized by an LLM. Our findings indicate that: (i) CSP is effective to detect dialogue inconsistencies; and (ii) consistent dialogue re-lexicalization is challenging for state-of-the-art LLMs, achieving only a 0.15 accuracy rate when compared to a CSP solver. Furthermore, through an ablation study, we reveal that constraints derived from domain knowledge pose the greatest difficulty in being respected. We argue that CSP captures core properties of dialogue consistency that have been poorly considered by approaches based on component pipelines.

Despite rapid advancement in the field of Constrained Natural Language Generation, little time has been spent on exploring the potential of language models which have had their vocabularies lexically, semantically, and/or phonetically constrained. We find that most language models generate compelling text even under significant constraints. We present a simple and universally applicable technique for modifying the output of a language model by compositionally applying filter functions to the language models vocabulary before a unit of text is generated. This approach is plug-and-play and requires no modification to the model. To showcase the value of this technique, we present an easy to use AI writing assistant called Constrained Text Generation Studio (CTGS). CTGS allows users to generate or choose from text with any combination of a wide variety of constraints, such as banning a particular letter, forcing the generated words to have a certain number of syllables, and/or forcing the words to be partial anagrams of another word. We introduce a novel dataset of prose that omits the letter e. We show that our method results in strictly superior performance compared to fine-tuning alone on this dataset. We also present a Huggingface space web-app presenting this technique called Gadsby. The code is available to the public here: https://github.com/Hellisotherpeople/Constrained-Text-Generation-Studio

Large monolithic generative models trained on massive amounts of data have become an increasingly dominant approach in AI research. In this paper, we argue that we should instead construct large generative systems by composing smaller generative models together. We show how such a compositional generative approach enables us to learn distributions in a more data-efficient manner, enabling generalization to parts of the data distribution unseen at training time. We further show how this enables us to program and construct new generative models for tasks completely unseen at training. Finally, we show that in many cases, we can discover separate compositional components from data.

The era of foundation models has revolutionized AI research, yet Graph Foundation Models (GFMs) remain constrained by the scarcity of large-scale graph corpora. Traditional graph data synthesis techniques primarily focus on simplistic structural operations, lacking the capacity to generate semantically rich nodes with meaningful textual attributes: a critical limitation for real-world applications. While large language models (LLMs) demonstrate exceptional text generation capabilities, their direct application to graph synthesis is impeded by context window limitations, hallucination phenomena, and structural consistency challenges. To address these issues, we introduce GraphMaster, the first multi-agent framework specifically designed for graph data synthesis in data-limited environments. GraphMaster orchestrates four specialized LLM agents (Manager, Perception, Enhancement, and Evaluation) that collaboratively optimize the synthesis process through iterative refinement, ensuring both semantic coherence and structural integrity. To rigorously evaluate our approach, we create new data-limited "Sub" variants of six standard graph benchmarks, specifically designed to test synthesis capabilities under realistic constraints. Additionally, we develop a novel interpretability assessment framework that combines human evaluation with a principled Grassmannian manifold-based analysis, providing both qualitative and quantitative measures of semantic coherence. Experimental results demonstrate that GraphMaster significantly outperforms traditional synthesis methods across multiple datasets, establishing a strong foundation for advancing GFMs in data-scarce environments.

This paper investigates the mathematical reasoning capabilities of large language models (LLMs) using 50 newly constructed high-school-level word problems. Unlike prior studies that focus solely on answer correctness, we rigorously analyze both final answers and solution steps to identify reasoning failures. Evaluating eight state-of-the-art models - including Mixtral, Llama, Gemini, GPT-4o, and OpenAI's o1 variants - we find that while newer models (e.g., o3-mini, deepseek-r1) achieve higher accuracy, all models exhibit errors in spatial reasoning, strategic planning, and arithmetic, sometimes producing correct answers through flawed logic. Common failure modes include unwarranted assumptions, over-reliance on numerical patterns, and difficulty translating physical intuition into mathematical steps. Manual analysis reveals that models struggle with problems requiring multi-step deduction or real-world knowledge, despite possessing broad mathematical knowledge. Our results underscore the importance of evaluating reasoning processes, not just answers, and caution against overestimating LLMs' problem-solving proficiency. The study highlights persistent gaps in LLMs' generalization abilities, emphasizing the need for targeted improvements in structured reasoning and constraint handling.

Inequality proving, crucial across diverse scientific and mathematical fields, tests advanced reasoning skills such as discovering tight bounds and strategic theorem application. This makes it a distinct, demanding frontier for large language models (LLMs), offering insights beyond general mathematical problem-solving. Progress in this area is hampered by existing datasets that are often scarce, synthetic, or rigidly formal. We address this by proposing an informal yet verifiable task formulation, recasting inequality proving into two automatically checkable subtasks: bound estimation and relation prediction. Building on this, we release IneqMath, an expert-curated dataset of Olympiad-level inequalities, including a test set and training corpus enriched with step-wise solutions and theorem annotations. We also develop a novel LLM-as-judge evaluation framework, combining a final-answer judge with four step-wise judges designed to detect common reasoning flaws. A systematic evaluation of 29 leading LLMs on IneqMath reveals a surprising reality: even top models like o1 achieve less than 10% overall accuracy under step-wise scrutiny; this is a drop of up to 65.5% from their accuracy considering only final answer equivalence. This discrepancy exposes fragile deductive chains and a critical gap for current LLMs between merely finding an answer and constructing a rigorous proof. Scaling model size and increasing test-time computation yield limited gains in overall proof correctness. Instead, our findings highlight promising research directions such as theorem-guided reasoning and self-refinement. Code and data are available at https://ineqmath.github.io/.

Generative models, particularly Large Language Models (LLMs), produce fluent outputs yet lack verifiable guarantees. We adapt Design by Contract (DbC) and type-theoretic principles to introduce a contract layer that mediates every LLM call. Contracts stipulate semantic and type requirements on inputs and outputs, coupled with probabilistic remediation to steer generation toward compliance. The layer exposes the dual view of LLMs as semantic parsers and probabilistic black-box components. Contract satisfaction is probabilistic and semantic validation is operationally defined through programmer-specified conditions on well-typed data structures. More broadly, this work postulates that any two agents satisfying the same contracts are functionally equivalent with respect to those contracts.

Large Language Models (LLMs) struggle with reliably generating highly structured outputs, such as program code, mathematical formulas, or well-formed markup. Constrained decoding approaches mitigate this problem by greedily restricting what tokens an LLM can output at each step to guarantee that the output matches a given constraint. Specifically, in grammar-constrained decoding (GCD), the LLM's output must follow a given grammar. In this paper, we demonstrate that GCD techniques (and in general constrained decoding techniques) can distort the LLM's distribution, leading to outputs that are grammatical but appear with likelihoods that are not proportional to the ones given by the LLM, and so ultimately are low-quality. We call the problem of aligning sampling with a grammar constraint, grammar-aligned decoding (GAD), and propose adaptive sampling with approximate expected futures (ASAp), a decoding algorithm that guarantees the output to be grammatical while provably producing outputs that match the conditional probability of the LLM's distribution conditioned on the given grammar constraint. Our algorithm uses prior sample outputs to soundly overapproximate the future grammaticality of different output prefixes. Our evaluation on code generation and structured NLP tasks shows how ASAp often produces outputs with higher likelihood (according to the LLM's distribution) than existing GCD techniques, while still enforcing the desired grammatical constraints.

Although LLM-based agents have attracted significant attention in domains such as software engineering and machine learning research, their role in advancing combinatorial optimization (CO) remains relatively underexplored. This gap underscores the need for a deeper understanding of their potential in tackling structured, constraint-intensive problems-a pursuit currently limited by the absence of comprehensive benchmarks for systematic investigation. To address this, we introduce CO-Bench, a benchmark suite featuring 36 real-world CO problems drawn from a broad range of domains and complexity levels. CO-Bench includes structured problem formulations and curated data to support rigorous investigation of LLM agents. We evaluate multiple agent frameworks against established human-designed algorithms, revealing key strengths and limitations of current approaches and identifying promising directions for future research. CO-Bench is publicly available at https://github.com/sunnweiwei/CO-Bench.

The field of natural language processing (NLP) has witnessed significant progress in recent years, with a notable focus on improving large language models' (LLM) performance through innovative prompting techniques. Among these, prompt engineering coupled with structures has emerged as a promising paradigm, with designs such as Chain-of-Thought, Tree of Thoughts, or Graph of Thoughts, in which the overall LLM reasoning is guided by a structure such as a graph. As illustrated with numerous examples, this paradigm significantly enhances the LLM's capability to solve numerous tasks, ranging from logical or mathematical reasoning to planning or creative writing. To facilitate the understanding of this growing field and pave the way for future developments, we devise a general blueprint for effective and efficient LLM reasoning schemes. For this, we conduct an in-depth analysis of the prompt execution pipeline, clarifying and clearly defining different concepts. We then build the first taxonomy of structure-enhanced LLM reasoning schemes. We focus on identifying fundamental classes of harnessed structures, and we analyze the representations of these structures, algorithms executed with these structures, and many others. We refer to these structures as reasoning topologies, because their representation becomes to a degree spatial, as they are contained within the LLM context. Our study compares existing prompting schemes using the proposed taxonomy, discussing how certain design choices lead to different patterns in performance and cost. We also outline theoretical underpinnings, relationships between prompting and others parts of the LLM ecosystem such as knowledge bases, and the associated research challenges. Our work will help to advance future prompt engineering techniques.

