Daily Papers

The expanding Lean 4 ecosystem poses challenges for navigating its vast libraries. This paper introduces LeanExplore, a search engine for Lean 4 declarations. LeanExplore enables users to semantically search for statements, both formally and informally, across select Lean 4 packages (including Batteries, Init, Lean, Mathlib, PhysLean, and Std). This search capability is powered by a hybrid ranking strategy, integrating scores from a multi-source semantic embedding model (capturing conceptual meaning from formal Lean code, docstrings, AI-generated informal translations, and declaration titles), BM25+ for keyword-based lexical relevance, and a PageRank-based score reflecting declaration importance and interconnectedness. The search engine is accessible via a dedicated website (https://www.leanexplore.com/) and a Python API (https://github.com/justincasher/lean-explore). Furthermore, the database can be downloaded, allowing users to self-host the service. LeanExplore integrates easily with LLMs via the model context protocol (MCP), enabling users to chat with an AI assistant about Lean declarations or utilize the search engine for building theorem-proving agents. This work details LeanExplore's architecture, data processing, functionalities, and its potential to enhance Lean 4 workflows and AI-driven mathematical research

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.

Solving mathematical problems using computer-verifiable languages like Lean has significantly impacted mathematical and computer science communities. State-of-the-art methods utilize single Large Language Models (LLMs) as agents or provers to either generate complete proof or perform tree searches. However, single-agent methods inherently lack a structured way to combine high-level reasoning in Natural Language (NL) with Formal Language (FL) verification feedback. To solve these issues, we propose MA-LoT: Multi-Agent Lean-based Long Chain-of-Thought framework, (to the best of our knowledge), the first multi-agent framework for Lean4 theorem proving that balance high-level NL reasoning and FL verification in Long CoT. Using this structured interaction, our approach enables deeper insights and long-term coherence in proof generation, with which past methods struggle. We do this by leveraging emergent formal reasoning ability in Long CoT using our novel LoT-Transfer Learning training-inference pipeline. Extensive experiments show that our framework achieves 54.51% accuracy rate on the Lean4 version of MiniF2F-Test dataset, largely outperforming GPT-4 (22.95%), single-agent tree search (InternLM-Step-Prover, 50.70%), and whole-proof generation (DeepSeek-Prover-v1.5, 48.36%) baselines. Furthermore, our findings highlight the potential of combining Long CoT with formal verification for a more insightful generation in a broader perspective.

Reasoning remains a challenging task for large language models (LLMs), especially within the logically constrained environment of automated theorem proving (ATP), due to sparse rewards and the vast scale of proofs. These challenges are amplified in benchmarks like PutnamBench, which contains university-level problems requiring complex, multi-step reasoning. To address this, we introduce self-generated goal-conditioned MDPs (sG-MDPs), a new framework in which agents generate and pursue their subgoals based on the evolving proof state. Given this more structured generation of goals, the resulting problem becomes more amenable to search. We then apply Monte Carlo Tree Search (MCTS)-like algorithms to solve the sG-MDP, instantiating our approach in Bourbaki (7B), a modular system that can ensemble multiple 7B LLMs for subgoal generation and tactic synthesis. On PutnamBench, Bourbaki (7B) solves 26 problems, achieving new state-of-the-art results with models at this scale.

The advancement in generative AI could be boosted with more accessible mathematics. Beyond human-AI chat, large language models (LLMs) are emerging in programming, algorithm discovery, and theorem proving, yet their genomics application is limited. This project introduces Math Agents and mathematical embedding as fresh entries to the "Moore's Law of Mathematics", using a GPT-based workflow to convert equations from literature into LaTeX and Python formats. While many digital equation representations exist, there's a lack of automated large-scale evaluation tools. LLMs are pivotal as linguistic user interfaces, providing natural language access for human-AI chat and formal languages for large-scale AI-assisted computational infrastructure. Given the infinite formal possibility spaces, Math Agents, which interact with math, could potentially shift us from "big data" to "big math". Math, unlike the more flexible natural language, has properties subject to proof, enabling its use beyond traditional applications like high-validation math-certified icons for AI alignment aims. This project aims to use Math Agents and mathematical embeddings to address the ageing issue in information systems biology by applying multiscalar physics mathematics to disease models and genomic data. Generative AI with episodic memory could help analyse causal relations in longitudinal health records, using SIR Precision Health models. Genomic data is suggested for addressing the unsolved Alzheimer's disease problem.

Scientific discovery is a complex cognitive process that has driven human knowledge and technological progress for centuries. While artificial intelligence (AI) has made significant advances in automating aspects of scientific reasoning, simulation, and experimentation, we still lack integrated AI systems capable of performing autonomous long-term scientific research and discovery. This paper examines the current state of AI for scientific discovery, highlighting recent progress in large language models and other AI techniques applied to scientific tasks. We then outline key challenges and promising research directions toward developing more comprehensive AI systems for scientific discovery, including the need for science-focused AI agents, improved benchmarks and evaluation metrics, multimodal scientific representations, and unified frameworks combining reasoning, theorem proving, and data-driven modeling. Addressing these challenges could lead to transformative AI tools to accelerate progress across disciplines towards scientific discovery.

We present Prover Agent, a novel AI agent for automated theorem proving that integrates large language models (LLMs) with a formal proof assistant, Lean. Prover Agent coordinates an informal reasoning LLM, a formal prover model, and feedback from Lean while also generating auxiliary lemmas. These auxiliary lemmas are not limited to subgoals in the formal proof but can also include special cases or potentially useful facts derived from the assumptions, which help in discovering a viable proof strategy. It achieves an 88.1% success rate on the MiniF2F benchmark, establishing a new state-of-the-art among methods using small language models (SLMs) with a much lower sample budget than previous approaches. We also present theoretical analyses and case studies that illustrate how these generated lemmas contribute to solving challenging problems. Our code is publicly available at: https://github.com/kAIto47802/Prover-Agent.

Agentic systems have recently become the dominant paradigm for formal theorem proving, achieving strong performance by coordinating multiple models and tools. However, existing approaches often rely on task-specific pipelines and trained formal provers, limiting their flexibility and reproducibility. In this paper, we propose the paradigm that directly uses a general coding agent as a formal math reasoner. This paradigm is motivated by (1) A general coding agent provides a natural interface for diverse reasoning tasks beyond proving, (2) Performance can be improved by simply replacing the underlying base model, without training, and (3) MCP enables flexible extension and autonomous calling of specialized tools, avoiding complex design. Based on this paradigm, we introduce Numina-Lean-Agent, which combines Claude Code with Numina-Lean-MCP to enable autonomous interaction with Lean, retrieval of relevant theorems, informal proving and auxiliary reasoning tools. Using Claude Opus 4.5 as the base model, Numina-Lean-Agent solves all problems in Putnam 2025 (12 / 12), matching the best closed-source system. Beyond benchmark evaluation, we further demonstrate its generality by interacting with mathematicians to successfully formalize the Brascamp-Lieb theorem. We release Numina-Lean-Agent and all solutions at https://github.com/project-numina/numina-lean-agent.

We present Ax-Prover, a multi-agent system for automated theorem proving in Lean that can solve problems across diverse scientific domains and operate either autonomously or collaboratively with human experts. To achieve this, Ax-Prover approaches scientific problem solving through formal proof generation, a process that demands both creative reasoning and strict syntactic rigor. Ax-Prover meets this challenge by equipping Large Language Models (LLMs), which provide knowledge and reasoning, with Lean tools via the Model Context Protocol (MCP), which ensure formal correctness. To evaluate its performance as an autonomous prover, we benchmark our approach against frontier LLMs and specialized prover models on two public math benchmarks and on two Lean benchmarks we introduce in the fields of abstract algebra and quantum theory. On public datasets, Ax-Prover is competitive with state-of-the-art provers, while it largely outperforms them on the new benchmarks. This shows that, unlike specialized systems that struggle to generalize, our tool-based agentic theorem prover approach offers a generalizable methodology for formal verification across diverse scientific domains. Furthermore, we demonstrate Ax-Prover's assistant capabilities in a practical use case, showing how it enabled an expert mathematician to formalize the proof of a complex cryptography theorem.

