Daily Papers

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.

Combinatorial problems are present in a wide range of industries. Constraint Programming (CP) is a well-suited problem-solving paradigm, but its core process, namely constraint modelling, is a bottleneck for wider adoption. Aiming to alleviate this bottleneck, recent studies have explored using Large Language Models (LLMs) as modelling assistants, transforming combinatorial problem descriptions to executable constraint models, similar to coding assistants. However, the existing evaluation datasets for constraint modelling are often limited to small, homogeneous, or domain-specific instances, which do not capture the diversity of real-world scenarios. This work addresses this gap by introducing CP-Bench, a novel benchmark dataset that includes a diverse set of well-known combinatorial problem classes sourced from the CP community, structured explicitly for evaluating LLM-driven CP modelling. With this dataset, and given the variety of constraint modelling frameworks, we compare and evaluate the modelling capabilities of LLMs for three distinct constraint modelling systems, which vary in abstraction level and underlying syntax: the high-level MiniZinc language and Python-based CPMpy library, and the lower-level Python interface of the OR-Tools CP-SAT solver. In order to enhance the ability of LLMs to produce valid constraint models, we systematically evaluate the use of prompt-based and inference-time compute methods adapted from existing LLM-based code generation research. Our results underscore the modelling convenience provided by Python-based frameworks, as well as the effectiveness of documentation-rich system prompts, which, augmented with repeated sampling and self-verification, achieve further improvements, reaching up to 70\% accuracy on this new, highly challenging benchmark.

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.

The adeptness of Large Language Models (LLMs) in comprehending and following natural language instructions is critical for their deployment in sophisticated real-world applications. Existing evaluations mainly focus on fragmented constraints or narrow scenarios, but they overlook the comprehensiveness and authenticity of constraints from the user's perspective. To bridge this gap, we propose CFBench, a large-scale Comprehensive Constraints Following Benchmark for LLMs, featuring 1,000 curated samples that cover more than 200 real-life scenarios and over 50 NLP tasks. CFBench meticulously compiles constraints from real-world instructions and constructs an innovative systematic framework for constraint types, which includes 10 primary categories and over 25 subcategories, and ensures each constraint is seamlessly integrated within the instructions. To make certain that the evaluation of LLM outputs aligns with user perceptions, we propose an advanced methodology that integrates multi-dimensional assessment criteria with requirement prioritization, covering various perspectives of constraints, instructions, and requirement fulfillment. Evaluating current leading LLMs on CFBench reveals substantial room for improvement in constraints following, and we further investigate influencing factors and enhancement strategies. The data and code are publicly available at https://github.com/PKU-Baichuan-MLSystemLab/CFBench

The Bernays-Sch\"onfinkel first-order logic fragment over simple linear real arithmetic constraints BS(SLR) is known to be decidable. We prove that BS(SLR) clause sets with both universally and existentially quantified verification conditions (conjectures) can be translated into BS(SLR) clause sets over a finite set of first-order constants. For the Horn case, we provide a Datalog hammer preserving validity and satisfiability. A toolchain from the BS(LRA) prover SPASS-SPL to the Datalog reasoner VLog establishes an effective way of deciding verification conditions in the Horn fragment. This is exemplified by the verification of supervisor code for a lane change assistant in a car and of an electronic control unit for a supercharged combustion engine.

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.

High-quality mathematical and logical datasets with verifiable answers are essential for strengthening the reasoning capabilities of large language models (LLMs). While recent data augmentation techniques have facilitated the creation of large-scale benchmarks, existing LLM-generated datasets often suffer from limited reliability, diversity, and scalability. To address these challenges, we introduce PuzzleClone, a formal framework for synthesizing verifiable data at scale using Satisfiability Modulo Theories (SMT). Our approach features three key innovations: (1) encoding seed puzzles into structured logical specifications, (2) generating scalable variants through systematic variable and constraint randomization, and (3) ensuring validity via a reproduction mechanism. Applying PuzzleClone, we construct a curated benchmark comprising over 83K diverse and programmatically validated puzzles. The generated puzzles span a wide spectrum of difficulty and formats, posing significant challenges to current state-of-the-art models. We conduct post training (SFT and RL) on PuzzleClone datasets. Experimental results show that training on PuzzleClone yields substantial improvements not only on PuzzleClone testset but also on logic and mathematical benchmarks. Post training raises PuzzleClone average from 14.4 to 56.2 and delivers consistent improvements across 7 logic and mathematical benchmarks up to 12.5 absolute percentage points (AMC2023 from 52.5 to 65.0). Our code and data are available at https://github.com/puzzleclone.

Recent advancements in large language models (LLMs) suggest great promises in code and proof generations. However, scaling automated formal verification to real-world projects requires resolving cross-module dependencies and global contexts, which are crucial challenges overlooked by existing LLM-based methods with a special focus on targeting isolated, function-level verification tasks. To systematically explore and address the significant challenges of verifying entire software repositories, we introduce RVBench, the first verification benchmark explicitly designed for repository-level evaluation, constructed from four diverse and complex open-source Verus projects. We further introduce RagVerus, an extensible framework that synergizes retrieval-augmented generation with context-aware prompting to automate proof synthesis for multi-module repositories. RagVerus triples proof pass rates on existing benchmarks under constrained model inference budgets, and achieves a 27% relative improvement on the more challenging RVBench benchmark, demonstrating a scalable and sample-efficient verification solution.

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.

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

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.

As large language models (LLMs) are increasingly applied to scientific reasoning, the complexity of answer formats and the diversity of equivalent expressions make answer verification a critical yet challenging task. Existing verification studies in scientific domains suffer from two major limitations: (a) the absence of systematic evaluation standards and insufficient disciplinary coverage, which hinders their comprehensive assessment; and (b) heavy reliance on cumbersome rule design or prompt engineering, which reduces their effectiveness in complex reasoning scenarios or limits their cross-disciplinary generalization. To address these challenges, we propose solutions at both the data and model levels. On the data side, we construct SCI-VerifyBench, a cross-disciplinary benchmark covering mathematics, physics, biology, chemistry, and general scientific QA. The benchmark is built from real LLM responses and enhanced with domain-specific equivalence transformations that generate challenging and realistic data. Model-based and expert annotations ensure both quality and diversity, enabling rigorous evaluation of verification ability. On the model side, we emphasize the importance of reasoning for verification and introduce SCI-Verifier, a unified reasoning-augmented verifier for scientific domains. Through post-training, SCI-Verifier demonstrates strong logical reasoning and equivalence judgment capabilities while maintaining concise and stable outputs. Together, SCI-VerifyBench and SCI-Verifier provide a principled framework for scientific verification, offering both systematic evaluation and practical pathways to enhance the reliability and applicability of LLMs in scientific domains.

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.

Scaling automated formal verification to real-world projects requires resolving cross-module dependencies and global contexts, which are challenges overlooked by existing function-centric methods. We introduce RagVerus, a framework that synergizes retrieval-augmented generation with context-aware prompting to automate proof synthesis for multi-module repositories, achieving a 27% relative improvement on our novel RepoVBench benchmark -- the first repository-level dataset for Verus with 383 proof completion tasks. RagVerus triples proof pass rates on existing benchmarks under constrained language model budgets, demonstrating a scalable and sample-efficient verification.

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.

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.

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.

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 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.

Formal theorem proving (FTP) has emerged as a critical foundation for evaluating the reasoning capabilities of large language models, enabling automated verification of mathematical proofs at scale. However, progress has been constrained by limited datasets due to the high cost of manual curation and the scarcity of challenging problems with verified formal-informal correspondences. We propose leveraging theoretical computer science (TCS) as a scalable source of rigorous proof problems, where algorithmic definitions enable automated generation of arbitrarily many challenging theorem-proof pairs. We demonstrate this approach on two TCS domains: Busy Beaver problems, which involve proving bounds on Turing machine halting behavior, and Mixed Boolean Arithmetic problems, which combine logical and arithmetic reasoning. Our framework automatically synthesizes problems with parallel formal (Lean4) and informal (Markdown) specifications, creating a scalable pipeline for generating verified proof challenges. Evaluation on frontier models reveals substantial gaps in automated theorem proving: while DeepSeekProver-V2-671B achieves 57.5\% success on Busy Beaver problems, it manages only 12\% on Mixed Boolean Arithmetic problems. These results highlight the difficulty of long-form proof generation even for problems that are computationally easy to verify, demonstrating the value of TCS domains for advancing automated reasoning research.

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.

Automated Theorem Proving (ATP) in formal languages is a foundational challenge for AI. While Large Language Models (LLMs) have driven remarkable progress, a significant gap remains between their powerful informal reasoning capabilities and their weak formal proving performance. Recent studies show that the informal accuracy exceeds 80% while formal success remains below 8% on benchmarks like PutnamBench. We argue this gap persists because current state-of-the-art provers, by tightly coupling reasoning and proving, are trained with paradigms that inadvertently punish deep reasoning in favor of shallow, tactic-based strategies. To bridge this fundamental gap, we propose a novel framework that decouples high-level reasoning from low-level proof generation. Our approach utilizes two distinct, specialized models: a powerful, general-purpose Reasoner to generate diverse, strategic subgoal lemmas, and an efficient Prover to rigorously verify them. This modular design liberates the model's full reasoning potential and bypasses the pitfalls of end-to-end training. We evaluate our method on a challenging set of post-2000 IMO problems, a problem set on which no prior open-source prover has reported success. Our decoupled framework successfully solves 5 of these problems, demonstrating a significant step towards automated reasoning on exceptionally difficult mathematical challenges. To foster future research, we release our full dataset of generated and verified lemmas for a wide range of IMO problems, available at https://tencent-imo.github.io/ .