We propose utilizing background operators for mathematical reasoning in large language models (LLMs). To achieve this, we define a set of fundamental mathematical predicates as the basic building blocks. For each mathematical problem, we develop a Prolog solution that includes problem-specific predicates and intermediate predicates derived from these background operators, ensuring that each solution adheres to the defined operator set. We introduce the MATH-Prolog corpus, which is derived from the counting and probability categories of the MATH corpus. For efficient data augmentation, we apply K-fold cross-validated self-training. This method incrementally generates new Prolog solutions for each fold, incorporating those verified as correct into the training set throughout the model training process. Our experimental results demonstrate that 5-fold crossvalidated self-training effectively identifies new, accurate Prolog solutions, achieving an accuracy of 84.6% on the cross-validated set, and 84.8% on the test set during fine-tuning the Meta-Llama-3.1-8B-Instruct model. This approach successfully uncovers new solutions with fully computable inference steps for previously unseen problems. Additionally, incorporating the background mathematical predicates into the prompt enhances solution coverage.

The integration of knowledge extracted from diverse models, whether described by domain experts or generated by machine learning algorithms, has historically been challenged by the absence of a suitable framework for specifying and integrating structures, learning processes, data transformations, and data models or rules. In this work, we extend algebraic specification methods to address these challenges within such a framework. In our work, we tackle the challenging task of developing a comprehensive framework for defining and analyzing deep learning architectures. We believe that previous efforts have fallen short by failing to establish a clear connection between the constraints a model must adhere to and its actual implementation. Our methodology employs graphical structures that resemble Ehresmann's sketches, interpreted within a universe of fuzzy sets. This approach offers a unified theory that elegantly encompasses both deterministic and non-deterministic neural network designs. Furthermore, we highlight how this theory naturally incorporates fundamental concepts from computer science and automata theory. Our extended algebraic specification framework, grounded in graphical structures akin to Ehresmann's sketches, offers a promising solution for integrating knowledge across disparate models and domains. By bridging the gap between domain-specific expertise and machine-generated insights, we pave the way for more comprehensive, collaborative, and effective approaches to knowledge integration and modeling.

Most state-of-the-art Visual-Language Models (VLMs) are seemingly limited by the linear separabilty of their visual embeddings on abstract reasoning tasks. This work investigates this "linear reasoning bottleneck" by introducing the Linear Separability Ceiling (LSC), the performance of a simple linear classifier on a VLM's visual embeddings. We find this bottleneck is widespread and stems not from poor perception, but from failures in the language model's reasoning pathways. We demonstrate this is a solvable alignment issue. The required intervention, however, is task-dependent: activating existing pathways suffices for semantic concepts, while complex relational reasoning requires adapting core model weights. Using postfix tuning as a methodological control, we find strong evidence for powerful, dormant reasoning pathways within VLMs. However, for complex relational tasks requiring deeper adaptation, explicitly improving representation quality causes the model to fail on new prompt formats despite its embeddings remaining well separated. Ultimately, this work provides a new lens for VLM analysis, showing that robust reasoning is a matter of targeted alignment, not simply improved representation learning.

Recent agent frameworks and inference-time algorithms often struggle with complex planning problems due to limitations in verifying generated plans or reasoning and varying complexity of instances within a single task. Many existing methods for these tasks either perform task-level verification without considering constraints or apply inference-time algorithms without adapting to instance-level complexity. To address these limitations, we propose PlanGEN, a model-agnostic and easily scalable agent framework with three key components: constraint, verification, and selection agents. Specifically, our approach proposes constraint-guided iterative verification to enhance performance of inference-time algorithms--Best of N, Tree-of-Thought, and REBASE. In PlanGEN framework, the selection agent optimizes algorithm choice based on instance complexity, ensuring better adaptability to complex planning problems. Experimental results demonstrate significant improvements over the strongest baseline across multiple benchmarks, achieving state-of-the-art results on NATURAL PLAN (sim8%uparrow), OlympiadBench (sim4%uparrow), DocFinQA (sim7%uparrow), and GPQA (sim1%uparrow). Our key finding highlights that constraint-guided iterative verification improves inference-time algorithms, and adaptive selection further boosts performance on complex planning and reasoning problems.

Recent advancements in Large Language Models (LLMs) have showcased their ability to perform complex reasoning tasks, but their effectiveness in planning remains underexplored. In this study, we evaluate the planning capabilities of OpenAI's o1 models across a variety of benchmark tasks, focusing on three key aspects: feasibility, optimality, and generalizability. Through empirical evaluations on constraint-heavy tasks (e.g., Barman, Tyreworld) and spatially complex environments (e.g., Termes, Floortile), we highlight o1-preview's strengths in self-evaluation and constraint-following, while also identifying bottlenecks in decision-making and memory management, particularly in tasks requiring robust spatial reasoning. Our results reveal that o1-preview outperforms GPT-4 in adhering to task constraints and managing state transitions in structured environments. However, the model often generates suboptimal solutions with redundant actions and struggles to generalize effectively in spatially complex tasks. This pilot study provides foundational insights into the planning limitations of LLMs, offering key directions for future research on improving memory management, decision-making, and generalization in LLM-based planning. Code available at https://github.com/VITA-Group/o1-planning.

Reasoning about time and temporal relations is an integral aspect of human cognition, essential for perceiving the world and navigating our experiences. Though large language models (LLMs) have demonstrated impressive performance in many reasoning tasks, temporal reasoning remains challenging due to its intrinsic complexity. In this work, we first study an essential task of temporal reasoning -- temporal graph generation, to unveil LLMs' inherent, global reasoning capabilities. We show that this task presents great challenges even for the most powerful LLMs, such as GPT-3.5/4. We also notice a significant performance gap by small models (<10B) that lag behind LLMs by 50%. Next, we study how to close this gap with a budget constraint, e.g., not using model finetuning. We propose a new prompting technique tailored for temporal reasoning, Narrative-of-Thought (NoT), that first converts the events set to a Python class, then prompts a small model to generate a temporally grounded narrative, guiding the final generation of a temporal graph. Extensive experiments showcase the efficacy of NoT in improving various metrics. Notably, NoT attains the highest F1 on the Schema-11 evaluation set, while securing an overall F1 on par with GPT-3.5. NoT also achieves the best structural similarity across the board, even compared with GPT-3.5/4. Our code is available at https://github.com/launchnlp/NoT.

Model editing is a growing area focused on updating the knowledge embedded within models. Among the various methodologies, ROME and MEMIT stand out as leading "locate-and-edit" model editing techniques. While MEMIT enables batched editing of memories, ROME is limited to changing one fact at a time. This paper introduces a unifying framework that brings ROME and MEMIT under a single conceptual umbrella, optimizing for the same goal, which we call the "preservation-memorization" objective. This objective aims to preserve the representations of certain selected vectors while memorizing the representations of new factual information. Specifically, ROME optimizes this objective using an equality constraint, whereas MEMIT employs a more flexible least-square constraint. In addition to making batched edits, MEMIT also edits the model at multiple layers. We disentangle the distribution of edits to multiple layers from the optimization objective of MEMIT and show that these edit-distribution algorithms should be considered separate entities worthy of their own line of research. Finally, we present EMMET - an Equality-constrained Mass Model Editing algorithm for Transformers, a new batched memory-editing algorithm. With EMMET, we present a closed form solution for the equality-constrained version of the preservation-memorization objective. We show that EMMET is able to perform batched-edits on par with MEMIT up to a batch-size of 256 and discuss the challenges in stabilizing EMMET. By articulating the "locate-and-edit" model editing algorithms under a simple conceptual framework of "preservation-memorization", we aim to bridge the gap between intuition and mathematics and hope to simplify the journey for future researchers in model editing.

Large Language Models (LLMs) are frequently used for multi-faceted language generation and evaluation tasks that involve satisfying intricate user constraints or taking into account multiple aspects and criteria. However, their performance can fall short, due to the model's lack of coherence and inability to plan and decompose the problem. We propose Branch-Solve-Merge (BSM), a Large Language Model program (Schlag et al., 2023) for tackling such challenging natural language tasks. It consists of branch, solve, and merge modules that are parameterized with specific prompts to the base LLM. These three modules plan a decomposition of the task into multiple parallel sub-tasks, independently solve them, and fuse the solutions to the sub-tasks. We apply our method to the tasks of LLM response evaluation and constrained text generation and evaluate its effectiveness with multiple LLMs, including Vicuna, LLaMA-2-chat, and GPT-4. BSM improves the evaluation correctness and consistency for each LLM by enhancing human-LLM agreement by up to 26%, reducing length and pairwise position biases by up to 50%, and allowing LLaMA-2-chat to match or outperform GPT-4 on most domains. On the constraint story generation task, BSM improves the coherence of the stories while also improving constraint satisfaction by 12%.