Formal, automated theorem proving has long been viewed as a challenge to artificial intelligence. We introduce here a new approach to computer theorem proving, one that employs specialized language models for Lean4 proof generation combined with recursive decomposition of difficult theorems into simpler entailing propositions. These models are coordinated through a multi-agent architecture that orchestrates autoformalization (if required), proof generation, decomposition of difficult theorems into simpler entailing propositions, and recursive proof (and/or decomposition) of these propositions. Without decomposition, we achieve a 90.4% pass rate on miniF2F. With decomposition, this is significantly improved. A key technical contribution lies in our extension of the Kimina Lean Server with abstract syntax tree (AST) parsing capabilities to facilitate automated, recursive proof decomposition. The system is made available on PyPI as goedels-poetry (at https://pypi.org/project/goedels-poetry ), and the open-source implementation KellyJDavis/goedels-poetry (at https://github.com/KellyJDavis/goedels-poetry ) facilitates both adaptation to alternative language models and extension with custom functionality.

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.

Large language models have recently made significant progress to generate rigorous mathematical proofs. In contrast, utilizing LLMs for theorem proving in formal languages (such as Lean) remains challenging and computationally expensive, particularly when addressing problems at the undergraduate level and beyond. In this work, we present Seed-Prover 1.5, a formal theorem-proving model trained via large-scale agentic reinforcement learning, alongside an efficient test-time scaling (TTS) workflow. Through extensive interactions with Lean and other tools, the model continuously accumulates experience during the RL process, substantially enhancing the capability and efficiency of formal theorem proving. Furthermore, leveraging recent advancements in natural language proving, our TTS workflow efficiently bridges the gap between natural and formal languages. Compared to state-of-the-art methods, Seed-Prover 1.5 achieves superior performance with a smaller compute budget. It solves 88\% of PutnamBench (undergraduate-level), 80\% of Fate-H (graduate-level), and 33\% of Fate-X (PhD-level) problems. Notably, using our system, we solved 11 out of 12 problems from Putnam 2025 within 9 hours. Our findings suggest that scaling learning from experience, driven by high-quality formal feedback, holds immense potential for the future of formal mathematical reasoning.

Large language models (LLMs) have recently shown strong performance on mathematical benchmarks. At the same time, they are prone to hallucination and sycophancy, often providing convincing but flawed proofs for incorrect mathematical statements provided by users. This significantly limits the applicability of LLMs in theorem proving, as verification of these flawed proofs must be done manually by expert mathematicians. However, existing benchmarks that measure sycophancy in mathematics are limited: they focus solely on final-answer problems, rely on very simple and often contaminated datasets, and construct benchmark samples using synthetic modifications that create ill-posed questions rather than well-posed questions that are demonstrably false. To address these issues, we introduce BrokenMath, the first benchmark for evaluating sycophantic behavior in LLMs within the context of natural language theorem proving. BrokenMath is built from advanced 2025 competition problems, which are perturbed with an LLM to produce false statements and subsequently refined through expert review. Using an LLM-as-a-judge framework, we evaluate state-of-the-art LLMs and agentic systems and find that sycophancy is widespread, with the best model, GPT-5, producing sycophantic answers 29% of the time. We further investigate several mitigation strategies, including test-time interventions and supervised fine-tuning on curated sycophantic examples. These approaches substantially reduce, but do not eliminate, sycophantic behavior.

Humans prove theorems by relying on substantial high-level reasoning and problem-specific insights. Proof assistants offer a formalism that resembles human mathematical reasoning, representing theorems in higher-order logic and proofs as high-level tactics. However, human experts have to construct proofs manually by entering tactics into the proof assistant. In this paper, we study the problem of using machine learning to automate the interaction with proof assistants. We construct CoqGym, a large-scale dataset and learning environment containing 71K human-written proofs from 123 projects developed with the Coq proof assistant. We develop ASTactic, a deep learning-based model that generates tactics as programs in the form of abstract syntax trees (ASTs). Experiments show that ASTactic trained on CoqGym can generate effective tactics and can be used to prove new theorems not previously provable by automated methods. Code is available at https://github.com/princeton-vl/CoqGym.

General-purpose Large Language Models (LLMs) have achieved remarkable success in intelligence, performing comparably to human experts on complex reasoning tasks such as coding and mathematical reasoning. However, generating formal proofs in specialized languages like Lean 4 remains a significant challenge for these models, limiting their application in complex theorem proving and automated verification. Current approaches typically require specializing models through fine-tuning on dedicated formal corpora, incurring high costs for data collection and training. In this work, we introduce Delta Prover, an agent-based framework that orchestrates the interaction between a general-purpose LLM and the Lean 4 proof environment. Delta Prover leverages the reflection and reasoning capabilities of general-purpose LLMs to interactively construct formal proofs in Lean 4, circumventing the need for model specialization. At its core, the agent integrates two novel, interdependent components: an algorithmic framework for reflective decomposition and iterative proof repair, and a custom Domain-Specific Language (DSL) built upon Lean 4 for streamlined subproblem management. Delta Prover achieves a state-of-the-art 95.9\% success rate on the miniF2F-test benchmark, surpassing all existing approaches, including those requiring model specialization. Furthermore, Delta Prover exhibits a significantly stronger test-time scaling law compared to standard Best-of-N proof strategies. Crucially, our findings demonstrate that general-purpose LLMs, when guided by an effective agentic structure, possess substantial untapped theorem-proving capabilities. This presents a computationally efficient alternative to specialized models for robust automated reasoning in formal environments.

The integration of Large Language Models (LLMs) into automated theorem proving has shown immense promise, yet is fundamentally constrained by challenges in scaling up both training-time reinforcement learning (RL) and inference-time compute. This paper introduces BFS-Prover-V2, a system designed to address this dual scaling problem. We present two primary innovations. The first is a novel multi-turn off-policy RL framework for continually improving the performance of LLM step-prover at training time. This framework, inspired by the principles of AlphaZero, utilizes a multi-stage expert iteration pipeline featuring adaptive tactic-level data filtering and periodic retraining to surmount the performance plateaus that typically curtail long-term RL in LLM-based agents. The second innovation is a planner-enhanced multi-agent search architecture that scales reasoning capabilities at inference time. This architecture employs a general reasoning model as a high-level planner to iteratively decompose complex theorems into a sequence of simpler subgoals. This hierarchical approach substantially reduces the search space, enabling a team of parallel prover agents to collaborate efficiently by leveraging a shared proof cache. We demonstrate that this dual approach to scaling yields state-of-the-art results on established formal mathematics benchmarks. BFS-Prover-V2 achieves 95.08\% and 41.4\% on the MiniF2F and ProofNet test sets respectively. While demonstrated in the domain of formal mathematics, the RL and inference techniques presented in this work are of broader interest and may be applied to other domains requiring long-horizon multi-turn reasoning and complex search.

Understanding domain-specific theorems often requires more than just text-based reasoning; effective communication through structured visual explanations is crucial for deeper comprehension. While large language models (LLMs) demonstrate strong performance in text-based theorem reasoning, their ability to generate coherent and pedagogically meaningful visual explanations remains an open challenge. In this work, we introduce TheoremExplainAgent, an agentic approach for generating long-form theorem explanation videos (over 5 minutes) using Manim animations. To systematically evaluate multimodal theorem explanations, we propose TheoremExplainBench, a benchmark covering 240 theorems across multiple STEM disciplines, along with 5 automated evaluation metrics. Our results reveal that agentic planning is essential for generating detailed long-form videos, and the o3-mini agent achieves a success rate of 93.8% and an overall score of 0.77. However, our quantitative and qualitative studies show that most of the videos produced exhibit minor issues with visual element layout. Furthermore, multimodal explanations expose deeper reasoning flaws that text-based explanations fail to reveal, highlighting the importance of multimodal explanations.

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.

Recent advances in multi-agent systems highlight the potential of specialized small agents that collaborate via division of labor. Existing tool-integrated reasoning systems, however, often follow a single-agent paradigm in which one large model interleaves long-horizon reasoning with precise tool operations, leading to cognitive-load interference and unstable coordination. We present MSARL, a Multi-Small-Agent Reinforcement Learning framework that explicitly decouples reasoning from tool use. In MSARL, a Reasoning Agent decomposes problems and plans tool invocations, while multiple Tool Agents specialize in specific external tools, each trained via a combination of imitation learning and reinforcement learning with role-specific rewards. On mathematical problem solving with code execution, MSARL significantly improves reasoning stability and final-answer accuracy over single-agent baselines. Moreover, the architecture generalizes to diverse tool-use tasks, demonstrating that cognitive-role decoupling with small agents is a scalable blueprint for multi-agent AI design.