Large language models (LLMs) have advanced significantly in code generation, yet their ability to follow complex programming instructions with layered and diverse constraints remains underexplored. Existing benchmarks often prioritize functional correctness, overlooking the nuanced requirements found in real-world development. We introduce MultiCodeIF, a comprehensive benchmark designed to evaluate instruction-following in code generation across multiple dimensions: constraint type, hierarchical levels, and iterative refinement. Built upon a structured taxonomy of 9 categories and 27 constraint types, MultiCodeIF enables granular assessment of both functional and non-functional instruction adherence. Using an automated pipeline, ConstraGen, we synthesize and evolve 2,021 code tasks sourced from 14 programming languages, supporting multi-turn evaluation through feedback-driven task variants. Empirical evaluation of six state-of-the-art LLMs uncovers substantial performance disparities. The top-performing model, Claude-3-7-Sonnet, achieves 63.0% average constraint satisfaction, while smaller models like Qwen3-1.7B fall to 44.8%. Models perform well on explicit constraints, but struggle with implicit or abstract constraints. Tasks with multiple hierarchical constraints significantly reduce model success rates, from 54.5% in single-level to just 18.8% in multi-level scenarios. However, structured feedback enables progressive improvement: average constraint satisfaction rises from 63.0% to 83.4% over four iterative refinement rounds. MultiCodeIF provides a scalable, constraint-aware, and feedback-sensitive framework to benchmark LLMs under realistic code generation scenarios, bridging the gap between synthetic evaluations and real-world instruction complexity. The full benchmark dataset, evaluation pipeline, and source code are available at https://github.com/SYSUSELab/MultiCodeIF.

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.

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.

Effective scheduling under tight resource, timing, and operational constraints underpins large-scale planning across sectors such as capital projects, manufacturing, logistics, and IT fleet transitions. However, the reliability of large language models (LLMs) when reasoning under high-constraint regimes is insufficiently characterized. To address this gap, we present R-ConstraintBench, a scalable framework that evaluates models on Resource-Constrained Project Scheduling Problems (RCPSP), an NP-Complete feasibility class, while difficulty increases via linear growth in constraints. R-ConstraintBench incrementally increases non-redundant precedence constraints in Directed Acyclic Graphs (DAGs) and then introduces downtime, temporal windows, and disjunctive constraints. As an illustrative example, we instantiate the benchmark in a data center migration setting and evaluate multiple LLMs using feasibility and error analysis, identifying degradation thresholds and constraint types most associated with failure. Empirically, strong models are near-ceiling on precedence-only DAGs, but feasibility performance collapses when downtime, temporal windows, and disjunctive constraints interact, implicating constraint interaction, not graph depth, as the principal bottleneck. Performance on clean synthetic ramps also does not guarantee transfer to domain-grounded scenarios, underscoring limited generalization.

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.

Large Language Model (LLM) reasoning for complex tasks inherently involves a trade-off between solution accuracy and computational efficiency. The subsequent step of verification, while intended to improve performance, further complicates this landscape by introducing its own challenging trade-off: sophisticated Generative Reward Models (GenRMs) can be computationally prohibitive if naively integrated with LLMs at test-time, while simpler, faster methods may lack reliability. To overcome these challenges, we introduce FlexiVe, a novel generative verifier that flexibly balances computational resources between rapid, reliable fast thinking and meticulous slow thinking using a Flexible Allocation of Verification Budget strategy. We further propose the Solve-Detect-Verify pipeline, an efficient inference-time scaling framework that intelligently integrates FlexiVe, proactively identifying solution completion points to trigger targeted verification and provide focused solver feedback. Experiments show FlexiVe achieves superior accuracy in pinpointing errors within reasoning traces on ProcessBench. Furthermore, on challenging mathematical reasoning benchmarks (AIME 2024, AIME 2025, and CNMO), our full approach outperforms baselines like self-consistency in reasoning accuracy and inference efficiency. Our system offers a scalable and effective solution to enhance LLM reasoning at test time.

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.

As a vital stage of automated rule checking (ARC), rule interpretation of regulatory texts requires considerable effort. However, interpreting regulatory clauses with implicit properties or complex computational logic is still challenging due to the lack of domain knowledge and limited expressibility of conventional logic representations. Thus, LLM-FuncMapper, an approach to identifying predefined functions needed to interpret various regulatory clauses based on the large language model (LLM), is proposed. First, by systematically analysis of building codes, a series of atomic functions are defined to capture shared computational logics of implicit properties and complex constraints, creating a database of common blocks for interpreting regulatory clauses. Then, a prompt template with the chain of thought is developed and further enhanced with a classification-based tuning strategy, to enable common LLMs for effective function identification. Finally, the proposed approach is validated with statistical analysis, experiments, and proof of concept. Statistical analysis reveals a long-tail distribution and high expressibility of the developed function database, with which almost 100% of computer-processible clauses can be interpreted and represented as computer-executable codes. Experiments show that LLM-FuncMapper achieve promising results in identifying relevant predefined functions for rule interpretation. Further proof of concept in automated rule interpretation also demonstrates the possibility of LLM-FuncMapper in interpreting complex regulatory clauses. To the best of our knowledge, this study is the first attempt to introduce LLM for understanding and interpreting complex regulatory clauses, which may shed light on further adoption of LLM in the construction domain.

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.

We present FIMO, an innovative dataset comprising formal mathematical problem statements sourced from the International Mathematical Olympiad (IMO) Shortlisted Problems. Designed to facilitate advanced automated theorem proving at the IMO level, FIMO is currently tailored for the Lean formal language. It comprises 149 formal problem statements, accompanied by both informal problem descriptions and their corresponding LaTeX-based informal proofs. Through initial experiments involving GPT-4, our findings underscore the existing limitations in current methodologies, indicating a substantial journey ahead before achieving satisfactory IMO-level automated theorem proving outcomes.

Agents based on large language models (LLMs) have demonstrated effectiveness in solving a wide range of tasks by integrating LLMs with key modules such as planning, memory, and tool usage. Increasingly, customers are adopting LLM agents across a variety of commercial applications critical to reliability, including support for mental well-being, chemical synthesis, and software development. Nevertheless, our observations and daily use of LLM agents indicate that they are prone to making erroneous plans, especially when the tasks are complex and require long-term planning. In this paper, we propose PDoctor, a novel and automated approach to testing LLM agents and understanding their erroneous planning. As the first work in this direction, we formulate the detection of erroneous planning as a constraint satisfiability problem: an LLM agent's plan is considered erroneous if its execution violates the constraints derived from the user inputs. To this end, PDoctor first defines a domain-specific language (DSL) for user queries and synthesizes varying inputs with the assistance of the Z3 constraint solver. These synthesized inputs are natural language paragraphs that specify the requirements for completing a series of tasks. Then, PDoctor derives constraints from these requirements to form a testing oracle. We evaluate PDoctor with three mainstream agent frameworks and two powerful LLMs (GPT-3.5 and GPT-4). The results show that PDoctor can effectively detect diverse errors in agent planning and provide insights and error characteristics that are valuable to both agent developers and users. We conclude by discussing potential alternative designs and directions to extend PDoctor.

Instance-specific algorithm configuration and algorithm portfolios have been shown to offer significant improvements over single algorithm approaches in a variety of application domains. In the SAT and CSP domains algorithm portfolios have consistently dominated the main competitions in these fields for the past five years. For a portfolio approach to be effective there are two crucial conditions that must be met. First, there needs to be a collection of complementary solvers with which to make a portfolio. Second, there must be a collection of problem features that can accurately identify structural differences between instances. This paper focuses on the latter issue: feature representation, because, unlike SAT, not every problem has well-studied features. We employ the well-known SATzilla feature set, but compute alternative sets on different SAT encodings of CSPs. We show that regardless of what encoding is used to convert the instances, adequate structural information is maintained to differentiate between problem instances, and that this can be exploited to make an effective portfolio-based CSP solver.

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.

In this article, we introduce a new parameterized family of topological invariants, taking the form of candidate decompositions, for multi-parameter persistence modules. We prove that our candidate decompositions are controllable approximations: when restricting to modules that can be decomposed into interval summands, we establish theoretical results about the approximation error between our candidate decompositions and the true underlying module in terms of the standard interleaving and bottleneck distances. Moreover, even when the underlying module does not admit such a decomposition, our candidate decompositions are nonetheless stable invariants; small perturbations in the underlying module lead to small perturbations in the candidate decomposition. Then, we introduce MMA (Multipersistence Module Approximation): an algorithm for computing stable instances of such invariants, which is based on fibered barcodes and exact matchings, two constructions that stem from the theory of single-parameter persistence. By design, MMA can handle an arbitrary number of filtrations, and has bounded complexity and running time. Finally, we present empirical evidence validating the generalization capabilities and running time speed-ups of MMA on several data sets.

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

JSON Schema is an important, evolving standard schema language for families of JSON documents. It is based on a complex combination of structural and Boolean assertions, and features negation and recursion. The static analysis of JSON Schema documents comprises practically relevant problems, including schema satisfiability, inclusion, and equivalence. These three problems can be reduced to witness generation: given a schema, generate an element of the schema, if it exists, and report failure otherwise. Schema satisfiability, inclusion, and equivalence have been shown to be decidable, by reduction to reachability in alternating tree automata. However, no witness generation algorithm has yet been formally described. We contribute a first, direct algorithm for JSON Schema witness generation. We study its effectiveness and efficiency, in experiments over several schema collections, including thousands of real-world schemas. Our focus is on the completeness of the language, where we only exclude the uniqueItems operator, and on the ability of the algorithm to run in a reasonable time on a large set of real-world examples, despite the exponential complexity of the underlying problem.

We study the ability of state-of-the art models to answer constraint satisfaction queries for information retrieval (e.g., 'a list of ice cream shops in San Diego'). In the past, such queries were considered to be tasks that could only be solved via web-search or knowledge bases. More recently, large language models (LLMs) have demonstrated initial emergent abilities in this task. However, many current retrieval benchmarks are either saturated or do not measure constraint satisfaction. Motivated by rising concerns around factual incorrectness and hallucinations of LLMs, we present KITAB, a new dataset for measuring constraint satisfaction abilities of language models. KITAB consists of book-related data across more than 600 authors and 13,000 queries, and also offers an associated dynamic data collection and constraint verification approach for acquiring similar test data for other authors. Our extended experiments on GPT4 and GPT3.5 characterize and decouple common failure modes across dimensions such as information popularity, constraint types, and context availability. Results show that in the absence of context, models exhibit severe limitations as measured by irrelevant information, factual errors, and incompleteness, many of which exacerbate as information popularity decreases. While context availability mitigates irrelevant information, it is not helpful for satisfying constraints, identifying fundamental barriers to constraint satisfaction. We open source our contributions to foster further research on improving constraint satisfaction abilities of future models.