Large language model (LLM) performance on reasoning problems typically does not generalize out of distribution. Previous work has claimed that this can be mitigated by modifying prompts to include examples with chains of thought--demonstrations of solution procedures--with the intuition that it is possible to in-context teach an LLM an algorithm for solving the problem. This paper presents a case study of chain of thought on problems from Blocksworld, a classical planning domain, and examine the performance of two state-of-the-art LLMs across two axes: generality of examples given in prompt, and complexity of problems queried with each prompt. While our problems are very simple, we only find meaningful performance improvements from chain of thought prompts when those prompts are exceedingly specific to their problem class, and that those improvements quickly deteriorate as the size n of the query-specified stack grows past the size of stacks shown in the examples. Our results hint that, contrary to previous claims in the literature, CoT's performance improvements do not stem from the model learning general algorithmic procedures via demonstrations and depend on carefully engineering highly problem specific prompts. This spotlights drawbacks of chain of thought, especially because of the sharp tradeoff between possible performance gains and the amount of human labor necessary to generate examples with correct reasoning traces.

Logical reasoning remains a challenge for natural language processing, but it can be improved by training language models to mimic theorem provers on procedurally generated problems. Previous work used domain-specific proof generation algorithms, which biases reasoning toward specific proof traces and limits auditability and extensibility. We present a simpler and more general declarative framework with flexible context-sensitive rules binding multiple languages (specifically, simplified English and the TPTP theorem-proving language). We construct first-order logic problems by selecting up to 32 premises and one hypothesis. We demonstrate that using semantic constraints during generation and careful English verbalization of predicates enhances logical reasoning without hurting natural English tasks. We use relatively small DeBERTa-v3 models to achieve state-of-the-art accuracy on the FOLIO human-authored logic dataset, surpassing GPT-4 in accuracy with or without an external solver by 12%.

Multi-turn instruction following capability constitutes a core competency of large language models (LLMs) in real-world applications. Existing evaluation benchmarks predominantly focus on fine-grained constraint satisfaction and domain-specific capability assessment, yet overlook the crucial structural dependency between dialogue turns that distinguishes multi-turn from single-turn interactions. This structural dependency not only reflects user intent but also establishes a second dimension for instruction following evaluation beyond constraint satisfaction. To address this gap, we propose StructFlowBench, a multi-turn instruction following benchmark with structural flow modeling. The benchmark innovatively defines a structural flow framework comprising six fundamental inter-turn relationships, which not only introduces novel structural constraints for model evaluation but also serves as generation parameters for creating customized dialogue flows tailored to specific scenarios. Adopting established LLM-based automatic evaluation methodologies, we conduct systematic evaluations of 13 leading open-source and closed-source LLMs. Experimental results reveal significant deficiencies in current models' comprehension of multi-turn dialogue structures. The code is available at https://github.com/MLGroupJLU/StructFlowBench.

Reasoning is central to a wide range of intellectual activities, and while the capabilities of large language models (LLMs) continue to advance, their performance in reasoning tasks remains limited. The processes and mechanisms underlying reasoning are not yet fully understood, but key elements include path exploration, selection of relevant knowledge, and multi-step inference. Problems are solved through the synthesis of these components. In this paper, we propose a benchmark that focuses on a specific aspect of reasoning ability: the direct evaluation of multi-step inference. To this end, we design a special reasoning task where multi-step inference is specifically focused by largely eliminating path exploration and implicit knowledge utilization. Our dataset comprises pairs of explicit instructions and corresponding questions, where the procedures necessary for solving the questions are entirely detailed within the instructions. This setup allows models to solve problems solely by following the provided directives. By constructing problems that require varying numbers of steps to solve and evaluating responses at each step, we enable a thorough assessment of state-of-the-art LLMs' ability to follow instructions. To ensure the robustness of our evaluation, we include multiple distinct tasks. Furthermore, by comparing accuracy across tasks, utilizing step-aware metrics, and applying separately defined measures of complexity, we conduct experiments that offer insights into the capabilities and limitations of LLMs in reasoning tasks. Our findings have significant implications for the development of LLMs and highlight areas for future research in advancing their reasoning abilities. Our dataset is available at https://huggingface.co/datasets/ifujisawa/procbench and code at https://github.com/ifujisawa/proc-bench.

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.

We present SongComposer, an innovative LLM designed for song composition. It could understand and generate melodies and lyrics in symbolic song representations, by leveraging the capability of LLM. Existing music-related LLM treated the music as quantized audio signals, while such implicit encoding leads to inefficient encoding and poor flexibility. In contrast, we resort to symbolic song representation, the mature and efficient way humans designed for music, and enable LLM to explicitly compose songs like humans. In practice, we design a novel tuple design to format lyric and three note attributes (pitch, duration, and rest duration) in the melody, which guarantees the correct LLM understanding of musical symbols and realizes precise alignment between lyrics and melody. To impart basic music understanding to LLM, we carefully collected SongCompose-PT, a large-scale song pretraining dataset that includes lyrics, melodies, and paired lyrics-melodies in either Chinese or English. After adequate pre-training, 10K carefully crafted QA pairs are used to empower the LLM with the instruction-following capability and solve diverse tasks. With extensive experiments, SongComposer demonstrates superior performance in lyric-to-melody generation, melody-to-lyric generation, song continuation, and text-to-song creation, outperforming advanced LLMs like GPT-4.

Compositional AI systems, which combine multiple artificial intelligence components together with other application components to solve a larger problem, have no known pattern of development and are often approached in a bespoke and ad hoc style. This makes development slower and harder to reuse for future applications. To support the full rapid development cycle of compositional AI applications, we have developed a novel framework called (Bee)* (written as a regular expression and pronounced as "beestar"). We illustrate how (Bee)* supports building integrated, scalable, and interactive compositional AI applications with a simplified developer experience.

Recent advancements in Chain-of-Thought prompting have facilitated significant breakthroughs for Large Language Models (LLMs) in complex reasoning tasks. Current research enhances the reasoning performance of LLMs by sampling multiple reasoning chains and ensembling based on the answer frequency. However, this approach fails in scenarios where the correct answers are in the minority. We identify this as a primary factor constraining the reasoning capabilities of LLMs, a limitation that cannot be resolved solely based on the predicted answers. To address this shortcoming, we introduce a hierarchical reasoning aggregation framework AoR (Aggregation of Reasoning), which selects answers based on the evaluation of reasoning chains. Additionally, AoR incorporates dynamic sampling, adjusting the number of reasoning chains in accordance with the complexity of the task. Experimental results on a series of complex reasoning tasks show that AoR outperforms prominent ensemble methods. Further analysis reveals that AoR not only adapts various LLMs but also achieves a superior performance ceiling when compared to current methods.

In a compound AI system, components such as an LLM call, a retriever, a code interpreter, or tools are interconnected. The system's behavior is primarily driven by parameters such as instructions or tool definitions. Recent advancements enable end-to-end optimization of these parameters using an LLM. Notably, leveraging an LLM as an optimizer is particularly efficient because it avoids gradient computation and can generate complex code and instructions. This paper presents a survey of the principles and emerging trends in LLM-based optimization of compound AI systems. It covers archetypes of compound AI systems, approaches to LLM-based end-to-end optimization, and insights into future directions and broader impacts. Importantly, this survey uses concepts from program analysis to provide a unified view of how an LLM optimizer is prompted to optimize a compound AI system. The exhaustive list of paper is provided at https://github.com/linyuhongg/LLM-based-Optimization-of-Compound-AI-Systems.

While Large Language Models (LLMs) demonstrate impressive performance in mathematics, existing math benchmarks come with significant limitations. Many focus on problems with fixed ground-truth answers, and are often saturated due to problem simplicity or the viability of guessing or memorization. Crucially, they capture only a narrow subset of relevant math problems. To address this research gap, we introduce \mc, a new benchmark of 126 challenging problems sourced from various math competitions, which targets constructive proofs, a widely encountered problem type requiring the construction of mathematical objects with specific properties. These proofs are particularly suitable for LLM evaluation, as solution correctness can be easily verified. Our automated verifiers also enable MathConstruct to generate problem variations, used to evaluate robustness. State-of-the-art LLMs solve only 54% of MathConstruct problems, highlighting its complexity and importance for LLM evaluation.

Creative coding tasks are often exploratory in nature. When producing digital artwork, artists usually begin with a high-level semantic construct such as a "stained glass filter" and programmatically implement it by varying code parameters such as shape, color, lines, and opacity to produce visually appealing results. Based on interviews with artists, it can be effortful to translate semantic constructs to program syntax, and current programming tools don't lend well to rapid creative exploration. To address these challenges, we introduce Spellburst, a large language model (LLM) powered creative-coding environment. Spellburst provides (1) a node-based interface that allows artists to create generative art and explore variations through branching and merging operations, (2) expressive prompt-based interactions to engage in semantic programming, and (3) dynamic prompt-driven interfaces and direct code editing to seamlessly switch between semantic and syntactic exploration. Our evaluation with artists demonstrates Spellburst's potential to enhance creative coding practices and inform the design of computational creativity tools that bridge semantic and syntactic spaces.