Labeled data for imitation learning of theorem proving in large libraries of formalized mathematics is scarce as such libraries require years of concentrated effort by human specialists to be built. This is particularly challenging when applying large Transformer language models to tactic prediction, because the scaling of performance with respect to model size is quickly disrupted in the data-scarce, easily-overfitted regime. We propose PACT ({\bf P}roof {\bf A}rtifact {\bf C}o-{\bf T}raining), a general methodology for extracting abundant self-supervised data from kernel-level proof terms for co-training alongside the usual tactic prediction objective. We apply this methodology to Lean, an interactive proof assistant which hosts some of the most sophisticated formalized mathematics to date. We instrument Lean with a neural theorem prover driven by a Transformer language model and show that PACT improves theorem proving success rate on a held-out suite of test theorems from 32\% to 48\%.

Large Reasoning Models (LRMs) like o3 and DeepSeek-R1 have achieved remarkable progress in natural language reasoning with long chain-of-thought. However, they remain computationally inefficient and struggle with accuracy when solving problems requiring complex mathematical operations. In this work, we present AgentMath, an agent framework that seamlessly integrates language models' reasoning capabilities with code interpreters' computational precision to efficiently tackle complex mathematical problems. Our approach introduces three key innovations: (1) An automated method that converts natural language chain-of-thought into structured tool-augmented trajectories, generating high-quality supervised fine-tuning (SFT) data to alleviate data scarcity; (2) A novel agentic reinforcement learning (RL) paradigm that dynamically interleaves natural language generation with real-time code execution. This enables models to autonomously learn optimal tool-use strategies through multi-round interactive feedback, while fostering emergent capabilities in code refinement and error correction; (3) An efficient training system incorporating innovative techniques, including request-level asynchronous rollout scheduling, agentic partial rollout, and prefix-aware weighted load balancing, achieving 4-5x speedup and making efficient RL training feasible on ultra-long sequences with scenarios with massive tool invocation. The evaluations show that AgentMath achieves state-of-the-art performance on challenging mathematical competition benchmarks including AIME24, AIME25, and HMMT25. Specifically, AgentMath-30B-A3B attains 90.6%, 86.4%, and 73.8% accuracy respectively, achieving advanced performance. The results validate the effectiveness of our approach and pave the way for building more sophisticated and scalable mathematical reasoning agents.

Theorem proving is a fundamental task in mathematics. With the advent of large language models (LLMs) and interactive theorem provers (ITPs) like Lean, there has been growing interest in integrating LLMs and ITPs to automate theorem proving. In this approach, the LLM generates proof steps (tactics), and the ITP checks the applicability of the tactics at the current goal. The two systems work together to complete the proof. In this paper, we introduce DS-Prover, a novel dynamic sampling method for theorem proving. This method dynamically determines the number of tactics to apply to expand the current goal, taking into account the remaining time compared to the total allocated time for proving a theorem. This makes the proof search process more efficient by adjusting the balance between exploration and exploitation as time passes. We also augment the training dataset by decomposing simplification and rewrite tactics with multiple premises into tactics with single premises. This gives the model more examples to learn from and helps it to predict the tactics with premises more accurately. We perform our experiments using the Mathlib dataset of the Lean theorem prover and report the performance on two standard datasets, MiniF2F and ProofNet. Our methods achieve significant performance gains on both datasets. We achieved a state-of-the-art performance (Pass@1) of 14.2% on the ProofNet dataset and a performance of 29.8% on MiniF2F, slightly surpassing the best-reported Pass@1 of 29.6% using Lean.

Theorem proving serves as a major testbed for evaluating complex reasoning abilities in large language models (LLMs). However, traditional automated theorem proving (ATP) approaches rely heavily on formal proof systems that poorly align with LLMs' strength derived from informal, natural language knowledge acquired during pre-training. In this work, we propose DeepTheorem, a comprehensive informal theorem-proving framework exploiting natural language to enhance LLM mathematical reasoning. DeepTheorem includes a large-scale benchmark dataset consisting of 121K high-quality IMO-level informal theorems and proofs spanning diverse mathematical domains, rigorously annotated for correctness, difficulty, and topic categories, accompanied by systematically constructed verifiable theorem variants. We devise a novel reinforcement learning strategy (RL-Zero) explicitly tailored to informal theorem proving, leveraging the verified theorem variants to incentivize robust mathematical inference. Additionally, we propose comprehensive outcome and process evaluation metrics examining proof correctness and the quality of reasoning steps. Extensive experimental analyses demonstrate DeepTheorem significantly improves LLM theorem-proving performance compared to existing datasets and supervised fine-tuning protocols, achieving state-of-the-art accuracy and reasoning quality. Our findings highlight DeepTheorem's potential to fundamentally advance automated informal theorem proving and mathematical exploration.

We introduce Agentic Reasoning, a framework that enhances large language model (LLM) reasoning by integrating external tool-using agents. Unlike conventional LLM-based reasoning approaches, which rely solely on internal inference, Agentic Reasoning dynamically engages web search, code execution, and structured reasoning-context memory to solve complex problems requiring deep research and multi-step logical deduction. Our framework introduces the Mind Map agent, which constructs a structured knowledge graph to track logical relationships, improving deductive reasoning. Additionally, the integration of web-search and coding agents enables real-time retrieval and computational analysis, enhancing reasoning accuracy and decision-making. Evaluations on PhD-level scientific reasoning (GPQA) and domain-specific deep research tasks demonstrate that our approach significantly outperforms existing models, including leading retrieval-augmented generation (RAG) systems and closed-source LLMs. Moreover, our results indicate that agentic reasoning improves expert-level knowledge synthesis, test-time scalability, and structured problem-solving. The code is at: https://github.com/theworldofagents/Agentic-Reasoning.

A fundamental challenge in formal theorem proving by LLMs is the lack of high-quality training data. Although reinforcement learning or expert iteration partially mitigates this issue by alternating between LLM generating proofs and finetuning them on correctly generated ones, performance quickly plateaus due to the scarcity of correct proofs (sparse rewards). To keep improving the models with limited data, we draw inspiration from mathematicians, who continuously develop new results, partly by proposing novel conjectures or exercises (which are often variants of known results) and attempting to solve them. We design the Self-play Theorem Prover (STP) that simultaneously takes on two roles, conjecturer and prover, each providing training signals to the other. The conjecturer is trained iteratively on previously generated conjectures that are barely provable by the current prover, which incentivizes it to generate increasingly challenging conjectures over time. The prover attempts to prove the conjectures with standard expert iteration. We evaluate STP with both Lean and Isabelle formal versifiers. With 19.8 billion tokens generated during the training in Lean, STP proves 26.3% of the statements in the LeanWorkbook dataset, doubling the previous best result of 13.2% achieved through expert iteration. The final model achieves state-of-the-art performance among whole-proof generation methods on miniF2F-test (61.7%, pass@3200), Proofnet-test (23.1%, pass@3200) and PutnamBench (8/644, pass@3200).

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/ .

Explanations for AI models in high-stakes domains like medicine often lack verifiability, which can hinder trust. To address this, we propose an interactive agent that produces explanations through an auditable sequence of actions. The agent learns a policy to strategically seek external visual evidence to support its diagnostic reasoning. This policy is optimized using reinforcement learning, resulting in a model that is both efficient and generalizable. Our experiments show that this action-based reasoning process significantly improves calibrated accuracy, reducing the Brier score by 18\% compared to a non-interactive baseline. To validate the faithfulness of the agent's explanations, we introduce a causal intervention method. By masking the visual evidence the agent chooses to use, we observe a measurable degradation in its performance (DeltaBrier=+0.029), confirming that the evidence is integral to its decision-making process. Our work provides a practical framework for building AI systems with verifiable and faithful reasoning capabilities.

Large Language Models (LLMs) have been successful in mathematical reasoning tasks such as formal theorem proving when integrated with interactive proof assistants like Lean. Existing approaches involve training or fine-tuning an LLM on a specific dataset to perform well on particular domains, such as undergraduate-level mathematics. These methods struggle with generalizability to advanced mathematics. A fundamental limitation is that these approaches operate on static domains, failing to capture how mathematicians often work across multiple domains and projects simultaneously or cyclically. We present LeanAgent, a novel lifelong learning framework for theorem proving that continuously generalizes to and improves on ever-expanding mathematical knowledge without forgetting previously learned knowledge. LeanAgent introduces several key innovations, including a curriculum learning strategy that optimizes the learning trajectory in terms of mathematical difficulty, a dynamic database for efficient management of evolving mathematical knowledge, and progressive training to balance stability and plasticity. LeanAgent successfully proves 162 theorems previously unproved by humans across 23 diverse Lean repositories, many from advanced mathematics. It performs up to 11times better than the static LLM baseline, proving challenging theorems in domains like abstract algebra and algebraic topology while showcasing a clear progression of learning from basic concepts to advanced topics. In addition, we analyze LeanAgent's superior performance on key lifelong learning metrics. LeanAgent achieves exceptional scores in stability and backward transfer, where learning new tasks improves performance on previously learned tasks. This emphasizes LeanAgent's continuous generalizability and improvement, explaining its superior theorem proving performance.