Formal verification can provably guarantee the correctness of critical system software, but the high proof burden has long hindered its wide adoption. Recently, Large Language Models (LLMs) have shown success in code analysis and synthesis. In this paper, we present a combination of LLMs and static analysis to synthesize invariants, assertions, and other proof structures for a Rust-based formal verification framework called Verus. In a few-shot setting, LLMs demonstrate impressive logical ability in generating postconditions and loop invariants, especially when analyzing short code snippets. However, LLMs lack the ability to retain and propagate context information, a strength of traditional static analysis. Based on these observations, we developed a prototype based on OpenAI's GPT-4 model. Our prototype decomposes the verification task into multiple smaller ones, iteratively queries GPT-4, and combines its output with lightweight static analysis. We evaluated the prototype with a developer in the automation loop on 20 vector-manipulating programs. The results demonstrate that it significantly reduces human effort in writing entry-level proof code.

This paper presents a quantitative program verification infrastructure for discrete probabilistic programs. Our infrastructure can be viewed as the probabilistic analogue of Boogie: its central components are an intermediate verification language (IVL) together with a real-valued logic. Our IVL provides a programming-language-style for expressing verification conditions whose validity implies the correctness of a program under investigation. As our focus is on verifying quantitative properties such as bounds on expected outcomes, expected run-times, or termination probabilities, off-the-shelf IVLs based on Boolean first-order logic do not suffice. Instead, a paradigm shift from the standard Boolean to a real-valued domain is required. Our IVL features quantitative generalizations of standard verification constructs such as assume- and assert-statements. Verification conditions are generated by a weakest-precondition-style semantics, based on our real-valued logic. We show that our verification infrastructure supports natural encodings of numerous verification techniques from the literature. With our SMT-based implementation, we automatically verify a variety of benchmarks. To the best of our knowledge, this establishes the first deductive verification infrastructure for expectation-based reasoning about probabilistic programs.

Large Language Models (LLMs) have demonstrated a powerful ability for text generation. However, achieving optimal results with a given prompt or instruction can be challenging, especially for billion-sized models. Additionally, undesired behaviors such as toxicity or hallucinations can manifest. While much larger models (e.g., ChatGPT) may demonstrate strength in mitigating these issues, there is still no guarantee of complete prevention. In this work, we propose formalizing text generation as a future-constrained generation problem to minimize undesirable behaviors and enforce faithfulness to instructions. The estimation of future constraint satisfaction, accomplished using LLMs, guides the text generation process. Our extensive experiments demonstrate the effectiveness of the proposed approach across three distinct text generation tasks: keyword-constrained generation (Lin et al., 2020), toxicity reduction (Gehman et al., 2020), and factual correctness in question-answering (Gao et al., 2023).

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.

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.

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.

Large Language Models (LLMs) have recently achieved remarkable progress in mathematical reasoning. To enable such capabilities, many existing works distill strong reasoning models into long chains of thought or design algorithms to construct high-quality math QA data for training. However, these efforts primarily focus on generating correct reasoning paths and answers, while largely overlooking the validity of the questions themselves. In this work, we propose Math Question Verification (MathQ-Verify), a novel five-stage pipeline designed to rigorously filter ill-posed or under-specified math problems. MathQ-Verify first performs format-level validation to remove redundant instructions and ensure that each question is syntactically well-formed. It then formalizes each question, decomposes it into atomic conditions, and verifies them against mathematical definitions. Next, it detects logical contradictions among these conditions, followed by a goal-oriented completeness check to ensure the question provides sufficient information for solving. To evaluate this task, we use existing benchmarks along with an additional dataset we construct, containing 2,147 math questions with diverse error types, each manually double-validated. Experiments show that MathQ-Verify achieves state-of-the-art performance across multiple benchmarks, improving the F1 score by up to 25 percentage points over the direct verification baseline. It further attains approximately 90% precision and 63% recall through a lightweight model voting scheme. MathQ-Verify offers a scalable and accurate solution for curating reliable mathematical datasets, reducing label noise and avoiding unnecessary computation on invalid questions. Our code and data are available at https://github.com/scuuy/MathQ-Verify.

Mathematical reasoning lies at the heart of artificial intelligence, underpinning applications in education, program verification, and research-level mathematical discovery. Mathematical competitions, in particular, present two challenging problem types: theorem proving, which requires rigorous proofs of stated conclusions, and answer construction, which involves hypothesizing and formally verifying mathematical objects. Large Language Models (LLMs) effectively generate creative candidate answers but struggle with formal verification, while symbolic provers ensure rigor but cannot efficiently handle creative conjecture generation. We introduce the Enumerate-Conjecture-Prove (ECP) framework, a modular neuro-symbolic method integrating LLM-based enumeration and pattern-driven conjecturing with formal theorem proving. We present ConstructiveBench, a dataset of 3,431 answer-construction problems in various math competitions with verified Lean formalizations. On the ConstructiveBench dataset, ECP improves the accuracy of answer construction from a Chain-of-Thought (CoT) baseline of 14.54% to 45.06% with the gpt-4.1-mini model. Moreover, combined with ECP's constructed answers, the state-of-the-art DeepSeek-Prover-V2-7B model generates correct proofs for 858 of the 3,431 constructive problems in Lean, achieving 25.01% accuracy compared to 9.86% for symbolic-only baselines. Our code and dataset are publicly available at https://github.com/JackSun200312/ECP.

This paper proposes a novel column generation framework for combinatorial software testing. In particular, it combines Mathematical Programming and Constraint Programming in a hybrid decomposition to generate covering arrays. The approach allows generating parameterized test cases with coverage guarantees between parameter interactions of a given application. Compared to exhaustive testing, combinatorial test case generation reduces the number of tests to run significantly. Our column generation algorithm is generic and can accommodate mixed coverage arrays over heterogeneous alphabets. The algorithm is realized in practice as a cloud service and recognized as one of the five winners of the company-wide cloud application challenge at Oracle. The service is currently helping software developers from a range of different product teams in their testing efforts while exposing declarative constraint models and hybrid optimization techniques to a broader audience.

The demonstrated code-understanding capability of LLMs raises the question of whether they can be used for automated program verification, a task that often demands high-level abstract reasoning about program properties, which is challenging for verification tools. We propose a general methodology to combine the power of LLMs and automated reasoners for automated program verification. We formally describe this methodology as a set of derivation rules and prove its soundness. We instantiate the calculus as a sound automated verification procedure, which led to practical improvements on a set of synthetic and competition benchmarks.

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.

Formally verifying properties of software code has been a highly desirable task, especially with the emergence of LLM-generated code. In the same vein, they provide an interesting avenue for the exploration of formal verification and mechanistic interpretability. Since the introduction of code-specific models, despite their successes in generating code in Lean4 and Isabelle, the task of generalized theorem proving still remains far from being fully solved and will be a benchmark for reasoning capability in LLMs. In this work, we introduce a framework that generates whole proofs in a formal language to be used within systems that utilize the power of built-in tactics and off-the-shelf automated theorem provers. Our framework includes 3 components: generating natural language statements of the code to be verified, an LLM that generates formal proofs for the given statement, and a module employing heuristics for building the final proof. To train the LLM, we employ a 2-stage fine-tuning process, where we first use SFT-based training to enable the model to generate syntactically correct Isabelle code and then RL-based training that encourages the model to generate proofs verified by a theorem prover. We validate our framework using the miniF2F-test benchmark and the Isabelle proof assistant and design a use case to verify the correctness of the AWS S3 bucket access policy code. We also curate a dataset based on the FVEL\textnormal{ER} dataset for future training tasks.

Traditional vulnerability detection methods rely heavily on predefined rule matching, which often fails to capture vulnerabilities accurately. With the rise of large language models (LLMs), leveraging their ability to understand code semantics has emerged as a promising direction for achieving more accurate and efficient vulnerability detection. However, current LLM-based approaches face significant challenges: instability in model outputs, limitations in context length, and hallucination. As a result, many existing solutions either use LLMs merely to enrich predefined rule sets, thereby keeping the detection process fundamentally rule-based, or over-rely on them, leading to poor robustness. To address these challenges, we propose a constraint-solving approach powered by LLMs named VULSOLVER. By modeling vulnerability detection as a constraint-solving problem, and by integrating static application security testing (SAST) with the semantic reasoning capabilities of LLMs, our method enables the LLM to act like a professional human security expert. We assess VULSOLVER on the OWASP Benchmark (1,023 labeled samples), achieving 96.29% accuracy, 96.55% F1-score, and 100% recall. Applied to popular GitHub repositories, VULSOLVER also identified 15 previously unknown high-severity vulnerabilities (CVSS 7.5-9.8), demonstrating its effectiveness in real-world security analysis.

The research in AI-based formal mathematical reasoning has shown an unstoppable growth trend. These studies have excelled in mathematical competitions like IMO, showing significant progress. However, these studies intertwined multiple skills simultaneously, i.e., problem-solving, reasoning, and writing formal specifications, making it hard to precisely identify the LLMs' strengths and weaknesses in each task. This paper focuses on formal verification, an immediate application scenario of formal reasoning, and decomposes it into six sub-tasks. We constructed 18k high-quality instruction-response pairs across five mainstream formal specification languages (Coq, Lean4, Dafny, ACSL, and TLA+) in six formal-verification-related tasks by distilling GPT-4o. They are split into a 14k+ fine-tuning dataset FM-alpaca and a 4k benchmark FM-Bench. We found that LLMs are good at writing proof segments when given either the code, or the detailed description of proof steps. Also, the fine-tuning brought about a nearly threefold improvement at most. Interestingly, we observed that fine-tuning with formal data also enhances mathematics, reasoning, and coding abilities. We hope our findings inspire further research. Fine-tuned models are released to facilitate subsequent studies

Large language models (LLMs) are increasingly integrated in software development, but ensuring correctness in LLM-generated code remains challenging and often requires costly manual review. Verifiable code generation -- jointly generating code, specifications, and proofs of code-specification alignment -- offers a promising path to address this limitation and further unleash LLMs' benefits in coding. Yet, there exists a significant gap in evaluation: current benchmarks often lack support for end-to-end verifiable code generation. In this paper, we introduce Verina (Verifiable Code Generation Arena), a high-quality benchmark enabling a comprehensive and modular evaluation of code, specification, and proof generation as well as their compositions. Verina consists of 189 manually curated coding tasks in Lean, with detailed problem descriptions, reference implementations, formal specifications, and extensive test suites. Our extensive evaluation of state-of-the-art LLMs reveals significant challenges in verifiable code generation, especially in proof generation, underscoring the need for improving LLM-based theorem provers in verification domains. The best model, OpenAI o4-mini, generates only 61.4% correct code, 51.0% sound and complete specifications, and 3.6% successful proofs, with one trial per task. We hope Verina will catalyze progress in verifiable code generation by providing a rigorous and comprehensive benchmark. We release our dataset on https://huggingface.co/datasets/sunblaze-ucb/verina and our evaluation code on https://github.com/sunblaze-ucb/verina.