We present ControlLLM, a novel framework that enables large language models (LLMs) to utilize multi-modal tools for solving complex real-world tasks. Despite the remarkable performance of LLMs, they still struggle with tool invocation due to ambiguous user prompts, inaccurate tool selection and parameterization, and inefficient tool scheduling. To overcome these challenges, our framework comprises three key components: (1) a task decomposer that breaks down a complex task into clear subtasks with well-defined inputs and outputs; (2) a Thoughts-on-Graph (ToG) paradigm that searches the optimal solution path on a pre-built tool graph, which specifies the parameter and dependency relations among different tools; and (3) an execution engine with a rich toolbox that interprets the solution path and runs the tools efficiently on different computational devices. We evaluate our framework on diverse tasks involving image, audio, and video processing, demonstrating its superior accuracy, efficiency, and versatility compared to existing methods.

We introduce SATBench, a benchmark for evaluating the logical reasoning capabilities of large language models (LLMs) through logical puzzles derived from Boolean satisfiability (SAT) problems. Unlike prior work that focuses on inference rule-based reasoning, which often involves deducing conclusions from a set of premises, our approach leverages the search-based nature of SAT problems, where the objective is to find a solution that fulfills a specified set of logical constraints. Each instance in SATBench is generated from a SAT formula, then translated into a story context and conditions using LLMs. The generation process is fully automated and allows for adjustable difficulty by varying the number of clauses. All 2100 puzzles are validated through both LLM-assisted and solver-based consistency checks, with human validation on a subset. Experimental results show that even the strongest model, o4-mini, achieves only 65.0% accuracy on hard UNSAT problems, close to the random baseline of 50%. SATBench exposes fundamental limitations in the search-based logical reasoning abilities of current LLMs and provides a scalable testbed for future research in logical reasoning.

In recent years, the rapid development of large reasoning models has resulted in the saturation of existing benchmarks for evaluating mathematical reasoning, highlighting the urgent need for more challenging and rigorous evaluation frameworks. To address this gap, we introduce OlymMATH, a novel Olympiad-level mathematical benchmark, designed to rigorously test the complex reasoning capabilities of LLMs. OlymMATH features 200 meticulously curated problems, each manually verified and available in parallel English and Chinese versions. The problems are systematically organized into two distinct difficulty tiers: (1) AIME-level problems (easy) that establish a baseline for mathematical reasoning assessment, and (2) significantly more challenging problems (hard) designed to push the boundaries of current state-of-the-art models. In our benchmark, these problems span four core mathematical fields, each including a verifiable numerical solution to enable objective, rule-based evaluation. Empirical results underscore the significant challenge presented by OlymMATH, with state-of-the-art models including DeepSeek-R1 and OpenAI's o3-mini demonstrating notably limited accuracy on the hard subset. Furthermore, the benchmark facilitates comprehensive bilingual assessment of mathematical reasoning abilities-a critical dimension that remains largely unaddressed in mainstream mathematical reasoning benchmarks. We release the OlymMATH benchmark at the STILL project: https://github.com/RUCAIBox/Slow_Thinking_with_LLMs.

Reasoning is a fundamental substrate for solving novel and complex problems. Deliberate efforts in learning and developing frameworks around System 2 reasoning have made great strides, yet problems of sufficient complexity remain largely out of reach for open models. To address this gap, we examine the potential of Generative Flow Networks as a fine-tuning method for LLMs to unlock advanced reasoning capabilities. In this paper, we present a proof of concept in the domain of formal reasoning, specifically in the Neural Theorem Proving (NTP) setting, where proofs specified in a formal language such as Lean can be deterministically and objectively verified. Unlike classical reward-maximization reinforcement learning, which frequently over-exploits high-reward actions and fails to effectively explore the state space, GFlowNets have emerged as a promising approach for sampling compositional objects, improving generalization, and enabling models to maintain diverse hypotheses. Our early results demonstrate GFlowNet fine-tuning's potential for enhancing model performance in a search setting, which is especially relevant given the paradigm shift towards inference time compute scaling and "thinking slowly."

Large Language Models (LLMs) have shown remarkable capabilities, with optimizing their input prompts playing a pivotal role in maximizing their performance. However, while LLM prompts consist of both the task-agnostic system prompts and task-specific user prompts, existing work on prompt optimization has focused on user prompts specific to individual queries or tasks, and largely overlooked the system prompt that is, once optimized, applicable across different tasks and domains. Motivated by this, we introduce the novel problem of bilevel system prompt optimization, whose objective is to design system prompts that are robust to diverse user prompts and transferable to unseen tasks. To tackle this problem, we then propose a meta-learning framework, which meta-learns the system prompt by optimizing it over various user prompts across multiple datasets, while simultaneously updating the user prompts in an iterative manner to ensure synergy between them. We conduct experiments on 14 unseen datasets spanning 5 different domains, on which we show that our approach produces system prompts that generalize effectively to diverse user prompts. Also, our findings reveal that the optimized system prompt enables rapid adaptation even to unseen tasks, requiring fewer optimization steps for test-time user prompts while achieving improved performance.

Various human-designed prompt engineering techniques have been proposed to improve problem solvers based on Large Language Models (LLMs), yielding many disparate code bases. We unify these approaches by describing LLM-based agents as computational graphs. The nodes implement functions to process multimodal data or query LLMs, and the edges describe the information flow between operations. Graphs can be recursively combined into larger composite graphs representing hierarchies of inter-agent collaboration (where edges connect operations of different agents). Our novel automatic graph optimizers (1) refine node-level LLM prompts (node optimization) and (2) improve agent orchestration by changing graph connectivity (edge optimization). Experiments demonstrate that our framework can be used to efficiently develop, integrate, and automatically improve various LLM agents. The code can be found at https://github.com/metauto-ai/gptswarm.

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.

The dominant paradigm for neural text generation is left-to-right decoding from autoregressive language models. Constrained or controllable generation under complex lexical constraints, however, requires foresight to plan ahead feasible future paths. Drawing inspiration from the A* search algorithm, we propose NeuroLogic A*esque, a decoding algorithm that incorporates heuristic estimates of future cost. We develop efficient lookahead heuristics that are efficient for large-scale language models, making our method a drop-in replacement for common techniques such as beam search and top-k sampling. To enable constrained generation, we build on NeuroLogic decoding (Lu et al., 2021), combining its flexibility in incorporating logical constraints with A*esque estimates of future constraint satisfaction. Our approach outperforms competitive baselines on five generation tasks, and achieves new state-of-the-art performance on table-to-text generation, constrained machine translation, and keyword-constrained generation. The improvements are particularly notable on tasks that require complex constraint satisfaction or in few-shot or zero-shot settings. NeuroLogic A*esque illustrates the power of decoding for improving and enabling new capabilities of large-scale language models.

Large Language Models (LLMs) have shown significant capability across various tasks, with their real-world effectiveness often driven by prompt design. While recent research has focused on optimizing prompt content, the role of prompt formatting, a critical but often overlooked dimension, has received limited systematic investigation. In this paper, we introduce Content-Format Integrated Prompt Optimization (CFPO), an innovative methodology that jointly optimizes both prompt content and formatting through an iterative refinement process. CFPO leverages natural language mutations to explore content variations and employs a dynamic format exploration strategy that systematically evaluates diverse format options. Our extensive evaluations across multiple tasks and open-source LLMs demonstrate that CFPO demonstrates measurable performance improvements compared to content-only optimization methods. This highlights the importance of integrated content-format optimization and offers a practical, model-agnostic approach to enhancing LLM performance. Code will be available at https://github.com/HenryLau7/CFPO.

Language models contain ranking-based knowledge and are powerful solvers of in-context ranking tasks. For instance, they may have parametric knowledge about the ordering of countries by size or may be able to rank reviews by sentiment. Recent work focuses on pairwise, pointwise, and listwise prompting techniques to elicit a language model's ranking knowledge. However, we find that even with careful calibration and constrained decoding, prompting-based techniques may not always be self-consistent in the rankings they produce. This motivates us to explore an alternative approach that is inspired by an unsupervised probing method called Contrast-Consistent Search (CCS). The idea is to train a probing model guided by a logical constraint: a model's representation of a statement and its negation must be mapped to contrastive true-false poles consistently across multiple statements. We hypothesize that similar constraints apply to ranking tasks where all items are related via consistent pairwise or listwise comparisons. To this end, we extend the binary CCS method to Contrast-Consistent Ranking (CCR) by adapting existing ranking methods such as the Max-Margin Loss, Triplet Loss, and Ordinal Regression objective. Our results confirm that, for the same language model, CCR probing outperforms prompting and even performs on a par with prompting much larger language models.