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

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.

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.

Effective prompt design is essential for improving the planning capabilities of large language model (LLM)-driven agents. However, existing structured prompting strategies are typically limited to single-agent, plan-only settings, and often evaluate performance solely based on task accuracy - overlooking critical factors such as token efficiency, modularity, and scalability in multi-agent environments. To address these limitations, we introduce CodeAgents, a prompting framework that codifies multi-agent reasoning and enables structured, token-efficient planning in multi-agent systems. In CodeAgents, all components of agent interaction - Task, Plan, Feedback, system roles, and external tool invocations - are codified into modular pseudocode enriched with control structures (e.g., loops, conditionals), boolean logic, and typed variables. This design transforms loosely connected agent plans into cohesive, interpretable, and verifiable multi-agent reasoning programs. We evaluate the proposed framework across three diverse benchmarks - GAIA, HotpotQA, and VirtualHome - using a range of representative LLMs. Results show consistent improvements in planning performance, with absolute gains of 3-36 percentage points over natural language prompting baselines. On VirtualHome, our method achieves a new state-of-the-art success rate of 56%. In addition, our approach reduces input and output token usage by 55-87% and 41-70%, respectively, underscoring the importance of token-aware evaluation metrics in the development of scalable multi-agent LLM systems. The code and resources are available at: https://anonymous.4open.science/r/CodifyingAgent-5A86

With the rise of artificial intelligence (AI), applying large language models (LLMs) to Operations Research (OR) problem-solving has attracted increasing attention. Most existing approaches attempt to improve OR problem-solving through prompt engineering or fine-tuning strategies for LLMs. However, these methods are fundamentally constrained by the limited capabilities of non-reasoning LLMs. To overcome these limitations, we propose OR-LLM-Agent, an AI agent built on reasoning LLMs for automated OR problem solving. The agent decomposes the task into three sequential stages: mathematical modeling, code generation, and debugging. Each task is handled by a dedicated sub-agent, which enables more targeted reasoning. We also construct BWOR, a high-quality dataset for evaluating LLM performance on OR tasks. Our analysis shows that existing benchmarks such as NL4OPT, MAMO, and IndustryOR suffer from certain issues, making them less suitable for reliably evaluating LLM performance. In contrast, BWOR provides a more consistent and discriminative assessment of model capabilities. Experimental results demonstrate that OR-LLM-Agent outperforms advanced methods, including GPT-o3, Gemini 2.5 Pro, and ORLM, by at least 7% in accuracy. These results demonstrate the effectiveness of task decomposition for OR problem solving.

Reasoning is a fundamental cognitive process underlying inference, problem-solving, and decision-making. While large language models (LLMs) demonstrate strong reasoning capabilities in closed-world settings, they struggle in open-ended and dynamic environments. Agentic reasoning marks a paradigm shift by reframing LLMs as autonomous agents that plan, act, and learn through continual interaction. In this survey, we organize agentic reasoning along three complementary dimensions. First, we characterize environmental dynamics through three layers: foundational agentic reasoning, which establishes core single-agent capabilities including planning, tool use, and search in stable environments; self-evolving agentic reasoning, which studies how agents refine these capabilities through feedback, memory, and adaptation; and collective multi-agent reasoning, which extends intelligence to collaborative settings involving coordination, knowledge sharing, and shared goals. Across these layers, we distinguish in-context reasoning, which scales test-time interaction through structured orchestration, from post-training reasoning, which optimizes behaviors via reinforcement learning and supervised fine-tuning. We further review representative agentic reasoning frameworks across real-world applications and benchmarks, including science, robotics, healthcare, autonomous research, and mathematics. This survey synthesizes agentic reasoning methods into a unified roadmap bridging thought and action, and outlines open challenges and future directions, including personalization, long-horizon interaction, world modeling, scalable multi-agent training, and governance for real-world deployment.

Large Language Models (LLMs) trained with reinforcement learning and verifiable rewards have achieved strong results on complex reasoning tasks. Recent work extends this paradigm to a multi-agent setting, where a meta-thinking agent proposes plans and monitors progress while a reasoning agent executes subtasks through sequential conversational turns. Despite promising performance, we identify a critical limitation: lazy agent behavior, in which one agent dominates while the other contributes little, undermining collaboration and collapsing the setup to an ineffective single agent. In this paper, we first provide a theoretical analysis showing why lazy behavior naturally arises in multi-agent reasoning. We then introduce a stable and efficient method for measuring causal influence, helping mitigate this issue. Finally, as collaboration intensifies, the reasoning agent risks getting lost in multi-turn interactions and trapped by previous noisy responses. To counter this, we propose a verifiable reward mechanism that encourages deliberation by allowing the reasoning agent to discard noisy outputs, consolidate instructions, and restart its reasoning process when necessary. Extensive experiments demonstrate that our framework alleviates lazy agent behavior and unlocks the full potential of multi-agent framework for complex reasoning tasks.

The rapid advancements of AI agents have ignited the long-held ambition of leveraging them to accelerate scientific discovery. Achieving this goal requires a deep understanding of the frontiers of human knowledge. As such, Humanity's Last Exam (HLE) provides an exceptionally challenging touchstone for evaluating scientific AI agents. In this work, we aim to construct the foundational architecture for general-purpose agents and validate the capabilities through leading performance on HLE. To achieve this, we introduce X-Master, a tool-augmented reasoning agent designed to emulate human researchers by interacting flexibly with external tools during its reasoning process. This agent, guided by the conceptualization of code as an interaction language, can flexibly leverage built-in Python libraries and our customized tools to augment the reasoning. We further scale its capabilities through X-Masters, a scattered-and-stacked agentic workflow that systematically enhances breadth and depth of reasoning. Our open-source solution, X-Masters, sets a new state-of-the-art record on HLE with a score of 32.1%, surpassing OpenAI's and Google's Deep Research (26.6% and 26.9%) and becoming the first to exceed the 30% threshold. This work allows us to gain a deeper understanding of complex task-solving and accumulates valuable experience that can inform future advancements, guiding subsequent model training.

We propose an online training procedure for a transformer-based automated theorem prover. Our approach leverages a new search algorithm, HyperTree Proof Search (HTPS), inspired by the recent success of AlphaZero. Our model learns from previous proof searches through online training, allowing it to generalize to domains far from the training distribution. We report detailed ablations of our pipeline's main components by studying performance on three environments of increasing complexity. In particular, we show that with HTPS alone, a model trained on annotated proofs manages to prove 65.4% of a held-out set of Metamath theorems, significantly outperforming the previous state of the art of 56.5% by GPT-f. Online training on these unproved theorems increases accuracy to 82.6%. With a similar computational budget, we improve the state of the art on the Lean-based miniF2F-curriculum dataset from 31% to 42% proving accuracy.

Enhancing the reasoning capabilities of large language models (LLMs) is crucial for enabling them to tackle complex, multi-step problems. Multi-agent frameworks have shown great potential in enhancing LLMs' reasoning capabilities. However, the lack of effective cooperation between LLM agents hinders their performance, especially for multi-step reasoning tasks. This paper proposes a novel cooperative multi-agent reasoning framework (CoPlanner) by separating reasoning steps and assigning distinct duties to different agents. CoPlanner consists of two LLM agents: a planning agent and a reasoning agent. The planning agent provides high-level strategic hints, while the reasoning agent follows these hints and infers answers. By training the planning agent's policy through the interactive reasoning process via Proximal Policy Optimization (PPO), the LLaMA-3-8B-based CoPlanner outperforms the previous best method by 9.94\% on LogiQA and 3.09\% on BBH. Our results demonstrate that the guidance from the planning agent and the effective cooperation between the agents contribute to the superior performance of CoPlanner in tackling multi-step reasoning problems.