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.

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

We present Hermes 4, a family of hybrid reasoning models that combine structured, multi-turn reasoning with broad instruction-following ability. We describe the challenges encountered during data curation, synthesis, training, and evaluation, and outline the solutions employed to address these challenges at scale. We comprehensively evaluate across mathematical reasoning, coding, knowledge, comprehension, and alignment benchmarks, and we report both quantitative performance and qualitative behavioral analysis. To support open research, all model weights are published publicly at https://huggingface.co/collections/NousResearch/hermes-4-collection-68a731bfd452e20816725728

We report on a new, simple, modular, and flexible approach for automated generation of illustrations for (readable) synthetic geometry proofs. The underlying proofs are generated using the Larus automated prover for coherent logic, and corresponding illustrations are generated in the GCLC language. Animated illustrations are also supported.

Large language models (LLMs) show remarkable promise for democratizing automated reasoning by generating formal specifications. However, a fundamental tension exists: LLMs are probabilistic, while formal verification demands deterministic guarantees. This paper addresses this epistemological gap by comprehensively investigating failure modes and uncertainty quantification (UQ) in LLM-generated formal artifacts. Our systematic evaluation of five frontier LLMs reveals Satisfiability Modulo Theories (SMT) based autoformalization's domain-specific impact on accuracy (from +34.8% on logical tasks to -44.5% on factual ones), with known UQ techniques like the entropy of token probabilities failing to identify these errors. We introduce a probabilistic context-free grammar (PCFG) framework to model LLM outputs, yielding a refined uncertainty taxonomy. We find uncertainty signals are task-dependent (e.g., grammar entropy for logic, AUROC>0.93). Finally, a lightweight fusion of these signals enables selective verification, drastically reducing errors (14-100%) with minimal abstention, transforming LLM-driven formalization into a reliable engineering discipline.

Evaluating language models fairly is becoming harder as static benchmarks available on the internet risk contamination by training data. This makes it unclear whether models are truly reasoning or just recalling answers. In this paper, we introduce BeyondBench, an evaluation framework that avoids this problem by using algorithmic problem generation. Unlike traditional benchmarks that risk contamination from internet-scale training data, BeyondBench creates mathematically grounded problems on the fly, ensuring each test remains fresh and uncontaminated. Our framework covers 44 algorithmic tasks with a total of 117 variations, grouped into three difficulty levels: the Easy Suite (29 tasks) for basic arithmetic and statistics, the Medium Suite (5 tasks, 49 variations) for sequence patterns and reasoning, and the Hard Suite (10 tasks, 68 variations) tackling NP-complete and constraint satisfaction problems. Each task generates problems from a combinatorial space larger than 10^15 unique instances, with solutions verified deterministically by mathematical proofs. We evaluated 101 language models, including 85 open-source and 16 closed-source models, spanning sizes from 0.5B to 141B parameters and multiple quantization schemes. Our results show consistent reasoning deficiencies across model families, with performance degrading sharply as problem complexity increases from polynomial to exponential. In our Hard Suite evaluations, models such as Gemini-2.5-pro, Llama-3.3-70B, and Qwen2.5-72B achieved average accuracies of 56.38%, 26.91%, and 33.60%, respectively. Moreover, we observe that performance drops drastically without tool usage, with GPT-5, GPT-5-mini, and GPT-5-nano showing a decline of 16.81%, 28.05%, and 47.59% accuracy on the hard suite. Our leaderboard is publicly available at https://ctrl-gaurav.github.io/BeyondBench/

We introduce DafnyCOMP, a benchmark for evaluating large language models (LLMs) on compositional specification generation in Dafny. Unlike prior benchmarks that focus on single-function tasks, DafnyCOMP targets programs composed of multiple interacting functions with data dependencies, requiring reasoning across component boundaries. The benchmark consists of 300 automatically synthesized multi-function programs. We evaluate several state-of-the-art LLM families and find that, while they perform well on single-function verification, their performance drops sharply on compositional tasks. Analysis reveals systematic failures in cross-functional reasoning, including fragile specifications, misalignment between implementations and proofs, and unstable reasoning. DafnyCOMP thus provides a diagnostic tool for measuring progress toward reliable, verifiable, and compositional code generation with LLMs.

Automated Theorem Proving (ATP) faces challenges due to its complexity and computational demands. Recent work has explored using Large Language Models (LLMs) for ATP action selection, but these methods can be resource-intensive. This study introduces FEAS, an agent that enhances the COPRA in-context learning framework within Lean. FEAS refines prompt generation, response parsing, and incorporates domain-specific heuristics for functional equations. It introduces FunEq, a curated dataset of functional equation problems with varying difficulty. FEAS outperforms baselines on FunEq, particularly with the integration of domain-specific heuristics. The results demonstrate FEAS's effectiveness in generating and formalizing high-level proof strategies into Lean proofs, showcasing the potential of tailored approaches for specific ATP challenges.

Recent math benchmarks for large language models (LLMs) such as MathArena indicate that state-of-the-art reasoning models achieve impressive performance on mathematical competitions like AIME, with the leading model, o3-mini, achieving scores comparable to top human competitors. However, these benchmarks evaluate models solely based on final numerical answers, neglecting rigorous reasoning and proof generation which are essential for real-world mathematical tasks. To address this, we introduce the first comprehensive evaluation of full-solution reasoning for challenging mathematical problems. Using expert human annotators, we evaluated several state-of-the-art reasoning models on the six problems from the 2025 USAMO within hours of their release. Our results reveal that all tested models struggled significantly, achieving less than 5% on average. Through detailed analysis of reasoning traces, we identify the most common failure modes and find several unwanted artifacts arising from the optimization strategies employed during model training. Overall, our results suggest that current LLMs are inadequate for rigorous mathematical reasoning tasks, highlighting the need for substantial improvements in reasoning and proof generation capabilities.

Enhancing the mathematical reasoning of large language models (LLMs) demands high-quality training data, yet conventional methods face critical challenges in scalability, cost, and data reliability. To address these limitations, we propose a novel program-assisted synthesis framework that systematically generates a high-quality mathematical corpus with guaranteed diversity, complexity, and correctness. This framework integrates mathematical knowledge systems and domain-specific tools to create executable programs. These programs are then translated into natural language problem-solution pairs and vetted by a bilateral validation mechanism that verifies solution correctness against program outputs and ensures program-problem consistency. We have generated 12.3 million such problem-solving triples. Experiments demonstrate that models fine-tuned on our data significantly improve their inference capabilities, achieving state-of-the-art performance on several benchmark datasets and showcasing the effectiveness of our synthesis approach.

Formal reasoning and automated theorem proving constitute a challenging subfield of machine learning, in which machines are tasked with proving mathematical theorems using formal languages like Lean. A formal verification system can check whether a formal proof is correct or not almost instantaneously, but generating a completely correct formal proof with large language models (LLMs) remains a formidable task. The usual approach in the literature is to prompt the LLM many times (up to several thousands) until one of the generated proofs passes the verification system. In this work, we present APOLLO (Automated PrOof repair via LLM and Lean cOllaboration), a modular, model-agnostic pipeline that combines the strengths of the Lean compiler with an LLM's reasoning abilities to achieve better proof-generation results at a low sampling budget. Apollo directs a fully automated process in which the LLM generates proofs for theorems, a set of agents analyze the proofs, fix the syntax errors, identify the mistakes in the proofs using Lean, isolate failing sub-lemmas, utilize automated solvers, and invoke an LLM on each remaining goal with a low top-K budget. The repaired sub-proofs are recombined and reverified, iterating up to a user-controlled maximum number of attempts. On the miniF2F benchmark, we establish a new state-of-the-art accuracy of 75.0% among 7B-parameter models while keeping the sampling budget below one thousand. Moreover, Apollo raises the state-of-the-art accuracy for Goedel-Prover-SFT to 65.6% while cutting sample complexity from 25,600 to a few hundred. General-purpose models (o3-mini, o4-mini) jump from 3-7% to over 40% accuracy. Our results demonstrate that targeted, compiler-guided repair of LLM outputs yields dramatic gains in both efficiency and correctness, suggesting a general paradigm for scalable automated theorem proving.

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.

In the realm of formal theorem proving, the Coq proof assistant stands out for its rigorous approach to verifying mathematical assertions and software correctness. Despite the advances in artificial intelligence and machine learning, the specialized nature of Coq syntax and semantics poses unique challenges for Large Language Models (LLMs). Addressing this gap, we present a comprehensive dataset specifically designed to enhance LLMs' proficiency in interpreting and generating Coq code. This dataset, derived from a collection of over 10,000 Coq source files, encompasses a wide array of propositions, proofs, and definitions, enriched with metadata including source references and licensing information. Our primary aim is to facilitate the development of LLMs capable of generating syntactically correct and semantically meaningful Coq constructs, thereby advancing the frontier of automated theorem proving. Initial experiments with this dataset have showcased its significant potential; models trained on this data exhibited enhanced accuracy in Coq code generation. Notably, a particular experiment revealed that a fine-tuned LLM was capable of generating 141 valid proofs for a basic lemma, highlighting the dataset's utility in facilitating the discovery of diverse and valid proof strategies. This paper discusses the dataset's composition, the methodology behind its creation, and the implications of our findings for the future of machine learning in formal verification. The dataset is accessible for further research and exploration: https://huggingface.co/datasets/florath/coq-facts-props-proofs-gen0-v1

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.