A recent approach to neurosymbolic reasoning is to explicitly combine the strengths of large language models (LLMs) and symbolic solvers to tackle complex reasoning tasks. However, current approaches face significant limitations, including poor generalizability due to task-specific prompts, inefficiencies caused by the lack of separation between knowledge and queries, and restricted inferential capabilities. These shortcomings hinder their scalability and applicability across diverse domains. In this paper, we introduce VERUS-LM, a novel framework designed to address these challenges. VERUS-LM employs a generic prompting mechanism, clearly separates domain knowledge from queries, and supports a wide range of different logical reasoning tasks. This framework enhances adaptability, reduces computational cost, and allows for richer forms of reasoning, such as optimization and constraint satisfaction. We show that our approach succeeds in diverse reasoning on a novel dataset, markedly outperforming LLMs. Additionally, our system achieves competitive results on common reasoning benchmarks when compared to other state-of-the-art approaches, and significantly surpasses them on the difficult AR-LSAT dataset. By pushing the boundaries of hybrid reasoning, VERUS-LM represents a significant step towards more versatile neurosymbolic AI systems

Fine-tuning large language models (LLMs) with a collection of large and diverse instructions has improved the model's generalization to different tasks, even for unseen tasks. However, most existing instruction datasets include only single instructions, and they struggle to follow complex instructions composed of multiple subtasks (Wang et al., 2023a). In this work, we propose a novel concept of compositional instructions called chain-of-instructions (CoI), where the output of one instruction becomes an input for the next like a chain. Unlike the conventional practice of solving single instruction tasks, our proposed method encourages a model to solve each subtask step by step until the final answer is reached. CoI-tuning (i.e., fine-tuning with CoI instructions) improves the model's ability to handle instructions composed of multiple subtasks. CoI-tuned models also outperformed baseline models on multilingual summarization, demonstrating the generalizability of CoI models on unseen composite downstream tasks.

LLMs have gained immense popularity among researchers and the general public for its impressive capabilities on a variety of tasks. Notably, the efficacy of LLMs remains significantly dependent on the quality and structure of the input prompts, making prompt design a critical factor for their performance. Recent advancements in automated prompt optimization have introduced diverse techniques that automatically enhance prompts to better align model outputs with user expectations. However, these methods often suffer from the lack of standardization and compatibility across different techniques, limited flexibility in customization, inconsistent performance across model scales, and they often exclusively rely on expensive proprietary LLM APIs. To fill in this gap, we introduce GREATERPROMPT, a novel framework that democratizes prompt optimization by unifying diverse methods under a unified, customizable API while delivering highly effective prompts for different tasks. Our framework flexibly accommodates various model scales by leveraging both text feedback-based optimization for larger LLMs and internal gradient-based optimization for smaller models to achieve powerful and precise prompt improvements. Moreover, we provide a user-friendly Web UI that ensures accessibility for non-expert users, enabling broader adoption and enhanced performance across various user groups and application scenarios. GREATERPROMPT is available at https://github.com/psunlpgroup/GreaterPrompt via GitHub, PyPI, and web user interfaces.

Large Reasoning Models (LRMs) like o1 and DeepSeek-R1 have shown remarkable progress in natural language reasoning with long chain-of-thought (CoT), yet they remain inefficient or inaccurate when handling complex mathematical operations. Addressing these limitations through computational tools (e.g., computation libraries and symbolic solvers) is promising, but it introduces a technical challenge: Code Interpreter (CI) brings external knowledge beyond the model's internal text representations, thus the direct combination is not efficient. This paper introduces CoRT, a post-training framework for teaching LRMs to leverage CI effectively and efficiently. As a first step, we address the data scarcity issue by synthesizing code-integrated reasoning data through Hint-Engineering, which strategically inserts different hints at appropriate positions to optimize LRM-CI interaction. We manually create 30 high-quality samples, upon which we post-train models ranging from 1.5B to 32B parameters, with supervised fine-tuning, rejection fine-tuning and reinforcement learning. Our experimental results demonstrate that Hint-Engineering models achieve 4\% and 8\% absolute improvements on DeepSeek-R1-Distill-Qwen-32B and DeepSeek-R1-Distill-Qwen-1.5B respectively, across five challenging mathematical reasoning datasets. Furthermore, Hint-Engineering models use about 30\% fewer tokens for the 32B model and 50\% fewer tokens for the 1.5B model compared with the natural language models. The models and code are available at https://github.com/ChengpengLi1003/CoRT.

This study investigates the reasoning robustness of large language models (LLMs) on mathematical problem-solving tasks under systematically introduced input perturbations. Using the GSM8K dataset as a controlled testbed, we evaluate how well state-of-the-art models maintain logical consistency and correctness when confronted with four categories of prompt perturbations: irrelevant context, pathological instructions, factually relevant but non-essential context, and a combination of the latter two. Our experiments, conducted on thirteen open-source and closed-source LLMs, reveal that introducing irrelevant context within the model's context window significantly degrades performance, suggesting that distinguishing essential from extraneous details remains a pressing challenge. Surprisingly, performance regressions are relatively insensitive to the complexity of the reasoning task, as measured by the number of steps required, and are not strictly correlated with model size. Moreover, we observe that certain perturbations inadvertently trigger chain-of-thought-like reasoning behaviors, even without explicit prompting. Our findings highlight critical vulnerabilities in current LLMs and underscore the need for improved robustness against noisy, misleading, and contextually dense inputs, paving the way for more resilient and reliable reasoning in real-world applications.

Large language models (LLMs) have achieved remarkable progress in solving various natural language processing tasks due to emergent reasoning abilities. However, LLMs have inherent limitations as they are incapable of accessing up-to-date information (stored on the Web or in task-specific knowledge bases), using external tools, and performing precise mathematical and logical reasoning. In this paper, we present Chameleon, an AI system that mitigates these limitations by augmenting LLMs with plug-and-play modules for compositional reasoning. Chameleon synthesizes programs by composing various tools (e.g., LLMs, off-the-shelf vision models, web search engines, Python functions, and heuristic-based modules) for accomplishing complex reasoning tasks. At the heart of Chameleon is an LLM-based planner that assembles a sequence of tools to execute to generate the final response. We showcase the effectiveness of Chameleon on two multi-modal knowledge-intensive reasoning tasks: ScienceQA and TabMWP. Chameleon, powered by GPT-4, achieves an 86.54% overall accuracy on ScienceQA, improving the best published few-shot result by 11.37%. On TabMWP, GPT-4-powered Chameleon improves the accuracy by 17.0%, lifting the state of the art to 98.78%. Our analysis also shows that the GPT-4-powered planner exhibits more consistent and rational tool selection via inferring potential constraints from instructions, compared to a ChatGPT-powered planner.

Seven years ago, researchers proposed a postprocessing method to equalize the error rates of a model across different demographic groups. The work launched hundreds of papers purporting to improve over the postprocessing baseline. We empirically evaluate these claims through thousands of model evaluations on several tabular datasets. We find that the fairness-accuracy Pareto frontier achieved by postprocessing contains all other methods we were feasibly able to evaluate. In doing so, we address two common methodological errors that have confounded previous observations. One relates to the comparison of methods with different unconstrained base models. The other concerns methods achieving different levels of constraint relaxation. At the heart of our study is a simple idea we call unprocessing that roughly corresponds to the inverse of postprocessing. Unprocessing allows for a direct comparison of methods using different underlying models and levels of relaxation.

We explore multi-step reasoning in vision-language models (VLMs). The problem is challenging, as reasoning data consisting of multiple steps of visual and language processing are barely available. To overcome the challenge, we first introduce a least-to-most visual reasoning paradigm, which interleaves steps of decomposing a question into sub-questions and invoking external tools for resolving sub-questions. Based on the paradigm, we further propose a novel data synthesis approach that can automatically create questions and multi-step reasoning paths for an image in a bottom-up manner. Our approach divides the complex synthesis task into a few simple sub-tasks, and (almost entirely) relies on open-sourced models to accomplish the sub-tasks. Therefore, the entire synthesis process is reproducible and cost-efficient, and the synthesized data is quality guaranteed. With the approach, we construct 50k visual reasoning examples. Then, we develop a visual reasoner through supervised fine-tuning, which is capable of generally enhancing the reasoning abilities of a wide range of existing VLMs in a plug-and-play fashion. Extensive experiments indicate that the visual reasoner can consistently and significantly improve four VLMs on four VQA benchmarks. Our code and dataset are available at https://github.com/steven-ccq/VisualReasoner.

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.

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 shown superior capability to solve reasoning problems with programs. While being a promising direction, most of such frameworks are trained and evaluated in settings with a prior knowledge of task requirements. However, as LLMs become more capable, it is necessary to assess their reasoning abilities in more realistic scenarios where many real-world problems are open-ended with ambiguous scope, and often require multiple formalisms to solve. To investigate this, we introduce the task of reasoning in the wild, where an LLM is tasked to solve a reasoning problem of unknown type by identifying the subproblems and their corresponding formalisms, and writing a program to solve each subproblem, guided by a tactic. We create a large tactic-guided trajectory dataset containing detailed solutions to a diverse set of reasoning problems, ranging from well-defined single-form reasoning (e.g., math, logic), to ambiguous and hybrid ones (e.g., commonsense, combined math and logic). This allows us to test various aspects of LLMs reasoning at the fine-grained level such as the selection and execution of tactics, and the tendency to take undesired shortcuts. In experiments, we highlight that existing LLMs fail significantly on problems with ambiguous and mixed scope, revealing critical limitations and overfitting issues (e.g. accuracy on GSM8K drops by at least 50\%). We further show the potential of finetuning a local LLM on the tactic-guided trajectories in achieving better performance. Project repo is available at github.com/gblackout/Reason-in-the-Wild

Large Language Models (LLMs) have exhibited significant potential in performing diverse tasks, including the ability to call functions or use external tools to enhance their performance. While current research on function calling by LLMs primarily focuses on single-turn interactions, this paper addresses the overlooked necessity for LLMs to engage in multi-turn function calling--critical for handling compositional, real-world queries that require planning with functions but not only use functions. To facilitate this, we introduce an approach, BUTTON, which generates synthetic compositional instruction tuning data via bottom-up instruction construction and top-down trajectory generation. In the bottom-up phase, we generate simple atomic tasks based on real-world scenarios and build compositional tasks using heuristic strategies based on atomic tasks. Corresponding functions are then developed for these compositional tasks. The top-down phase features a multi-agent environment where interactions among simulated humans, assistants, and tools are utilized to gather multi-turn function calling trajectories. This approach ensures task compositionality and allows for effective function and trajectory generation by examining atomic tasks within compositional tasks. We produce a dataset BUTTONInstruct comprising 8k data points and demonstrate its effectiveness through extensive experiments across various LLMs.