We introduce rStar2-Agent, a 14B math reasoning model trained with agentic reinforcement learning to achieve frontier-level performance. Beyond current long CoT, the model demonstrates advanced cognitive behaviors, such as thinking carefully before using Python coding tools and reflecting on code execution feedback to autonomously explore, verify, and refine intermediate steps in complex problem-solving. This capability is enabled through three key innovations that makes agentic RL effective at scale: (i) an efficient RL infrastructure with a reliable Python code environment that supports high-throughput execution and mitigates the high rollout costs, enabling training on limited GPU resources (64 MI300X GPUs); (ii) GRPO-RoC, an agentic RL algorithm with a Resample-on-Correct rollout strategy that addresses the inherent environment noises from coding tools, allowing the model to reason more effectively in a code environment; (iii) An efficient agent training recipe that starts with non-reasoning SFT and progresses through multi-RL stages, yielding advanced cognitive abilities with minimal compute cost. To this end, rStar2-Agent boosts a pre-trained 14B model to state of the art in only 510 RL steps within one week, achieving average pass@1 scores of 80.6% on AIME24 and 69.8% on AIME25, surpassing DeepSeek-R1 (671B) with significantly shorter responses. Beyond mathematics, rStar2-Agent-14B also demonstrates strong generalization to alignment, scientific reasoning, and agentic tool-use tasks. Code and training recipes are available at https://github.com/microsoft/rStar.

Large language models (LLMs) excel at complex reasoning tasks but remain computationally expensive, limiting their practical deployment. To address this, recent works have focused on distilling reasoning capabilities into smaller language models (sLMs) using chain-of-thought (CoT) traces from teacher LLMs. However, this approach struggles in scenarios requiring rare factual knowledge or precise computation, where sLMs often hallucinate due to limited capability. In this work, we propose Agent Distillation, a framework for transferring not only reasoning capability but full task-solving behavior from LLM-based agents into sLMs with retrieval and code tools. We improve agent distillation along two complementary axes: (1) we introduce a prompting method called first-thought prefix to enhance the quality of teacher-generated trajectories; and (2) we propose a self-consistent action generation for improving test-time robustness of small agents. We evaluate our method on eight reasoning tasks across factual and mathematical domains, covering both in-domain and out-of-domain generalization. Our results show that sLMs as small as 0.5B, 1.5B, 3B parameters can achieve performance competitive with next-tier larger 1.5B, 3B, 7B models fine-tuned using CoT distillation, demonstrating the potential of agent distillation for building practical, tool-using small agents. Our code is available at https://github.com/Nardien/agent-distillation.

We consider the problem of how a trusted, but computationally bounded agent (a 'verifier') can learn to interact with one or more powerful but untrusted agents ('provers') in order to solve a given task. More specifically, we study the case in which agents are represented using neural networks and refer to solutions of this problem as neural interactive proofs. First we introduce a unifying framework based on prover-verifier games, which generalises previously proposed interaction protocols. We then describe several new protocols for generating neural interactive proofs, and provide a theoretical comparison of both new and existing approaches. Finally, we support this theory with experiments in two domains: a toy graph isomorphism problem that illustrates the key ideas, and a code validation task using large language models. In so doing, we aim to create a foundation for future work on neural interactive proofs and their application in building safer AI systems.

Enabling effective collaboration among LLMs is a crucial step toward developing autonomous systems capable of solving complex problems. While LLMs are typically used as single-model generators, where humans critique and refine their outputs, the potential for jointly-trained collaborative models remains largely unexplored. Despite promising results in multi-agent communication and debate settings, little progress has been made in training models to work together on tasks. In this paper, we present a first step toward "Multi-agent LLM training" (MALT) on reasoning problems. Our approach employs a sequential multi-agent setup with heterogeneous LLMs assigned specialized roles: a generator, verifier, and refinement model iteratively solving problems. We propose a trajectory-expansion-based synthetic data generation process and a credit assignment strategy driven by joint outcome based rewards. This enables our post-training setup to utilize both positive and negative trajectories to autonomously improve each model's specialized capabilities as part of a joint sequential system. We evaluate our approach across MATH, GSM8k, and CQA, where MALT on Llama 3.1 8B models achieves relative improvements of 14.14%, 7.12%, and 9.40% respectively over the same baseline model. This demonstrates an early advance in multi-agent cooperative capabilities for performance on mathematical and common sense reasoning questions. More generally, our work provides a concrete direction for research around multi-agent LLM training approaches.

Recent progress in large language models (LLMs) has been propelled by reinforcement learning with verifiable rewards (RLVR) and test-time scaling. However, the limited output length of LLMs constrains the depth of reasoning attainable in a single inference process. Multi-agent reasoning systems offer a promising alternative by employing multiple agents including Solver, Verifier, and Corrector, to iteratively refine solutions. While effective in closed-source models like Gemini 2.5 Pro, they struggle to generalize to open-source models due to insufficient critic and correction capabilities. To address this, we propose MarsRL, a novel reinforcement learning framework with agentic pipeline parallelism, designed to jointly optimize all agents in the system. MarsRL introduces agent-specific reward mechanisms to mitigate reward noise and employs pipeline-inspired training to enhance efficiency in handling long trajectories. Applied to Qwen3-30B-A3B-Thinking-2507, MarsRL improves AIME2025 accuracy from 86.5% to 93.3% and BeyondAIME from 64.9% to 73.8%, even surpassing Qwen3-235B-A22B-Thinking-2507. These findings highlight the potential of MarsRL to advance multi-agent reasoning systems and broaden their applicability across diverse reasoning tasks.

Recent advances in the intrinsic reasoning capabilities of large language models (LLMs) have given rise to LLM-based agent systems that exhibit near-human performance on a variety of automated tasks. However, although these systems share similarities in terms of their use of LLMs, different reasoning frameworks of the agent system steer and organize the reasoning process in different ways. In this survey, we propose a systematic taxonomy that decomposes agentic reasoning frameworks and analyze how these frameworks dominate framework-level reasoning by comparing their applications across different scenarios. Specifically, we propose an unified formal language to further classify agentic reasoning systems into single-agent methods, tool-based methods, and multi-agent methods. After that, we provide a comprehensive review of their key application scenarios in scientific discovery, healthcare, software engineering, social simulation, and economics. We also analyze the characteristic features of each framework and summarize different evaluation strategies. Our survey aims to provide the research community with a panoramic view to facilitate understanding of the strengths, suitable scenarios, and evaluation practices of different agentic reasoning frameworks.

Large language models (LLMs) have shown promise in proving formal theorems using proof assistants such as Lean. However, existing methods are difficult to reproduce or build on, due to private code, data, and large compute requirements. This has created substantial barriers to research on machine learning methods for theorem proving. This paper removes these barriers by introducing LeanDojo: an open-source Lean playground consisting of toolkits, data, models, and benchmarks. LeanDojo extracts data from Lean and enables interaction with the proof environment programmatically. It contains fine-grained annotations of premises in proofs, providing valuable data for premise selection: a key bottleneck in theorem proving. Using this data, we develop ReProver (Retrieval-Augmented Prover): the first LLM-based prover that is augmented with retrieval for selecting premises from a vast math library. It is inexpensive and needs only one GPU week of training. Our retriever leverages LeanDojo's program analysis capability to identify accessible premises and hard negative examples, which makes retrieval much more effective. Furthermore, we construct a new benchmark consisting of 96,962 theorems and proofs extracted from Lean's math library. It features challenging data split requiring the prover to generalize to theorems relying on novel premises that are never used in training. We use this benchmark for training and evaluation, and experimental results demonstrate the effectiveness of ReProver over non-retrieval baselines and GPT-4. We thus provide the first set of open-source LLM-based theorem provers without any proprietary datasets and release it under a permissive MIT license to facilitate further research.

We explore the application of transformer-based language models to automated theorem proving. This work is motivated by the possibility that a major limitation of automated theorem provers compared to humans -- the generation of original mathematical terms -- might be addressable via generation from language models. We present an automated prover and proof assistant, GPT-f, for the Metamath formalization language, and analyze its performance. GPT-f found new short proofs that were accepted into the main Metamath library, which is to our knowledge, the first time a deep-learning based system has contributed proofs that were adopted by a formal mathematics community.

LLM-based formal proof assistants (e.g., in Lean) hold great promise for automating mathematical discovery. But beyond syntactic correctness, do these systems truly understand mathematical structure as humans do? We investigate this question through the lens of mathematical inequalities -- a fundamental tool across many domains. While modern provers can solve basic inequalities, we probe their ability to handle human-intuitive compositionality. We introduce Ineq-Comp, a benchmark built from elementary inequalities through systematic transformations, including variable duplication, algebraic rewriting, and multi-step composition. Although these problems remain easy for humans, we find that most provers -- including Goedel, STP, and Kimina-7B -- struggle significantly. DeepSeek-Prover-V2-7B shows relative robustness -- possibly because it is trained to decompose the problems into sub-problems -- but still suffers a 20\% performance drop (pass@32). Strikingly, performance remains poor for all models even when formal proofs of the constituent parts are provided in context, revealing that the source of weakness is indeed in compositional reasoning. Our results expose a persisting gap between the generalization behavior of current AI provers and human mathematical intuition.