Large reasoning models (e.g., R1, o3) have demonstrated remarkable mathematical problem-solving abilities. However, the high reported accuracy of these advanced models on popular datasets, reliance on purely numerical evaluation and potential benchmark leakage, often masks their true reasoning shortcomings. To address this, we propose leveraging the inherent rigor and methodological complexity of mathematical proofs as a diagnostic tool to expose these hidden failures. Specifically, we introduce the RFMDataset (Reveal Failure Modes), a collection of 200 diverse mathematical proof problems, and thoroughly evaluate advanced models' performance on it. Our in-depth analysis of their failures uncovers 10 fine-grained error types, which shows fundamental limitations in current large reasoning models: 1) large reasoning models grapple profoundly with mathematical proofs, with some generating entirely correct proofs for less than 20% of problems and failing even on basic ones; 2) models exhibit a diverse spectrum of reasoning failures, prominently demonstrating the lack of guarantees for the correctness and rigor of single-step reasoning; and 3) models show hallucination and incompleteness during the reasoning process. Our findings reveal that models' self-reflection is insufficient to resolve the current logical dilemmas, necessitating formalized and fine-grained logical training.

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.

Using large language models (LLMs) to generate source code from natural language prompts is a popular and promising idea with a wide range of applications. One of its limitations is that the generated code can be faulty at times, often in a subtle way, despite being presented to the user as correct. In this paper, we explore ways in which formal methods can assist with increasing the quality of code generated by an LLM. Instead of emitting code in a target language directly, we propose that the user guides the LLM to first generate an opaque intermediate representation, in the verification-aware language Dafny, that can be automatically validated for correctness against agreed on specifications. The correct Dafny program is then compiled to the target language and returned to the user. All user-system interactions throughout the procedure occur via natural language; Dafny code is never exposed. We describe our current prototype and report on its performance on the HumanEval Python code generation benchmarks.

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.

Software testing and verification are critical for ensuring the reliability and security of modern software systems. Traditionally, formal verification techniques, such as model checking and theorem proving, have provided rigorous frameworks for detecting bugs and vulnerabilities. However, these methods often face scalability challenges when applied to complex, real-world programs. Recently, the advent of Large Language Models (LLMs) has introduced a new paradigm for software analysis, leveraging their ability to understand insecure coding practices. Although LLMs demonstrate promising capabilities in tasks such as bug prediction and invariant generation, they lack the formal guarantees of classical methods. This paper presents a comprehensive study of state-of-the-art software testing and verification, focusing on three key approaches: classical formal methods, LLM-based analysis, and emerging hybrid techniques, which combine their strengths. We explore each approach's strengths, limitations, and practical applications, highlighting the potential of hybrid systems to address the weaknesses of standalone methods. We analyze whether integrating formal rigor with LLM-driven insights can enhance the effectiveness and scalability of software verification, exploring their viability as a pathway toward more robust and adaptive testing frameworks.

Code large language models (Code LLMs) have made significant progress in code generation by translating natural language descriptions into functional code; however, real-world applications often demand stricter adherence to detailed requirements such as coding style, line count, and structural constraints, beyond mere correctness. To address this, the paper introduces forward and backward constraints generation to improve the instruction-following capabilities of Code LLMs in controlled code generation, ensuring outputs align more closely with human-defined guidelines. The authors further present IFEvalCode, a multilingual benchmark comprising 1.6K test samples across seven programming languages (Python, Java, JavaScript, TypeScript, Shell, C++, and C#), with each sample featuring both Chinese and English queries. Unlike existing benchmarks, IFEvalCode decouples evaluation into two metrics: correctness (Corr.) and instruction-following (Instr.), enabling a more nuanced assessment. Experiments on over 40 LLMs reveal that closed-source models outperform open-source ones in controllable code generation and highlight a significant gap between the models' ability to generate correct code versus code that precisely follows instructions.

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.

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/

As a seemingly self-explanatory task, problem-solving has been a significant component of science and engineering. However, a general yet concrete formulation of problem-solving itself is missing. With the recent development of AI-based problem-solving agents, the demand for process-level verifiability is rapidly increasing yet underexplored. To fill these gaps, we present a principled formulation of problem-solving as a deterministic Markov decision process; a novel framework, FPS (Formal Problem-Solving), which utilizes existing FTP (formal theorem proving) environments to perform process-verified problem-solving; and D-FPS (Deductive FPS), decoupling solving and answer verification for better human-alignment. The expressiveness, soundness and completeness of the frameworks are proven. We construct three benchmarks on problem-solving: FormalMath500, a formalization of a subset of the MATH500 benchmark; MiniF2F-Solving and PutnamBench-Solving, adaptations of FTP benchmarks MiniF2F and PutnamBench. For faithful, interpretable, and human-aligned evaluation, we propose RPE (Restricted Propositional Equivalence), a symbolic approach to determine the correctness of answers by formal verification. We evaluate four prevalent FTP models and two prompting methods as baselines, solving at most 23.77% of FormalMath500, 27.47% of MiniF2F-Solving, and 0.31% of PutnamBench-Solving.

As large language models (LLMs) reach high scores on established mathematical benchmarks, such as GSM8K and MATH, the research community has turned to International Mathematical Olympiad (IMO) problems to push the evaluation frontier. However, existing Olympiad-level benchmarks suffer from practical constraints that introduce grading noise and potential bias, such as heterogeneous answer formats requiring model-based judges and a reliance on potentially flawed solutions. We introduce RIMO, a two-track benchmark designed to preserve peak Olympiad difficulty while eliminating this evaluation noise. The first track, RIMO-N, rewrites 335 IMO problems to admit a single, unique integer answer, allowing for deterministic correctness checking. The second track, RIMO-P, features 456 proof problems with expert-checked solutions, which are decomposed into a sequence of sub-problems to evaluate the step-by-step reasoning process via an automated grading system. Our benchmarking of ten frontier LLMs, including GPT-4o and Gemini 2.5 Flash, reveals that while these systems excel on older benchmarks, their performance drops sharply on RIMO. These results highlight a substantial gap between current LLM capabilities and actual Olympiad-level reasoning. By providing a challenging yet easy-to-evaluate suite, RIMO offers a high-resolution yardstick for future research, presenting a clear target for closing the profound reasoning gap our findings expose.

Existing math datasets evaluate the reasoning abilities of large language models (LLMs) by either using the final answer or the intermediate reasoning steps derived from static examples. However, the former approach fails to surface model's uses of shortcuts and wrong reasoning while the later poses challenges in accommodating alternative solutions. In this work, we seek to use symbolic programs as a means for automated evaluation if a model can consistently produce correct final answers across various inputs to the program. We begin by extracting programs for popular math datasets (GSM8K and MATH) using GPT4-o. For those executable programs verified using the original input-output pairs, they are found to encapsulate the proper reasoning required to solve the original text questions. We then prompt GPT4-o to generate new questions using alternative input-output pairs based the extracted program. We apply the resulting datasets to evaluate a collection of LLMs. In our experiments, we observe significant accuracy drops using our proposed evaluation compared with original static examples, suggesting the fragility of math reasoning in state-of-the-art LLMs.

Proving mathematical theorems using computer-verifiable formal languages like Lean significantly impacts mathematical reasoning. One approach to formal theorem proving involves generating complete proofs using Large Language Models (LLMs) based on Natural Language (NL) proofs. Similar methods have shown promising results in code generation. However, most modern LLMs exhibit suboptimal performance due to the scarcity of aligned NL and Formal Language (FL) theorem-proving data. This scarcity results in a paucity of methodologies for training LLMs and techniques to fully utilize their capabilities in composing formal proofs. To address the challenges, this paper proposes **TheoremLlama**, an end-to-end framework to train a general-purpose LLM to become a Lean4 expert. This framework encompasses NL-FL aligned dataset generation methods, training approaches for the LLM formal theorem prover, and techniques for LLM Lean4 proof writing. Using the dataset generation method, we provide *Open Bootstrapped Theorems* (OBT), an NL-FL aligned and bootstrapped dataset. A key innovation in this framework is the NL-FL bootstrapping method, where NL proofs are integrated into Lean4 code for training datasets, leveraging the NL reasoning ability of LLMs for formal reasoning. The **TheoremLlama** framework achieves cumulative accuracies of 36.48% and 33.61% on MiniF2F-Valid and Test datasets respectively, surpassing the GPT-4 baseline of 22.95% and 25.41%. We have also open-sourced our model checkpoints and generated dataset, and will soon make all the code publicly available.

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.

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.

Proof-oriented programs mix computational content with proofs of program correctness. However, the human effort involved in programming and proving is still substantial, despite the use of Satisfiability Modulo Theories (SMT) solvers to automate proofs in languages such as F*. Seeking to spur research on using AI to automate the construction of proof-oriented programs, we curate a dataset of 600K lines of open-source F* programs and proofs, including software used in production systems ranging from Windows and Linux, to Python and Firefox. Our dataset includes around 32K top-level F* definitions, each representing a type-directed program and proof synthesis problem -- producing a definition given a formal specification expressed as an F* type. We provide a program-fragment checker that queries F* to check the correctness of candidate solutions. We believe this is the largest corpus of SMT-assisted program proofs coupled with a reproducible program-fragment checker. Grounded in this dataset, we investigate the use of AI to synthesize programs and their proofs in F*, with promising results. Our main finding in that the performance of fine-tuned smaller language models (such as Phi-2 or StarCoder) compare favorably with large language models (such as GPT-4), at a much lower computational cost. We also identify various type-based retrieval augmentation techniques and find that they boost performance significantly. With detailed error analysis and case studies, we identify potential strengths and weaknesses of models and techniques and suggest directions for future improvements.

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.