Though LLMs are capable of generating plausible programs, it's challenging to interact with the LLMs further to revise the program, especially if the user's specific requirements are different from the initial proposal. In this paper, we introduce ANPL, an interactive programming system that ensures users can always refine the generated code towards their specific programmatic intents via structured decompositions. Borrowing the paradigm of sketching from program synthesis, an ANPL program consists of a set of input-outputs that it must satisfy, a ``sketch'' -- control/data flow expressed in precise code (e.g. Python), and ``holes'' -- sub-modules to be implemented by the LLM specified with natural language. The user revises an ANPL program by either modifying the sketch, changing the language used to describe the holes, or providing additional input-outputs to a particular hole, turning it into a sub-ANPL program that can be solved recursively. This workflow allows the users to offload programming burdens to the LLM as much as possible while retaining the ability to pinpoint and resolve bugs locally, without exposing the rest of the program to the LLM. We deploy ANPL on the Abstraction and Reasoning Corpus (ARC), a set of unique tasks that are challenging for state-of-the-art AI systems, showing it outperforms baseline programming systems that (a) without the ability to decompose tasks interactively and (b) without the guarantee that the modules can be correctly composed together. Additional evaluations on APPS, HumanEval, and real-world programming tasks have validated that the ANPL framework is applicable to multiple programming domains. We release the ANPL solutions to the ARC tasks as a dataset, providing insights into how humans decompose novel tasks programmatically. See our code at https://iprc-dip.github.io/ANPL/.

Large language models (LLMs) have recently been shown to deliver impressive performance in various NLP tasks. To tackle multi-step reasoning tasks, few-shot chain-of-thought (CoT) prompting includes a few manually crafted step-by-step reasoning demonstrations which enable LLMs to explicitly generate reasoning steps and improve their reasoning task accuracy. To eliminate the manual effort, Zero-shot-CoT concatenates the target problem statement with "Let's think step by step" as an input prompt to LLMs. Despite the success of Zero-shot-CoT, it still suffers from three pitfalls: calculation errors, missing-step errors, and semantic misunderstanding errors. To address the missing-step errors, we propose Plan-and-Solve (PS) Prompting. It consists of two components: first, devising a plan to divide the entire task into smaller subtasks, and then carrying out the subtasks according to the plan. To address the calculation errors and improve the quality of generated reasoning steps, we extend PS prompting with more detailed instructions and derive PS+ prompting. We evaluate our proposed prompting strategy on ten datasets across three reasoning problems. The experimental results over GPT-3 show that our proposed zero-shot prompting consistently outperforms Zero-shot-CoT across all datasets by a large margin, is comparable to or exceeds Zero-shot-Program-of-Thought Prompting, and has comparable performance with 8-shot CoT prompting on the math reasoning problem. The code can be found at https://github.com/AGI-Edgerunners/Plan-and-Solve-Prompting.

Human reasoning relies on constructing and manipulating mental models-simplified internal representations of situations that we use to understand and solve problems. Conceptual diagrams (for example, sketches drawn by humans to aid reasoning) externalize these mental models, abstracting irrelevant details to efficiently capture relational and spatial information. In contrast, Large Language Models (LLMs) and Large Multimodal Models (LMMs) predominantly reason through textual representations, limiting their effectiveness in complex multi-step combinatorial and planning tasks. In this paper, we propose a zero-shot fully automatic framework that enables LMMs to reason through multiple chains of self-generated intermediate conceptual diagrams, significantly enhancing their combinatorial planning capabilities. Our approach does not require any human initialization beyond a natural language description of the task. It integrates both textual and diagrammatic reasoning within an optimized graph-of-thought inference framework, enhanced by beam search and depth-wise backtracking. Evaluated on multiple challenging PDDL planning domains, our method substantially improves GPT-4o's performance (for example, from 35.5% to 90.2% in Blocksworld). On more difficult planning domains with solution depths up to 40, our approach outperforms even the o1-preview reasoning model (for example, over 13% improvement in Parking). These results highlight the value of conceptual diagrams as a complementary reasoning medium in LMMs.

In this work, we use large language models (LLMs) to augment and accelerate research on the P versus NP problem, one of the most important open problems in theoretical computer science and mathematics. Specifically, we propose Socratic reasoning, a general framework that promotes in-depth thinking with LLMs for complex problem-solving. Socratic reasoning encourages LLMs to recursively discover, solve, and integrate problems while facilitating self-evaluation and refinement. Our pilot study on the P vs. NP problem shows that GPT-4 successfully produces a proof schema and engages in rigorous reasoning throughout 97 dialogue turns, concluding "P neq NP", which is in alignment with (Xu and Zhou, 2023). The investigation uncovers novel insights within the extensive solution space of LLMs, shedding light on LLM for Science.

Large language models encode a vast amount of semantic knowledge and possess remarkable understanding and reasoning capabilities. Previous research has explored how to ground language models in robotic tasks to ensure that the sequences generated by the language model are both logically correct and practically executable. However, low-level execution may deviate from the high-level plan due to environmental perturbations or imperfect controller design. In this paper, we propose DoReMi, a novel language model grounding framework that enables immediate Detection and Recovery from Misalignments between plan and execution. Specifically, LLMs are leveraged for both planning and generating constraints for planned steps. These constraints can indicate plan-execution misalignments and we use a vision question answering (VQA) model to check constraints during low-level skill execution. If certain misalignment occurs, our method will call the language model to re-plan in order to recover from misalignments. Experiments on various complex tasks including robot arms and humanoid robots demonstrate that our method can lead to higher task success rates and shorter task completion times. Videos of DoReMi are available at https://sites.google.com/view/doremi-paper.

We initiate a formal investigation into the design and analysis of LLM-based algorithms, i.e. algorithms that contain one or multiple calls of large language models (LLMs) as sub-routines and critically rely on the capabilities of LLMs. While LLM-based algorithms, ranging from basic LLM calls with prompt engineering to complicated LLM-powered agent systems and compound AI systems, have achieved remarkable empirical success, the design and optimization of them have mostly relied on heuristics and trial-and-errors, which is largely due to a lack of formal and analytical study for these algorithms. To fill this gap, we start by identifying the computational-graph representation of LLM-based algorithms, the design principle of task decomposition, and some key abstractions, which then facilitate our formal analysis for the accuracy and efficiency of LLM-based algorithms, despite the black-box nature of LLMs. Through extensive analytical and empirical investigation in a series of case studies, we demonstrate that the proposed framework is broadly applicable to a wide range of scenarios and diverse patterns of LLM-based algorithms, such as parallel, hierarchical and recursive task decomposition. Our proposed framework holds promise for advancing LLM-based algorithms, by revealing the reasons behind curious empirical phenomena, guiding the choices of hyperparameters, predicting the empirical performance of algorithms, and inspiring new algorithm design. To promote further study of LLM-based algorithms, we release our source code at https://github.com/modelscope/agentscope/tree/main/examples/paper_llm_based_algorithm.

This paper introduces the Decomposed Requirements Following Ratio (DRFR), a new metric for evaluating Large Language Models' (LLMs) ability to follow instructions. Addressing a gap in current methodologies, DRFR breaks down complex instructions into simpler criteria, facilitating a detailed analysis of LLMs' compliance with various aspects of tasks. Alongside this metric, we present InFoBench, a benchmark comprising 500 diverse instructions and 2,250 decomposed questions across multiple constraint categories. Our experiments compare DRFR with traditional scoring methods and explore annotation sources, including human experts, crowd-sourced workers, and GPT-4. The findings demonstrate DRFR's higher reliability and the effectiveness of using GPT-4 as a cost-efficient annotator. The evaluation of several advanced LLMs using this framework reveals their strengths and areas needing improvement, particularly in complex instruction-following. This study contributes a novel metric and benchmark, offering insights for future LLM development and evaluation.

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).