Recent advancements, such as DeepSeek-Prover-V2-671B and Kimina-Prover-Preview-72B, demonstrate a prevailing trend in leveraging reinforcement learning (RL)-based large-scale training for automated theorem proving. Surprisingly, we discover that even without any training, careful neuro-symbolic coordination of existing off-the-shelf reasoning models and tactic step provers can achieve comparable performance. This paper introduces DSP+, an improved version of the Draft, Sketch, and Prove framework, featuring a fine-grained and integrated neuro-symbolic enhancement for each phase: (1) In the draft phase, we prompt reasoning models to generate concise natural-language subgoals to benefit the sketch phase, removing thinking tokens and references to human-written proofs; (2) In the sketch phase, subgoals are autoformalized with hypotheses to benefit the proving phase, and sketch lines containing syntactic errors are masked according to predefined rules; (3) In the proving phase, we tightly integrate symbolic search methods like Aesop with step provers to establish proofs for the sketch subgoals. Experimental results show that, without any additional model training or fine-tuning, DSP+ solves 80.7\%, 32.8\%, and 24 out of 644 problems from miniF2F, ProofNet, and PutnamBench, respectively, while requiring fewer budgets compared to state-of-the-arts. DSP+ proves imo\_2019\_p1, an IMO problem in miniF2F that is not solved by any prior work. Additionally, DSP+ generates proof patterns comprehensible by human experts, facilitating the identification of formalization errors; For example, eight wrongly formalized statements in miniF2F are discovered. Our results highlight the potential of classical reasoning patterns besides the RL-based training. All components will be open-sourced.

Recent advancements in Large Language Models (LLMs) have led to the development of intelligent LLM-based agents capable of interacting with graphical user interfaces (GUIs). These agents demonstrate strong reasoning and adaptability, enabling them to perform complex tasks that traditionally required predefined rules. However, the reliance on step-by-step reasoning in LLM-based agents often results in inefficiencies, particularly for routine tasks. In contrast, traditional rule-based systems excel in efficiency but lack the intelligence and flexibility to adapt to novel scenarios. To address this challenge, we propose a novel evolutionary framework for GUI agents that enhances operational efficiency while retaining intelligence and flexibility. Our approach incorporates a memory mechanism that records the agent's task execution history. By analyzing this history, the agent identifies repetitive action sequences and evolves high-level actions that act as shortcuts, replacing these low-level operations and improving efficiency. This allows the agent to focus on tasks requiring more complex reasoning, while simplifying routine actions. Experimental results on multiple benchmark tasks demonstrate that our approach significantly outperforms existing methods in both efficiency and accuracy. The code will be open-sourced to support further research.

Reasoning is a fundamental cognitive process that enables logical inference, problem-solving, and decision-making. With the rapid advancement of large language models (LLMs), reasoning has emerged as a key capability that distinguishes advanced AI systems from conventional models that empower chatbots. In this survey, we categorize existing methods along two orthogonal dimensions: (1) Regimes, which define the stage at which reasoning is achieved (either at inference time or through dedicated training); and (2) Architectures, which determine the components involved in the reasoning process, distinguishing between standalone LLMs and agentic compound systems that incorporate external tools, and multi-agent collaborations. Within each dimension, we analyze two key perspectives: (1) Input level, which focuses on techniques that construct high-quality prompts that the LLM condition on; and (2) Output level, which methods that refine multiple sampled candidates to enhance reasoning quality. This categorization provides a systematic understanding of the evolving landscape of LLM reasoning, highlighting emerging trends such as the shift from inference-scaling to learning-to-reason (e.g., DeepSeek-R1), and the transition to agentic workflows (e.g., OpenAI Deep Research, Manus Agent). Additionally, we cover a broad spectrum of learning algorithms, from supervised fine-tuning to reinforcement learning such as PPO and GRPO, and the training of reasoners and verifiers. We also examine key designs of agentic workflows, from established patterns like generator-evaluator and LLM debate to recent innovations. ...

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.

The scarcity of high-quality, logically sound data is a critical bottleneck for advancing the mathematical reasoning of Large Language Models (LLMs). Our work confronts this challenge by turning decades of automated theorem proving research into a scalable data engine. Rather than relying on error-prone LLMs or complex proof-assistant syntax like Lean and Isabelle, our framework leverages E-prover's saturation capabilities on the vast TPTP axiom library to derive a massive, guaranteed-valid corpus of theorems. Our pipeline is principled and simple: saturate axioms, filter for "interesting" theorems, and generate tasks. With no LLMs in the loop, we eliminate factual errors by construction. This purely symbolic data is then transformed into three difficulty-controlled challenges: entailment verification, premise selection, and proof reconstruction. Our zero-shot experiments on frontier models reveal a clear weakness: performance collapses on tasks requiring deep, structural reasoning. Our framework provides both the diagnostic tool to measure this gap and a scalable source of symbolic training data to address it. We make the code and data publicly available. https://github.com/sileod/reasoning_core https://hf.co/datasets/reasoning-core/rc1

Neural theorem proving combines large language models (LLMs) with proof assistants such as Lean, where the correctness of formal proofs can be rigorously verified, leaving no room for hallucination. With existing neural theorem provers pretrained on a fixed collection of data and offering valuable suggestions at times, it is challenging for them to continually prove novel theorems in a fully autonomous mode, where human insights may be critical. In this paper, we explore LLMs as copilots that assist humans in proving theorems. We introduce Lean Copilot, a general framework for running LLM inference natively in Lean. It enables programmers to build various LLM-based proof automation tools that integrate seamlessly into the workflow of Lean users. Lean users can use our pretrained models or bring their own ones that run either locally (with or without GPUs) or on the cloud. Using Lean Copilot, we build LLM-based tools that suggest proof steps, complete proof goals, and select relevant premises. Experimental results on the Mathematics in Lean textbook demonstrate the effectiveness of our method compared to existing rule-based proof automation in Lean (aesop). When assisting humans, Lean Copilot requires only 2.08 manually-entered proof steps on average (3.86 required by aesop); when automating the theorem proving process, Lean Copilot automates 74.2% proof steps on average, 85% better than aesop (40.1%). We open source all code and artifacts under a permissive MIT license to facilitate further research.

Recent advances in automated theorem proving (ATP) through LLMs have highlighted the potential of formal reasoning with Lean 4 codes. However, ATP has not yet be revolutionized by the recent posttraining scaling as demonstrated by Open AI O1/O3 and Deepseek R1. In this work, we investigate the entire posttraining of ATP, aiming to align it with breakthroughs in reasoning models in natural languages.To begin, we continual train current ATP models with a hybrid dataset, which consists of numerous statement-proof pairs, and additional data aimed at incorporating cognitive behaviors that emulate human reasoning and hypothesis refinement. Next, we explore reinforcement learning with the use of outcome reward returned by Lean 4 compiler. Through our designed continual training and reinforcement learning processes, we have successfully improved existing formal provers, including both DeepSeek-Prover-v1.5 and Goedel-Prover, achieving state-of-the-art performance in the field of whole-proof generation. For example, we achieve a 59.8% pass rate (pass@32) on MiniF2F. This is an on-going project and we will progressively update our findings, release our data and training details.

Machine-assisted theorem proving refers to the process of conducting structured reasoning to automatically generate proofs for mathematical theorems. Recently, there has been a surge of interest in using machine learning models in conjunction with proof assistants to perform this task. In this paper, we introduce Pantograph, a tool that provides a versatile interface to the Lean 4 proof assistant and enables efficient proof search via powerful search algorithms such as Monte Carlo Tree Search. In addition, Pantograph enables high-level reasoning by enabling a more robust handling of Lean 4's inference steps. We provide an overview of Pantograph's architecture and features. We also report on an illustrative use case: using machine learning models and proof sketches to prove Lean 4 theorems. Pantograph's innovative features pave the way for more advanced machine learning models to perform complex proof searches and high-level reasoning, equipping future researchers to design more versatile and powerful theorem provers.