Formal verification is the next frontier for ensuring the correctness of code generated by Large Language Models (LLMs). While methods that co-generate code and formal specifications in formal languages, like Dafny, can, in principle, prove alignment with user intent, progress is bottlenecked by specification quality evaluation. Current benchmarks rely on matching against ground-truth specifications, a manual and expertise-intensive process that has limited existing datasets to a few hundred simple problems and also suffers from a reliability issue. To address this, we introduce VeriEquivBench, a new benchmark with 2,389 complex algorithmic problems that probe the limitations of current models in both code generation and formal reasoning. Our evaluation framework replaces ground-truth matching with a formally grounded metric, the equivalence score, and rigorously verifies the quality of generated specifications and code. Our results show that generating formally verifiable code remains a profound challenge for state-of-the-art LLMs. This underscores both the difficulty of the task and the need for benchmarks like VeriEquivBench to drive progress toward scalable and reliable coding agents.

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.

Large language models (LLMs) have shown increasing competence in solving mathematical reasoning problems. However, many open-source LLMs still struggle with errors in calculation and semantic understanding during intermediate reasoning steps. In this work, we introduce Prove, a simple yet effective framework that leverages translated programs derived from natural language solutions as a verification mechanism to filter out potentially incorrect reasoning paths before aggregating final answers. Unlike vanilla majority voting, our approach filters out solutions whose corresponding program output is inconsistent with the generated solution, aggregating only those that pass verification. We conducted extensive experiments using 13 open-source LLMs from various model families and sizes, ranging from 0.5B to 13B parameters, across eight mathematical benchmarks. Our results show that Prove consistently outperforms vanilla majority voting as a heuristic for solving mathematical reasoning tasks across all model sizes and datasets, achieving improvements of up to 18% on GSM8K and 8% on MATH-500. Our codes are available at https://github.com/declare-lab/prove.

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

Automated Theorem Proving (ATP) in formal languages remains a formidable challenge in AI, demanding rigorous logical deduction and navigating vast search spaces. While large language models (LLMs) have shown promising performance, existing stepwise provers often suffer from biased search guidance, leading to inefficiencies and suboptimal proof strategies. This paper introduces the Multi-Perspective Search Prover (MPS-Prover), a novel stepwise ATP system designed to overcome these limitations. MPS-Prover incorporates two key innovations: a highly effective post-training data curation strategy that prunes approximately 40% of redundant training data without sacrificing performance, and a multi-perspective tree search mechanism. This search integrates a learned critic model with strategically designed heuristic rules to diversify tactic selection, prevent getting trapped in unproductive states, and enhance search robustness. Extensive evaluations demonstrate that MPS-Prover achieves state-of-the-art performance on multiple challenging benchmarks, including miniF2F and ProofNet, outperforming prior 7B parameter models. Furthermore, our analyses reveal that MPS-Prover generates significantly shorter and more diverse proofs compared to existing stepwise and whole-proof methods, highlighting its efficiency and efficacy. Our work advances the capabilities of LLM-based formal reasoning and offers a robust framework and a comprehensive analysis for developing more powerful theorem provers.

Complex logical reasoning tasks require a long sequence of reasoning, which a large language model (LLM) with chain-of-thought prompting still falls short. To alleviate this issue, neurosymbolic approaches incorporate a symbolic solver. Specifically, an LLM only translates a natural language problem into a satisfiability (SAT) problem that consists of first-order logic formulas, and a sound symbolic solver returns a mathematically correct solution. However, we discover that LLMs have difficulties to capture complex logical semantics hidden in the natural language during translation. To resolve this limitation, we propose a Compositional First-Order Logic Translation. An LLM first parses a natural language sentence into newly defined logical dependency structures that consist of an atomic subsentence and its dependents, then sequentially translate the parsed subsentences. Since multiple logical dependency structures and sequential translations are possible for a single sentence, we also introduce two Verification algorithms to ensure more reliable results. We utilize an SAT solver to rigorously compare semantics of generated first-order logic formulas and select the most probable one. We evaluate the proposed method, dubbed CLOVER, on seven logical reasoning benchmarks and show that it outperforms the previous neurosymbolic approaches and achieves new state-of-the-art results.

Despite significant advancements in the general capability of large language models (LLMs), they continue to struggle with consistent and accurate reasoning, especially in complex tasks such as mathematical and code reasoning. One key limitation is that LLMs are trained primarily on correct solutions, reducing their ability to detect and learn from errors, which hampers their ability to reliably verify and rank outputs. To address this, we scale up the inference-time computation by generating multiple reasoning paths and employing verifiers to assess and rank the generated outputs by correctness. To facilitate this, we introduce a comprehensive dataset consisting of correct and incorrect solutions for math and code tasks, generated by multiple LLMs. This diverse set of solutions enables verifiers to more effectively distinguish and rank correct answers from erroneous outputs. The training methods for building verifiers were selected based on an extensive comparison of existing approaches. Moreover, to leverage the unique strengths of different reasoning strategies, we propose a novel collaborative method integrating Chain-of-Thought (CoT) and Program-of-Thought (PoT) solutions for verification. CoT provides a clear, step-by-step reasoning process that enhances interpretability, while PoT, being executable, offers a precise and error-sensitive validation mechanism. By taking both of their strengths, our approach significantly improves the accuracy and reliability of reasoning verification. Our verifiers, Math-Rev and Code-Rev, demonstrate substantial performance gains to existing LLMs, achieving state-of-the-art results on benchmarks such as GSM8k and MATH and even outperforming GPT-4o with Qwen-72B-Instruct as the reasoner.

Recent advances in Large Language Models (LLMs) have demonstrated remarkable general reasoning capabilities. However, systematically evaluating and enhancing these reasoning capabilities is challenging due to the lack of controllable and scalable tools for fine-grained analysis. Existing benchmarks and datasets often lack the necessary variable control for multi-dimensional, systematic analysis and training, or have narrow problem types and formats. To address these limitations, we introduce SATQuest, a systematic verifier designed to evaluate and enhance logical reasoning in LLMs by generating diverse, Satisfiability-based logical reasoning problems directly from Conjunctive Normal Form (CNF) instances. SATQuest structures these problems along three orthogonal dimensions: instance scale, problem type, and question format, employing randomized, SAT-based problem generation and objective answer verification via PySAT. This design mitigates memorization issues, allows for nuanced insights into reasoning performance, and enables effective reinforcement fine-tuning. Our extensive evaluation of various LLMs using SATQuest identified significant limitations in their logical reasoning, particularly in generalizing beyond familiar mathematical formats. Furthermore, we show that reinforcement fine-tuning with SATQuest rewards substantially improves targeted task performance and generalizes to more complex instances, while highlighting remaining challenges in cross-format adaptation. Through these demonstrations, we showcase SATQuest's potential as a foundational tool and a valuable starting point for advancing LLM logical reasoning.

Remarkable progress has been made on automated reasoning with natural text, by using Language Models (LMs) and methods such as Chain-of-Thought and Selection-Inference. These techniques search for proofs in the forward direction from axioms to the conclusion, which suffers from a combinatorial explosion of the search space, and thus high failure rates for problems requiring longer chains of reasoning. The classical automated reasoning literature has shown that reasoning in the backward direction (i.e. from the intended conclusion to supporting axioms) is significantly more efficient at proof-finding. Importing this intuition into the LM setting, we develop a Backward Chaining algorithm, called LAMBADA, that decomposes reasoning into four sub-modules. These sub-modules are simply implemented by few-shot prompted LM inference. We show that LAMBADA achieves sizable accuracy boosts over state-of-the-art forward reasoning methods on challenging logical reasoning datasets, particularly when deep and accurate proof chains are required.

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.

Answer verification methods are widely employed in language model training pipelines spanning data curation, evaluation, and reinforcement learning with verifiable rewards (RLVR). While prior work focus on developing unified verifiers applicable across multiple reasoning scenarios, significant challenges remain in computation-oriented scientific domains, such as algebraic equivalence checking and physical constant substitution. In this paper, we introduce \model, a tool-augmented verifier that leverages external executors to perform precise computations and symbolic simplifications. \model enables robust verification that goes beyond simple semantic matching. We propose a novel two-stage pipeline, which begin with cold-start fine-tuning and followed by multi-turn reinforcement learning with tool integration. Extensive experiments conducted on STEM subjects, general QA, and long-form reasoning tasks demonstrates strong generalization of \model. The results shows that the \model achieves state-of-the-art performance on VerifyBench-Hard and SCI-Bench. And we also employ our \model in RLVR as a reward model, the results show that it consistently outperforms both rubric-based and model-based verifiers on AIME'24 and AIME'25, demonstrating strong potential to enhance reasoning capabilities of LLM. Our model is released at https://huggingface.co/Nanbeige/CoSineVerifier-Tool-4B{https://huggingface.co/Nanbeige/CoSineVerifier-Tool-4B}.

Large Language Models (LLMs) excel at code generation, but ensuring their outputs to be functionally correct, especially in complex programming tasks, is a persistent challenge. While traditional Test-Driven Development (TDD) offers a path for code refinement, its efficacy with LLMs is often undermined by the scarcity of high-quality test cases or the pitfalls of automated test generation, including biased tests or inaccurate output predictions that can misdirect the correction process. This paper introduces Property-Generated Solver, a novel framework that leverages Property-Based Testing (PBT) to validate high-level program properties or invariants, instead of relying on specific input-output examples. These properties are often simpler to define and verify than directly predicting exhaustive test oracles, breaking the "cycle of self-deception" where tests might share flaws with the code they are meant to validate. Property-Generated Solver employs two collaborative LLM-based agents: a Generator dedicated to code generation and iterative refinement, and a Tester that manages the PBT life-cycle and formulate semantically rich feedback from property violations. The resulting comprehensive and actionable feedback then guides the Generator in its refinement efforts. By establishing PBT as the core validation engine within this iterative, closed-loop paradigm, Property-Generated Solver provides a robust mechanism for steering LLMs towards more correct and generalizable code. Extensive experimental results on multiple code generation benchmarks demonstrate that Property-Generated Solver achieves substantial pass@1 improvements, ranging from 23.1% to 37.3% relative gains over established TDD methods.

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.