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

Visual Grounding (VG) tasks, such as referring expression detection and segmentation tasks are important for linking visual entities to context, especially in complex reasoning tasks that require detailed query interpretation. This paper explores VG beyond basic perception, highlighting challenges for methods that require reasoning like human cognition. Recent advances in large language methods (LLMs) and Vision-Language methods (VLMs) have improved abilities for visual comprehension, contextual understanding, and reasoning. These methods are mainly split into end-to-end and compositional methods, with the latter offering more flexibility. Compositional approaches that integrate LLMs and foundation models show promising performance but still struggle with complex reasoning with language-based logical representations. To address these limitations, we propose NAVER, a compositional visual grounding method that integrates explicit probabilistic logic reasoning within a finite-state automaton, equipped with a self-correcting mechanism. This design improves robustness and interpretability in inference through explicit logic reasoning. Our results show that NAVER achieves SoTA performance comparing to recent end-to-end and compositional baselines. The code is available at https://github.com/ControlNet/NAVER .

We present a system for generating indoor scenes in response to text prompts. The prompts are not limited to a fixed vocabulary of scene descriptions, and the objects in generated scenes are not restricted to a fixed set of object categories -- we call this setting indoor scene generation. Unlike most prior work on indoor scene generation, our system does not require a large training dataset of existing 3D scenes. Instead, it leverages the world knowledge encoded in pre-trained large language models (LLMs) to synthesize programs in a domain-specific layout language that describe objects and spatial relations between them. Executing such a program produces a specification of a constraint satisfaction problem, which the system solves using a gradient-based optimization scheme to produce object positions and orientations. To produce object geometry, the system retrieves 3D meshes from a database. Unlike prior work which uses databases of category-annotated, mutually-aligned meshes, we develop a pipeline using vision-language models (VLMs) to retrieve meshes from massive databases of un-annotated, inconsistently-aligned meshes. Experimental evaluations show that our system outperforms generative models trained on 3D data for traditional, closed-universe scene generation tasks; it also outperforms a recent LLM-based layout generation method on open-universe scene generation.

In SPARQL, the query forms SELECT and CONSTRUCT have been the subject of several studies, both theoretical and practical. However, the composition of such queries and their interweaving when forming involved nested queries has not yet received much interest in the literature. We mainly tackle the problem of composing such queries. For this purpose, we introduce a language close to SPARQL where queries can be nested at will, involving either CONSTRUCT or SELECT query forms and provide a formal semantics for it. This semantics is based on a uniform interpretation of queries. This uniformity is due to an extension of the notion of RDF graphs to include isolated items such as variables. As a key feature of this work, we show how classical SELECT queries can be easily encoded as a particular case of CONSTRUCT queries.

Few-shot prompting is a surprisingly powerful way to use Large Language Models (LLMs) to solve various tasks. However, this approach struggles as the task complexity increases or when the individual reasoning steps of the task themselves are hard to learn, especially when embedded in more complex tasks. To address this, we propose Decomposed Prompting, a new approach to solve complex tasks by decomposing them (via prompting) into simpler sub-tasks that can be delegated to a library of prompting-based LLMs dedicated to these sub-tasks. This modular structure allows each prompt to be optimized for its specific sub-task, further decomposed if necessary, and even easily replaced with more effective prompts, trained models, or symbolic functions if desired. We show that the flexibility and modularity of Decomposed Prompting allows it to outperform prior work on few-shot prompting using GPT3. On symbolic reasoning tasks, we can further decompose sub-tasks that are hard for LLMs into even simpler solvable sub-tasks. When the complexity comes from the input length, we can recursively decompose the task into the same task but with smaller inputs. We also evaluate our approach on textual multi-step reasoning tasks: on long-context multi-hop QA task, we can more effectively teach the sub-tasks via our separate sub-tasks prompts; and on open-domain multi-hop QA, we can incorporate a symbolic information retrieval within our decomposition framework, leading to improved performance on both tasks. Datasets, Code and Prompts available at https://github.com/allenai/DecomP.

In the quest to facilitate the deep intelligence of Large Language Models (LLMs) accessible in final-end user-bot interactions, the art of prompt crafting emerges as a critical yet complex task for the average user. Contrast to previous model-oriented yet instruction-agnostic Automatic Prompt Optimization methodologies, yielding polished results for predefined target models while suffering rapid degradation with out-of-box models, we present Free-form Instruction-oriented Prompt Optimization (FIPO). This approach is supported by our large-scale prompt preference dataset and employs a modular fine-tuning schema. The FIPO schema reimagines the optimization process into manageable modules, anchored by a meta prompt that dynamically adapts content. This allows for the flexible integration of the raw task instruction, the optional instruction response, and the optional ground truth to produce finely optimized task prompts. The FIPO preference dataset is meticulously constructed using the optimal and suboptimal LLMs, undergoing rigorous cross-verification by human experts and analytical models. Applying the insights from the data with Tulu2 models and fine-tuning strategies, we validate the efficacy of FIPO schema across five public benchmarks. Codes, data and scripts are here: https://github.com/LuJunru/FIPO_Project.

Prompt engineering is a challenging yet crucial task for optimizing the performance of large language models (LLMs). It requires complex reasoning to examine the model's errors, hypothesize what is missing or misleading in the current prompt, and communicate the task with clarity. While recent works indicate that LLMs can be meta-prompted to perform automatic prompt engineering, their potentials may not be fully untapped due to the lack of sufficient guidance to elicit complex reasoning capabilities in LLMs in the meta-prompt. In this work, we investigate the problem of "prompt engineering a prompt engineer" -- constructing a meta-prompt that more effectively guides LLMs to perform automatic prompt engineering. We introduce and analyze key components, such as a step-by-step reasoning template and context specification, which lead to improved performance. In addition, inspired by common optimization concepts such as batch size, step size and momentum, we introduce their verbalized counterparts to the meta-prompt and investigate their effects. Our final method, named PE2, finds a prompt that outperforms "let's think step by step" by 6.3% on the MultiArith dataset and 3.1% on the GSM8K dataset. To demonstrate its versatility, we apply PE2 to the Instruction Induction benchmark, a suite of counterfactual tasks, and a lengthy, real-world industrial prompt. In these settings, PE2 achieves strong performance and outperforms prior automatic prompt engineering baselines. Further, we show that PE2 makes meaningful and targeted prompt edits, amends erroneous or incomplete prompts, and presents non-trivial counterfactual reasoning abilities.

Recent advances in Hierarchical Multi-label Classification (HMC), particularly neurosymbolic-based approaches, have demonstrated improved consistency and accuracy by enforcing constraints on a neural model during training. However, such work assumes the existence of such constraints a-priori. In this paper, we relax this strong assumption and present an approach based on Error Detection Rules (EDR) that allow for learning explainable rules about the failure modes of machine learning models. We show that these rules are not only effective in detecting when a machine learning classifier has made an error but also can be leveraged as constraints for HMC, thereby allowing the recovery of explainable constraints even if they are not provided. We show that our approach is effective in detecting machine learning errors and recovering constraints, is noise tolerant, and can function as a source of knowledge for neurosymbolic models on multiple datasets, including a newly introduced military vehicle recognition dataset.

Existing reasoning evaluation frameworks for Large Language Models (LLMs) and Large Vision-Language Models (LVLMs) predominantly either assess text-based reasoning or vision-language understanding capabilities, with limited dynamic interplay between textual and visual constraints. To address this limitation, we introduce CrossWordBench, a benchmark designed to evaluate the reasoning capabilities of both LLMs and LVLMs through the medium of crossword puzzles-a task requiring multimodal adherence to semantic constraints from text-based clues and intersectional constraints from visual grid structures. CrossWordBench leverages a controllable puzzle generation framework that produces puzzles in multiple formats (text and image) and offers different evaluation strategies ranging from direct puzzle solving to interactive modes. Our extensive evaluation of over 20 models reveals that reasoning LLMs outperform non-reasoning models substantially by effectively leveraging crossing-letter constraints. We further demonstrate that LVLMs struggle with the task, showing a strong correlation between their puzzle-solving performance and grid-parsing accuracy. Our findings offer insights into the limitations of the reasoning capabilities of current LLMs and LVLMs, and provide an effective approach for creating multimodal constrained tasks for future evaluations.

We introduce "Method Actors" as a mental model for guiding LLM prompt engineering and prompt architecture. Under this mental model, LLMs should be thought of as actors; prompts as scripts and cues; and LLM responses as performances. We apply this mental model to the task of improving LLM performance at playing Connections, a New York Times word puzzle game that prior research identified as a challenging benchmark for evaluating LLM reasoning. Our experiments with GPT-4o show that a "Method Actors" approach can significantly improve LLM performance over both a vanilla and "Chain of Thoughts" approach. A vanilla approach solves 27% of Connections puzzles in our dataset and a "Chain of Thoughts" approach solves 41% of puzzles, whereas our strongest "Method Actor" approach solves 86% of puzzles. We also test OpenAI's newest model designed specifically for complex reasoning tasks, o1-preview. When asked to solve a puzzle all at once, o1-preview solves 79% of Connections puzzles in our dataset, and when allowed to build puzzle solutions one guess at a time over multiple API calls, o1-preview solves 100% of the puzzles. Incorporating a "Method Actor" prompt architecture increases the percentage of puzzles that o1-preview solves perfectly from 76% to 87%.