Nowadays, formal theorem provers have made monumental progress on high-school and competition-level mathematics, but few of them generalize to more advanced mathematics. In this paper, we present REAL-Prover, a new open-source stepwise theorem prover for Lean 4 to push this boundary. This prover, based on our fine-tuned large language model (REAL-Prover-v1) and integrated with a retrieval system (Leansearch-PS), notably boosts performance on solving college-level mathematics problems. To train REAL-Prover-v1, we developed HERALD-AF, a data extraction pipeline that converts natural language math problems into formal statements, and a new open-source Lean 4 interactive environment (Jixia-interactive) to facilitate synthesis data collection. In our experiments, our prover using only supervised fine-tune achieves competitive results with a 23.7% success rate (Pass@64) on the ProofNet dataset-comparable to state-of-the-art (SOTA) models. To further evaluate our approach, we introduce FATE-M, a new benchmark focused on algebraic problems, where our prover achieves a SOTA success rate of 56.7% (Pass@64).

The chemical reaction recommendation is to select proper reaction condition parameters for chemical reactions, which is pivotal to accelerating chemical science. With the rapid development of large language models (LLMs), there is growing interest in leveraging their reasoning and planning capabilities for reaction condition recommendation. Despite their success, existing methods rarely explain the rationale behind the recommended reaction conditions, limiting their utility in high-stakes scientific workflows. In this work, we propose ChemMAS, a multi-agent system that reframes condition prediction as an evidence-based reasoning task. ChemMAS decomposes the task into mechanistic grounding, multi-channel recall, constraint-aware agentic debate, and rationale aggregation. Each decision is backed by interpretable justifications grounded in chemical knowledge and retrieved precedents. Experiments show that ChemMAS achieves 20-35% gains over domain-specific baselines and outperforms general-purpose LLMs by 10-15% in Top-1 accuracy, while offering falsifiable, human-trustable rationales, which establishes a new paradigm for explainable AI in scientific discovery.

Formal methods is pivotal for verifying the reliability of critical systems through rigorous mathematical proofs. However, its adoption is hindered by labor-intensive manual proofs and the expertise required to use theorem provers. Recent advancements in large language models (LLMs) offer new opportunities for automated theorem proving. Two promising approaches are generating tactics step by step and generating a whole proof directly with an LLM. However, existing work makes no attempt to combine the two approaches. In this work, we introduce HybridProver, a dual-model proof synthesis framework that combines tactic-based generation and whole-proof synthesis to harness the benefits of both approaches. HybridProver generates whole proof candidates for evaluation directly, then extracts proof sketches from those candidates. It then uses a tactic-based generation model that integrates automated tools to complete the sketches via stepwise refinement. We implement HybridProver for the Isabelle theorem prover and fine-tune LLMs on our optimized Isabelle datasets. Evaluation on the miniF2F dataset illustrates HybridProver's effectiveness. We achieve a 59.4% success rate on miniF2F, where the previous SOTA is 56.1%. Our ablation studies show that this SOTA result is attributable to combining whole-proof and tactic-based generation. Additionally, we show how the dataset quality, training parameters, and sampling diversity affect the final result during automated theorem proving with LLMs. All of our code, datasets, and LLMs are open source.

The rapid advancement of large language models (LLMs) has significantly enhanced the capabilities of AI-driven agents across various tasks. However, existing agentic systems, whether based on fixed pipeline algorithms or pre-defined meta-learning frameworks, cannot search the whole agent design space due to the restriction of human-designed components, and thus might miss the globally optimal agent design. In this paper, we introduce G\"odel Agent, a self-evolving framework inspired by the G\"odel machine, enabling agents to recursively improve themselves without relying on predefined routines or fixed optimization algorithms. G\"odel Agent leverages LLMs to dynamically modify its own logic and behavior, guided solely by high-level objectives through prompting. Experimental results on mathematical reasoning and complex agent tasks demonstrate that implementation of G\"odel Agent can achieve continuous self-improvement, surpassing manually crafted agents in performance, efficiency, and generalizability.

Large Language Models (LLMs) demonstrate impressive mathematical reasoning abilities, but their solutions frequently contain errors that cannot be automatically verified. Formal theorem proving systems such as Lean 4 offer automated verification with complete accuracy, motivating recent efforts to build specialized prover LLMs that generate verifiable proofs in formal languages. However, a significant gap remains: current prover LLMs solve substantially fewer problems than general-purpose LLMs operating in natural language. We introduce Hilbert, an agentic framework that bridges this gap by combining the complementary strengths of informal reasoning and formal verification. Our system orchestrates four components: an informal LLM that excels at mathematical reasoning, a specialized prover LLM optimized for Lean 4 tactics, a formal verifier, and a semantic theorem retriever. Given a problem that the prover is unable to solve, Hilbert employs recursive decomposition to split the problem into subgoals that it solves with the prover or reasoner LLM. It leverages verifier feedback to refine incorrect proofs as necessary. Experimental results demonstrate that Hilbert substantially outperforms existing approaches on key benchmarks, achieving 99.2% on miniF2F, 6.6% points above the best publicly available method. Hilbert achieves the best known result on PutnamBench. It solves 462/660 problems (70.0%), outperforming proprietary approaches like SeedProver (50.4%) and achieving a 422% improvement over the best publicly available baseline. Thus, Hilbert effectively narrows the gap between informal reasoning and formal proof generation.

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.

Software development is a complex, multi-phase process traditionally requiring collaboration among individuals with diverse expertise. We propose AgentMesh, a Python-based framework that uses multiple cooperating LLM-powered agents to automate software development tasks. In AgentMesh, specialized agents - a Planner, Coder, Debugger, and Reviewer - work in concert to transform a high-level requirement into fully realized code. The Planner agent first decomposes user requests into concrete subtasks; the Coder agent implements each subtask in code; the Debugger agent tests and fixes the code; and the Reviewer agent validates the final output for correctness and quality. We describe the architecture and design of these agents and their communication, and provide implementation details including prompt strategies and workflow orchestration. A case study illustrates AgentMesh handling a non-trivial development request via sequential task planning, code generation, iterative debugging, and final code review. We discuss how dividing responsibilities among cooperative agents leverages the strengths of large language models while mitigating single-agent limitations. Finally, we examine current limitations - such as error propagation and context scaling - and outline future work toward more robust, scalable multi-agent AI systems for software engineering automation.

Theorem proving in natural mathematical language - the mixture of symbolic and natural language used by humans - plays a central role in mathematical advances and education, and tests aspects of reasoning that are core to intelligence. Yet it has remained underexplored with modern generative models. We study large-scale language models on two new generation tasks: suggesting the next step in a mathematical proof, and full proof generation. We develop NaturalProver, a language model that generates proofs by conditioning on background references (e.g. theorems and definitions that are either retrieved or human-provided), and optionally enforces their presence with constrained decoding. On theorems from the NaturalProofs benchmark, NaturalProver improves the quality of next-step suggestions and generated proofs over fine-tuned GPT-3, according to human evaluations from university-level mathematics students. NaturalProver is capable of proving some theorems that require short (2-6 step) proofs, and providing next-step suggestions that are rated as correct and useful over 40% of the time, which is to our knowledge the first demonstration of these capabilities using neural language models.

Traditional language model-based theorem proving assumes that by training on a sufficient amount of formal proof data, a model will learn to prove theorems. Our key observation is that a wealth of informal information that is not present in formal proofs can be useful for learning to prove theorems. For instance, humans think through steps of a proof, but this thought process is not visible in the resulting code. We present Lean-STaR, a framework for training language models to produce informal thoughts prior to each step of a proof, thereby boosting the model's theorem-proving capabilities. Lean-STaR uses retrospective ground-truth tactics to generate synthetic thoughts for training the language model. At inference time, the trained model directly generates the thoughts prior to the prediction of the tactics in each proof step. Building on the self-taught reasoner framework, we then apply expert iteration to further fine-tune the model on the correct proofs it samples and verifies using the Lean solver. Lean-STaR achieves state-of-the-art results on the miniF2F-test benchmark within the Lean theorem proving environment, significantly outperforming base models (43.4% rightarrow 46.3%, Pass@64). We also analyze the impact of the augmented thoughts on various aspects of the theorem proving process, providing insights into their effectiveness.

Large language models (LLMs) face challenges in solving complex mathematical problems that require comprehensive capacities to parse the statements, associate domain knowledge, perform compound logical reasoning, and integrate the intermediate rationales. Tackling all these problems once could be arduous for LLMs, thus leading to confusion in generation. In this work, we explore the potential of enhancing LLMs with agents by meticulous decomposition and modeling of mathematical reasoning process. Specifically, we propose a formal description of the mathematical solving and extend LLMs with an agent-based zero-shot framework named Planner-Reasoner-Executor-Reflector (PRER). We further provide and implement two MathAgents that define the logical forms and inherent relations via a pool of actions in different grains and orientations: MathAgent-M adapts its actions to LLMs, while MathAgent-H aligns with humankind. Experiments on miniF2F and MATH have demonstrated the effectiveness of PRER and proposed MathAgents, achieving an increase of 12.3%(53.9%66.2%) on the MiniF2F, 9.2% (49.8%59.0%) on MATH, and 13.2%(23.2%35.4%) for level-5 problems of MATH against GPT-4. Further analytical results provide more insightful perspectives on exploiting the behaviors of LLMs as agents.