In this paper, we introduce BMMR, a large-scale bilingual, multimodal, multi-disciplinary reasoning dataset for the community to develop and evaluate large multimodal models (LMMs). BMMR comprises 110k college-level questions spanning 300 UNESCO-defined subjects, spanning diverse formats-multiple-choice, fill-in-the-blank, and open-ended QA-and sourced from both print and digital media such as books, exams, and quizzes. All data are curated and filtered via a human-in-the-loop and scalable framework, and each instance is paired with a high-quality reasoning path. The dataset is organized into two parts: BMMR-Eval that comprises 20,458 high-quality instances to comprehensively assess LMMs' knowledge and reasoning across multiple disciplines in both Chinese and English; and BMMR-Train that contains 88,991 instances to support further research and development, extending the current focus on mathematical reasoning to diverse disciplines and domains. In addition, we propose the process-based multi-discipline verifier (i.e., BMMR-Verifier) for accurate and fine-grained evaluation of reasoning paths. Extensive experiments on 24 models reveal that (i) even SOTA models (e.g., o3 and Gemini-2.5-Pro) leave substantial headroom on BMMR-Eval; (ii) reasoning models exhibit discipline bias and outperform LMMs only on specific subjects; (iii) open-source models still trail their proprietary counterparts; and (iv) fine-tuning on BMMR-Train narrows this gap. Additionally, we conduct reasoning-chain analyses using BMMR-Verifier and other in-depth studies, uncovering the challenges LMMs currently face in multidisciplinary reasoning. We will release the data, and we hope our work can offer insights and contributions to the community.

Large Language Models (LLMs) have demonstrated remarkable capabilities in natural language generation and reasoning. However, their integration into automated software ecosystems is often hindered by the "Structure Gap" - the inherent tension between the probabilistic nature of token generation and the deterministic requirements of structured data formats (e.g., JSON, XML). Traditional Supervised Fine-Tuning (SFT) often fails to enforce strict syntactic constraints, leading to "hallucinated" keys or malformed structures, while constrained decoding methods impose significant inference latency. In this paper, we propose a lightweight, efficient Reinforcement Learning (RL) framework to bridge this gap. We introduce a novel Multi-dimensional Reward Function that decomposes the structured output task into a hierarchy of constraints: structural integrity, format correctness, content accuracy, and validity. Leveraging Gradient Regularized Policy Optimization (GRPO), we enable the model to internalize these constraints without the need for a separate critic network, reducing peak VRAM usage by 40% compared to PPO. We validate our approach on multiple tasks, including complex recipe generation and structured math reasoning (GSM8K-JSON). Experimental results demonstrate that our method achieves 89.7% structural accuracy and 92.1% JSON validity, significantly outperforming both zero-shot baselines (e.g., GPT-3.5) and SFT on larger models like LLaMA-3-8B. Furthermore, we provide a detailed analysis of training dynamics, revealing a distinct self-paced curriculum where the model sequentially acquires syntactic proficiency before semantic accuracy. Our model is publicly available at https://huggingface.co/Freakz3z/Qwen-JSON.

Large Language Models (LLMs) such as GPT-4 and Llama3 have significantly impacted various fields by enabling high-quality synthetic data generation and reducing dependence on expensive human-generated datasets. Despite this, challenges remain in the areas of generalization, controllability, diversity, and truthfulness within the existing generative frameworks. To address these challenges, this paper presents UniGen, a comprehensive LLM-powered framework designed to produce diverse, accurate, and highly controllable datasets. UniGen is adaptable, supporting all types of text datasets and enhancing the generative process through innovative mechanisms. To augment data diversity, UniGen incorporates an attribute-guided generation module and a group checking feature. For accuracy, it employs a code-based mathematical assessment for label verification alongside a retrieval-augmented generation technique for factual validation. The framework also allows for user-specified constraints, enabling customization of the data generation process to suit particular requirements. Extensive experiments demonstrate the superior quality of data generated by UniGen, and each module within UniGen plays a critical role in this enhancement. Additionally, UniGen is applied in two practical scenarios: benchmarking LLMs and data augmentation. The results indicate that UniGen effectively supports dynamic and evolving benchmarking, and that data augmentation improves LLM capabilities in various domains, including agent-oriented abilities and reasoning skills.

In this paper we present a novel solution that combines the capabilities of Large Language Models (LLMs) with Formal Verification strategies to verify and automatically repair software vulnerabilities. Initially, we employ Bounded Model Checking (BMC) to locate the software vulnerability and derive a counterexample. The counterexample provides evidence that the system behaves incorrectly or contains a vulnerability. The counterexample that has been detected, along with the source code, are provided to the LLM engine. Our approach involves establishing a specialized prompt language for conducting code debugging and generation to understand the vulnerability's root cause and repair the code. Finally, we use BMC to verify the corrected version of the code generated by the LLM. As a proof of concept, we create ESBMC-AI based on the Efficient SMT-based Context-Bounded Model Checker (ESBMC) and a pre-trained Transformer model, specifically gpt-3.5-turbo, to detect and fix errors in C programs. Our experimentation involved generating a dataset comprising 1000 C code samples, each consisting of 20 to 50 lines of code. Notably, our proposed method achieved an impressive success rate of up to 80% in repairing vulnerable code encompassing buffer overflow and pointer dereference failures. We assert that this automated approach can effectively incorporate into the software development lifecycle's continuous integration and deployment (CI/CD) process.

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.

Recent work shows Large Language Models (LLMs) struggle to understand natural language constraints for various text generation tasks in zero- and few-shot settings. While, in the code domain, there is wide usage of constraints in code format to maintain the integrity of code written in Domain-Specific Languages (DSLs) like JSON and YAML which are widely used for system-level programming tasks in enterprises. Given that LLMs are increasingly used for system-level code tasks, evaluating if they can comprehend these code constraints is crucial. However, no work has been done to evaluate their controllability over code constraints. Hence, we introduce ConCodeEval, a first-of-its-kind benchmark having two novel tasks for code constraints across five representations. Our findings suggest that language models struggle with code constraints. Code languages that perform excellently for normal code tasks do not perform well when the same languages represent fine-grained constraints.

Automated code generation with large language models has gained significant traction, but there remains no guarantee on the correctness of generated code. We aim to use formal verification to provide mathematical guarantees that the generated code is correct. However, generating formally verified code with LLMs is hindered by the scarcity of training data and the complexity of formal proofs. To tackle this challenge, we introduce AlphaVerus, a self-improving framework that bootstraps formally verified code generation by iteratively translating programs from a higher-resource language and leveraging feedback from a verifier. AlphaVerus operates in three phases: exploration of candidate translations, Treefinement -- a novel tree search algorithm for program refinement using verifier feedback, and filtering misaligned specifications and programs to prevent reward hacking. Through this iterative process, AlphaVerus enables a LLaMA-3.1-70B model to generate verified code without human intervention or model finetuning. AlphaVerus shows an ability to generate formally verified solutions for HumanEval and MBPP, laying the groundwork for truly trustworthy code-generation agents.

Formulating optimization problems for industrial applications demands significant manual effort and domain expertise. While Large Language Models (LLMs) show promise in automating this process, evaluating their performance remains difficult due to the absence of robust metrics. Existing solver-based approaches often face inconsistency, infeasibility issues, and high computational costs. To address these issues, we propose ORGEval, a graph-theoretic evaluation framework for assessing LLMs' capabilities in formulating linear and mixed-integer linear programs. ORGEval represents optimization models as graphs, reducing equivalence detection to graph isomorphism testing. We identify and prove a sufficient condition, when the tested graphs are symmetric decomposable (SD), under which the Weisfeiler-Lehman (WL) test is guaranteed to correctly detect isomorphism. Building on this, ORGEval integrates a tailored variant of the WL-test with an SD detection algorithm to evaluate model equivalence. By focusing on structural equivalence rather than instance-level configurations, ORGEval is robust to numerical variations. Experimental results show that our method can successfully detect model equivalence and produce 100\% consistent results across random parameter configurations, while significantly outperforming solver-based methods in runtime, especially on difficult problems. Leveraging ORGEval, we construct the Bench4Opt dataset and benchmark state-of-the-art LLMs on optimization modeling. Our results reveal that although optimization modeling remains challenging for all LLMs, DeepSeek-V3 and Claude-Opus-4 achieve the highest accuracies under direct prompting, outperforming even leading reasoning models.

Formal verification (FV) has witnessed growing significance with current emerging program synthesis by the evolving large language models (LLMs). However, current formal verification mainly resorts to symbolic verifiers or hand-craft rules, resulting in limitations for extensive and flexible verification. On the other hand, formal languages for automated theorem proving, such as Isabelle, as another line of rigorous verification, are maintained with comprehensive rules and theorems. In this paper, we propose FVEL, an interactive Formal Verification Environment with LLMs. Specifically, FVEL transforms a given code to be verified into Isabelle, and then conducts verification via neural automated theorem proving with an LLM. The joined paradigm leverages the rigorous yet abundant formulated and organized rules in Isabelle and is also convenient for introducing and adjusting cutting-edge LLMs. To achieve this goal, we extract a large-scale FVELER3. The FVELER dataset includes code dependencies and verification processes that are formulated in Isabelle, containing 758 theories, 29,125 lemmas, and 200,646 proof steps in total with in-depth dependencies. We benchmark FVELER in the FVEL environment by first fine-tuning LLMs with FVELER and then evaluating them on Code2Inv and SV-COMP. The results show that FVEL with FVELER fine-tuned Llama3- 8B solves 17.39% (69 -> 81) more problems, and Mistral-7B 12% (75 -> 84) more problems in SV-COMP. And the proportion of proof errors is reduced. Project page: https://fveler.github.io/.

We introduce refutationally complete superposition calculi for intentional and extensional clausal lambda-free higher-order logic, two formalisms that allow partial application and applied variables. The calculi are parameterized by a term order that need not be fully monotonic, making it possible to employ the lambda-free higher-order lexicographic path and Knuth-Bendix orders. We implemented the calculi in the Zipperposition prover and evaluated them on Isabelle/HOL and TPTP benchmarks. They appear promising as a stepping stone towards complete, highly efficient automatic theorem provers for full higher-order logic.