Large language models (LLMs) have shown increasing in-context learning capabilities through scaling up model and data size. Despite this progress, LLMs are still unable to solve algorithmic reasoning problems. While providing a rationale with the final answer has led to further improvements in multi-step reasoning problems, Anil et al. 2022 showed that even simple algorithmic reasoning tasks such as parity are far from solved. In this work, we identify and study four key stages for successfully teaching algorithmic reasoning to LLMs: (1) formulating algorithms as skills, (2) teaching multiple skills simultaneously (skill accumulation), (3) teaching how to combine skills (skill composition) and (4) teaching how to use skills as tools. We show that it is possible to teach algorithmic reasoning to LLMs via in-context learning, which we refer to as algorithmic prompting. We evaluate our approach on a variety of arithmetic and quantitative reasoning tasks, and demonstrate significant boosts in performance over existing prompting techniques. In particular, for long parity, addition, multiplication and subtraction, we achieve an error reduction of approximately 10x, 9x, 5x and 2x respectively compared to the best available baselines.

We consider the task of text generation in language models with constraints specified in natural language. To this end, we first create a challenging benchmark Cognac that provides as input to the model a topic with example text, along with a constraint on text to be avoided. Unlike prior work, our benchmark contains knowledge-intensive constraints sourced from databases like Wordnet and Wikidata, which allows for straightforward evaluation while striking a balance between broad attribute-level and narrow lexical-level controls. We find that even state-of-the-art language models like GPT-3 fail often on this task, and propose a solution to leverage a language model's own internal knowledge to guide generation. Our method, called CognacGen, first queries the language model to generate guidance terms for a specified topic or constraint, and uses the guidance to modify the model's token generation probabilities. We propose three forms of guidance (binary verifier, top-k tokens, textual example), and employ prefix-tuning approaches to distill the guidance to tackle diverse natural language constraints. Through extensive empirical evaluations, we demonstrate that CognacGen can successfully generalize to unseen instructions and outperform competitive baselines in generating constraint conforming text.

Solving complex visual tasks such as "Who invented the musical instrument on the right?" involves a composition of skills: understanding space, recognizing instruments, and also retrieving prior knowledge. Recent work shows promise by decomposing such tasks using a large language model (LLM) into an executable program that invokes specialized vision models. However, generated programs are error-prone: they omit necessary steps, include spurious ones, and are unable to recover when the specialized models give incorrect outputs. Moreover, they require loading multiple models, incurring high latency and computation costs. We propose Visual Program Distillation (VPD), an instruction tuning framework that produces a vision-language model (VLM) capable of solving complex visual tasks with a single forward pass. VPD distills the reasoning ability of LLMs by using them to sample multiple candidate programs, which are then executed and verified to identify a correct one. It translates each correct program into a language description of the reasoning steps, which are then distilled into a VLM. Extensive experiments show that VPD improves the VLM's ability to count, understand spatial relations, and reason compositionally. Our VPD-trained PaLI-X outperforms all prior VLMs, achieving state-of-the-art performance across complex vision tasks, including MMBench, OK-VQA, A-OKVQA, TallyQA, POPE, and Hateful Memes. An evaluation with human annotators also confirms that VPD improves model response factuality and consistency. Finally, experiments on content moderation demonstrate that VPD is also helpful for adaptation to real-world applications with limited data.

Modelling compositionality has been a longstanding area of research in the field of vector space semantics. The categorical approach to compositionality maps grammar onto vector spaces in a principled way, but comes under fire for requiring the formation of very high-dimensional matrices and tensors, and therefore being computationally infeasible. In this paper I show how a linear simplification of recursive neural tensor network models can be mapped directly onto the categorical approach, giving a way of computing the required matrices and tensors. This mapping suggests a number of lines of research for both categorical compositional vector space models of meaning and for recursive neural network models of compositionality.

Structure reasoning is a fundamental capability of large language models (LLMs), enabling them to reason about structured commonsense and answer multi-hop questions. However, existing benchmarks for structure reasoning mainly focus on horizontal and coordinate structures (e.g. graphs), overlooking the hierarchical relationships within them. Hierarchical structure reasoning is crucial for human cognition, particularly in memory organization and problem-solving. It also plays a key role in various real-world tasks, such as information extraction and decision-making. To address this gap, we propose HiBench, the first framework spanning from initial structure generation to final proficiency assessment, designed to benchmark the hierarchical reasoning capabilities of LLMs systematically. HiBench encompasses six representative scenarios, covering both fundamental and practical aspects, and consists of 30 tasks with varying hierarchical complexity, totaling 39,519 queries. To evaluate LLMs comprehensively, we develop five capability dimensions that depict different facets of hierarchical structure understanding. Through extensive evaluation of 20 LLMs from 10 model families, we reveal key insights into their capabilities and limitations: 1) existing LLMs show proficiency in basic hierarchical reasoning tasks; 2) they still struggle with more complex structures and implicit hierarchical representations, especially in structural modification and textual reasoning. Based on these findings, we create a small yet well-designed instruction dataset, which enhances LLMs' performance on HiBench by an average of 88.84\% (Llama-3.1-8B) and 31.38\% (Qwen2.5-7B) across all tasks. The HiBench dataset and toolkit are available here, https://github.com/jzzzzh/HiBench, to encourage evaluation.

Compositional generalization is crucial for artificial intelligence agents to solve complex vision-language reasoning tasks. Neuro-symbolic approaches have demonstrated promise in capturing compositional structures, but they face critical challenges: (a) reliance on predefined predicates for symbolic representations that limit adaptability, (b) difficulty in extracting predicates from raw data, and (c) using non-differentiable operations for combining primitive concepts. To address these issues, we propose NeSyCoCo, a neuro-symbolic framework that leverages large language models (LLMs) to generate symbolic representations and map them to differentiable neural computations. NeSyCoCo introduces three innovations: (a) augmenting natural language inputs with dependency structures to enhance the alignment with symbolic representations, (b) employing distributed word representations to link diverse, linguistically motivated logical predicates to neural modules, and (c) using the soft composition of normalized predicate scores to align symbolic and differentiable reasoning. Our framework achieves state-of-the-art results on the ReaSCAN and CLEVR-CoGenT compositional generalization benchmarks and demonstrates robust performance with novel concepts in the CLEVR-SYN benchmark.

A fundamental problem in combinatorial optimization is identifying equivalent formulations, which can lead to more efficient solution strategies and deeper insights into a problem's computational complexity. The need to automatically identify equivalence between problem formulations has grown as optimization copilots--systems that generate problem formulations from natural language descriptions--have proliferated. However, existing approaches to checking formulation equivalence lack grounding, relying on simple heuristics which are insufficient for rigorous validation. Inspired by Karp reductions, in this work we introduce quasi-Karp equivalence, a formal criterion for determining when two optimization formulations are equivalent based on the existence of a mapping between their decision variables. We propose EquivaMap, a framework that leverages large language models to automatically discover such mappings, enabling scalable and reliable equivalence verification. To evaluate our approach, we construct the first open-source dataset of equivalent optimization formulations, generated by applying transformations such as adding slack variables or valid inequalities to existing formulations. Empirically, EquivaMap significantly outperforms existing methods, achieving substantial improvements in correctly identifying formulation equivalence.

This is the first work to look at the application of large language models (LLMs) for the purpose of model space edits in automated planning tasks. To set the stage for this union, we explore two different flavors of model space problems that have been studied in the AI planning literature and explore the effect of an LLM on those tasks. We empirically demonstrate how the performance of an LLM contrasts with combinatorial search (CS) -- an approach that has been traditionally used to solve model space tasks in planning, both with the LLM in the role of a standalone model space reasoner as well as in the role of a statistical signal in concert with the CS approach as part of a two-stage process. Our experiments show promising results suggesting further forays of LLMs into the exciting world of model space reasoning for planning tasks in the future.

Recent reasoning-oriented LLMs have demonstrated strong performance on challenging tasks such as mathematics and science examinations. However, core cognitive faculties of human intelligence, such as abstract reasoning and generalization, remain underexplored. To address this, we evaluate recent reasoning-oriented LLMs on the Abstraction and Reasoning Corpus (ARC) benchmark, which explicitly demands both faculties. We formulate ARC as a program synthesis task and propose nine candidate solvers. Experimental results show that repeated-sampling planning-aided code generation (RSPC) achieves the highest test accuracy and demonstrates consistent generalization across most LLMs. To further improve performance, we introduce an ARC solver, Knowledge Augmentation for Abstract Reasoning (KAAR), which encodes core knowledge priors within an ontology that classifies priors into three hierarchical levels based on their dependencies. KAAR progressively expands LLM reasoning capacity by gradually augmenting priors at each level, and invokes RSPC to generate candidate solutions after each augmentation stage. This stage-wise reasoning reduces interference from irrelevant priors and improves LLM performance. Empirical results show that KAAR maintains strong generalization and consistently outperforms non-augmented RSPC across all evaluated LLMs, achieving around 5% absolute gains and up to 64.52% relative improvement. Despite these achievements, ARC remains a challenging benchmark for reasoning-oriented LLMs, highlighting future avenues of progress in 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.