Verification is crucial for effective mathematical reasoning. We present a new temporal consistency method where verifiers iteratively refine their judgments based on the previous assessment. Unlike one-round verification or multi-model debate approaches, our method leverages consistency in a sequence of self-reflection actions to improve verification accuracy. Empirical evaluations across diverse mathematical process error identification benchmarks (Mathcheck, ProcessBench, and PRM800K) show consistent performance improvements over baseline methods. When applied to the recent DeepSeek R1 distilled models, our method demonstrates strong performance, enabling 7B/8B distilled models to outperform all 70B/72B models and GPT-4o on ProcessBench. Notably, the distilled 14B model with our method achieves performance comparable to Deepseek-R1. Our codes are available at https://github.com/jcguo123/Temporal-Consistency

Recent progress in large language models (LLMs) has shown promise in formal theorem proving, yet existing benchmarks remain limited to isolated, static proof tasks, failing to capture the iterative, engineering-intensive workflows of real-world formal mathematics libraries. Motivated by analogous advances in software engineering, we introduce the paradigm of Automated Proof Engineering (APE), which aims to automate proof engineering tasks such as feature addition, proof refactoring, and bug fixing using LLMs. To facilitate research in this direction, we present APE-Bench I, the first realistic benchmark built from real-world commit histories of Mathlib4, featuring diverse file-level tasks described in natural language and verified via a hybrid approach combining the Lean compiler and LLM-as-a-Judge. We further develop Eleanstic, a scalable parallel verification infrastructure optimized for proof checking across multiple versions of Mathlib. Empirical results on state-of-the-art LLMs demonstrate strong performance on localized edits but substantial degradation on handling complex proof engineering. This work lays the foundation for developing agentic workflows in proof engineering, with future benchmarks targeting multi-file coordination, project-scale verification, and autonomous agents capable of planning, editing, and repairing formal libraries.

Large language models demonstrate remarkable reasoning capabilities but often produce unreliable or incorrect responses. Existing verification methods are typically model-specific or domain-restricted, requiring significant computational resources and lacking scalability across diverse reasoning tasks. To address these limitations, we propose VerifiAgent, a unified verification agent that integrates two levels of verification: meta-verification, which assesses completeness and consistency in model responses, and tool-based adaptive verification, where VerifiAgent autonomously selects appropriate verification tools based on the reasoning type, including mathematical, logical, or commonsense reasoning. This adaptive approach ensures both efficiency and robustness across different verification scenarios. Experimental results show that VerifiAgent outperforms baseline verification methods (e.g., deductive verifier, backward verifier) among all reasoning tasks. Additionally, it can further enhance reasoning accuracy by leveraging feedback from verification results. VerifiAgent can also be effectively applied to inference scaling, achieving better results with fewer generated samples and costs compared to existing process reward models in the mathematical reasoning domain. Code is available at https://github.com/Jiuzhouh/VerifiAgent

In order to properly train a machine learning model, data must be properly collected. To guarantee a proper data collection, verifying that the collected data set holds certain properties is a possible solution. For example, guaranteeing that the data set contains samples across the whole input space, or that the data set is balanced w.r.t. different classes. We present a formal approach for verifying a set of arbitrarily stated properties over a data set. The proposed approach relies on the transformation of the data set into a first order logic formula, which can be later verified w.r.t. the different properties also stated in the same logic. A prototype tool, which uses the z3 solver, has been developed; the prototype can take as an input a set of properties stated in a formal language and formally verify a given data set w.r.t. to the given set of properties. Preliminary experimental results show the feasibility and performance of the proposed approach, and furthermore the flexibility for expressing properties of interest.

We present Generative Logic (GL), a deterministic architecture that begins from user-supplied axiomatic definitions -- written in a minimalist Mathematical Programming Language (MPL) -- and systematically explores their deductive neighborhood. Definitions are compiled into a distributed grid of simple Logic Blocks (LBs) that exchange messages; any time several expressions unify under an inference rule, a new fact is emitted with full provenance to its sources, yielding replayable, auditable proof graphs. A prototype software implementation instantiates the workflow on first-order Peano arithmetic. Starting only from the Peano axioms, GL enumerates candidate implications, applies normalization and type filters, and automatically reconstructs machine-checkable proofs of foundational arithmetic laws including associativity and commutativity of addition, associativity and commutativity of multiplication, and distributivity. Generated proofs export to navigable HTML so that every inference step can be inspected independently. We outline a hardware-software co-design path toward massively parallel realizations and describe prospective integration with probabilistic models (e.g., Large Language Models (LLMs)) for autoformalization and conjecture seeding. The Python and MPL code to reproduce the Peano experiments, along with the full HTML proof graphs, are available in the project's GitHub repository at https://github.com/Generative-Logic/GL/tree/35a111ea9ba53afe051703d6050be0c3923e9724 and are permanently archived at https://doi.org/10.5281/zenodo.16408441. We invite community feedback and collaboration.

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

Large language models (LLMs) have recently demonstrated remarkable progress in formal theorem proving. Yet their ability to serve as practical assistants for mathematicians, filling in missing steps within complex proofs, remains underexplored. We identify this challenge as the task of subgoal completion, where an LLM must discharge short but nontrivial proof obligations left unresolved in a human-provided sketch. To study this problem, we introduce FormalML, a Lean 4 benchmark built from foundational theories of machine learning. Using a translation tactic that converts procedural proofs into declarative form, we extract 4937 problems spanning optimization and probability inequalities, with varying levels of difficulty. FormalML is the first subgoal completion benchmark to combine premise retrieval and complex research-level contexts. Evaluation of state-of-the-art provers highlights persistent limitations in accuracy and efficiency, underscoring the need for more capable LLM-based theorem provers for effective subgoal completion,

We introduce the Formally Verified Automated Programming Progress Standards, or FVAPPS, a benchmark of 4715 samples for writing programs and proving their correctness, the largest formal verification benchmark, including 1083 curated and quality controlled samples. Previously, APPS provided a benchmark and dataset for programming puzzles to be completed in Python and checked against unit tests, of the kind seen in technical assessments in the software engineering industry. Building upon recent approaches for benchmarks in interactive theorem proving, we generalize the unit tests to Lean 4 theorems given without proof (i.e., using Lean's "sorry" keyword). On the 406 theorems of 100 randomly selected samples, Sonnet correctly proves 30% and Gemini correctly proves 18%. We challenge the machine learning and program synthesis communities to solve both each general purpose programming problem and its associated correctness specifications. The benchmark is available at https://huggingface.co/datasets/quinn-dougherty/fvapps.

While Large Language Models (LLMs) have demonstrated enhanced capabilities in function-calling, these advancements primarily rely on accessing the functions' responses. This methodology is practical for simpler APIs but faces scalability issues with irreversible APIs that significantly impact the system, such as a database deletion API. Similarly, processes requiring extensive time for each API call and those necessitating forward planning, like automated action pipelines, present complex challenges. Furthermore, scenarios often arise where a generalized approach is needed because algorithms lack direct access to the specific implementations of these functions or secrets to use them. Traditional tool planning methods are inadequate in these cases, compelling the need to operate within black-box environments. Unlike their performance in tool manipulation, LLMs excel in black-box tasks, such as program synthesis. Therefore, we harness the program synthesis capabilities of LLMs to strategize tool usage in black-box settings, ensuring solutions are verified prior to implementation. We introduce TOPGUN, an ingeniously crafted approach leveraging program synthesis for black box tool planning. Accompanied by SwissNYF, a comprehensive suite that integrates black-box algorithms for planning and verification tasks, addressing the aforementioned challenges and enhancing the versatility and effectiveness of LLMs in complex API interactions. The public code for SwissNYF is available at https://github.com/iclr-dummy-user/SwissNYF.

Assurance cases can be used to argue for the safety of products in safety engineering. In safety-critical areas, the construction of assurance cases is indispensable. Trustworthiness Derivation Trees (TDTs) enhance assurance cases by incorporating formal methods, rendering it possible for automatic reasoning about assurance cases. We present Trustworthiness Derivation Tree Analyzer (Trusta), a desktop application designed to automatically construct and verify TDTs. The tool has a built-in Prolog interpreter in its backend, and is supported by the constraint solvers Z3 and MONA. Therefore, it can solve constraints about logical formulas involving arithmetic, sets, Horn clauses etc. Trusta also utilizes large language models to make the creation and evaluation of assurance cases more convenient. It allows for interactive human examination and modification. We evaluated top language models like ChatGPT-3.5, ChatGPT-4, and PaLM 2 for generating assurance cases. Our tests showed a 50%-80% similarity between machine-generated and human-created cases. In addition, Trusta can extract formal constraints from text in natural languages, facilitating an easier interpretation and validation process. This extraction is subject to human review and correction, blending the best of automated efficiency with human insight. To our knowledge, this marks the first integration of large language models in automatic creating and reasoning about assurance cases, bringing a novel approach to a traditional challenge. Through several industrial case studies, Trusta has proven to quickly find some subtle issues that are typically missed in manual inspection, demonstrating its practical value in enhancing the assurance case development process.

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%.

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.

Large Language Models (LLMs) have made significant strides in mathematical reasoning, underscoring the need for a comprehensive and fair evaluation of their capabilities. However, existing benchmarks often fall short, either lacking extensive coverage of undergraduate-level mathematical problems or probably suffering from test-set contamination. To address these issues, we introduce UGMathBench, a diverse and dynamic benchmark specifically designed for evaluating undergraduate-level mathematical reasoning with LLMs. UGMathBench comprises 5,062 problems across 16 subjects and 111 topics, featuring 10 distinct answer types. Each problem includes three randomized versions, with additional versions planned for release as leading open-source LLMs become saturated in UGMathBench. Furthermore, we propose two key metrics: effective accuracy (EAcc), which measures the percentage of correctly solved problems across all three versions, and reasoning gap (Delta), which assesses reasoning robustness by calculating the difference between the average accuracy across all versions and EAcc. Our extensive evaluation of 23 leading LLMs reveals that the highest EAcc achieved is 56.3\% by OpenAI-o1-mini, with large Delta values observed across different models. This highlights the need for future research aimed at developing "large reasoning models" with high EAcc and Delta = 0. We anticipate that the release of UGMathBench, along with its detailed evaluation codes, will serve as a valuable resource to advance the development of LLMs in solving mathematical problems.