The remarkable growth in large language model (LLM) capabilities has spurred exploration into multi-agent systems, with debate frameworks emerging as a promising avenue for enhanced problem-solving. These multi-agent debate (MAD) approaches, where agents collaboratively present, critique, and refine arguments, potentially offer improved reasoning, robustness, and diverse perspectives over monolithic models. Despite prior studies leveraging MAD, a systematic understanding of its effectiveness compared to self-agent methods, particularly under varying conditions, remains elusive. This paper seeks to fill this gap by conceptualizing MAD as a test-time computational scaling technique, distinguished by collaborative refinement and diverse exploration capabilities. We conduct a comprehensive empirical investigation comparing MAD with strong self-agent test-time scaling baselines on mathematical reasoning and safety-related tasks. Our study systematically examines the influence of task difficulty, model scale, and agent diversity on MAD's performance. Key findings reveal that, for mathematical reasoning, MAD offers limited advantages over self-agent scaling but becomes more effective with increased problem difficulty and decreased model capability, while agent diversity shows little benefit. Conversely, for safety tasks, MAD's collaborative refinement can increase vulnerability, but incorporating diverse agent configurations facilitates a gradual reduction in attack success through the collaborative refinement process. We believe our findings provide critical guidance for the future development of more effective and strategically deployed MAD systems.

Recent research has shown that LLM performance on reasoning tasks can be enhanced by scaling test-time compute. One promising approach, particularly with decomposable problems, involves arranging intermediate solutions as a graph on which transformations are performed to explore the solution space. However, prior works rely on pre-determined, task-specific transformation schedules which are subject to a set of searched hyperparameters. In this work, we view thought graph transformations as actions in a Markov decision process, and implement policy agents to drive effective action policies for the underlying reasoning LLM agent. In particular, we investigate the ability for another LLM to act as a policy agent on thought graph environments and introduce ARIES, a multi-agent architecture for reasoning with LLMs. In ARIES, reasoning LLM agents solve decomposed subproblems, while policy LLM agents maintain visibility of the thought graph states, and dynamically adapt the problem-solving strategy. Through extensive experiments, we observe that using off-the-shelf LLMs as policy agents with no supervised fine-tuning (SFT) can yield up to 29% higher accuracy on HumanEval relative to static transformation schedules, as well as reducing inference costs by 35% and avoid any search requirements. We also conduct a thorough analysis of observed failure modes, highlighting that limitations on LLM sizes and the depth of problem decomposition can be seen as challenges to scaling LLM-guided reasoning.

Large Reasoning Models (LRMs) have demonstrated remarkable problem-solving abilities in mathematics, as evaluated by existing benchmarks exclusively on well-defined problems. However, such evaluation setup constitutes a critical gap, since a genuine intelligent agent should not only solve problems (as a math quiz solver), but also be able~to ask for information when the problems lack sufficient information, enabling proactivity in responding users' requests. To bridge such gap, we proposes a new dataset consisting of two types of incomplete problems with diverse contexts. Based on the dataset, our systematical evaluation of LRMs reveals their inability in proactively asking for information. In addition, we uncover the behaviors related to overthinking and hallucination of LRMs, and highlight the potential and challenges of supervised fine-tuning in learning such ability. We hope to provide new insights in developing LRMs with genuine intelligence, rather than just solving problems.

Large language models (LLMs) have shown promising first-order logic (FOL) reasoning capabilities with applications in various areas. However, their effectiveness in complex mathematical reasoning involving multi-step FOL deductions is still under-researched. While LLMs perform competitively on established mathematical reasoning benchmarks, they struggle with multi-step FOL tasks, as demonstrated by Deepseek-Prover-V2-7B's low accuracy (4.2%) on our proposed theorem proving dataset. This issue arises from the limited exploration of diverse proof strategies and the potential for early reasoning mistakes to undermine entire proofs. To address these issues, we propose DREAM, a self-adaptive solution that enhances the Diversity and REAsonability of LLMs' generation strategies. DREAM incorporates an Axiom-Driven Strategy Diversification mechanism to promote varied strategic outcomes and a Sub-Proposition Error Feedback to help LLMs reflect on and correct their proofs. Our contributions include pioneering advancements in LLMs' mathematical reasoning through FOL theorem proving, introducing a novel inference stage solution that improves performance by 0.6% to 6.4%, and providing a curated dataset of 447 mathematical theorems in Lean 4 format for evaluation.

Large-language models (LLMs) have demonstrated powerful problem-solving capabilities, in particular when organized in multi-agent systems. However, the advent of such systems also raises several questions on the ability of a complex network of agents to effectively self-organize and collaborate. While measuring performance on standard reasoning benchmarks indicates how well multi-agent systems can solve reasoning tasks, it is unclear whether these systems are able to leverage their topology effectively. Here, we propose AgentsNet, a new benchmark for multi-agent reasoning. By drawing inspiration from classical problems in distributed systems and graph theory, AgentsNet measures the ability of multi-agent systems to collaboratively form strategies for problem-solving, self-organization, and effective communication given a network topology. We evaluate a variety of baseline methods on AgentsNet including homogeneous networks of agents which first have to agree on basic protocols for organization and communication. We find that some frontier LLMs are already demonstrating strong performance for small networks but begin to fall off once the size of the network scales. While existing multi-agent benchmarks cover at most 2-5 agents, AgentsNet is practically unlimited in size and can scale with new generations of LLMs. As such, we also probe frontier models in a setup with up to 100 agents.

Current long chain-of-thought (long-CoT) models excel at mathematical reasoning but rely on slow and error-prone natural language traces. Tool-augmented agents address arithmetic via code execution, but often falter on complex logical tasks. We introduce a fine-tuning framework, DualDistill, that distills complementary reasoning strategies from multiple teachers into a unified student model. Using this approach, we train Agentic-R1, which dynamically selects the optimal strategy for each query, invoking tools for arithmetic and algorithmic problems, and using text-based reasoning for abstract ones. Our method improves accuracy across a range of tasks, including both computation-intensive and standard benchmarks, demonstrating the effectiveness of multi-strategy distillation in achieving robust and efficient reasoning. Our project is available at https://github.com/StigLidu/DualDistill

High-dimensional decision-making tasks, such as business partner selection, involve evaluating large candidate pools with heterogeneous numerical, categorical, and textual features. While large language models (LLMs) offer strong in-context reasoning capabilities, single-agent or debate-style systems often struggle with scalability and consistency in such settings. We propose PartnerMAS, a hierarchical multi-agent framework that decomposes evaluation into three layers: a Planner Agent that designs strategies, Specialized Agents that perform role-specific assessments, and a Supervisor Agent that integrates their outputs. To support systematic evaluation, we also introduce a curated benchmark dataset of venture capital co-investments, featuring diverse firm attributes and ground-truth syndicates. Across 140 cases, PartnerMAS consistently outperforms single-agent and debate-based multi-agent baselines, achieving up to 10--15\% higher match rates. Analysis of agent reasoning shows that planners are most responsive to domain-informed prompts, specialists produce complementary feature coverage, and supervisors play an important role in aggregation. Our findings demonstrate that structured collaboration among LLM agents can generate more robust outcomes than scaling individual models, highlighting PartnerMAS as a promising framework for high-dimensional decision-making in data-rich domains.

Recent advances in LLMs have enabled their use as autonomous agents across a range of tasks, yet they continue to struggle with formulating and adhering to coherent long-term strategies. In this paper, we investigate whether LLM agents can self-improve when placed in environments that explicitly challenge their strategic planning abilities. Using the board game Settlers of Catan, accessed through the open-source Catanatron framework, we benchmark a progression of LLM-based agents, from a simple game-playing agent to systems capable of autonomously rewriting their own prompts and their player agent's code. We introduce a multi-agent architecture in which specialized roles (Analyzer, Researcher, Coder, and Player) collaborate to iteratively analyze gameplay, research new strategies, and modify the agent's logic or prompt. By comparing manually crafted agents to those evolved entirely by LLMs, we evaluate how effectively these systems can diagnose failure and adapt over time. Our results show that self-evolving agents, particularly when powered by models like Claude 3.7 and GPT-4o, outperform static baselines by autonomously adopting their strategies, passing along sample behavior to game-playing agents, and demonstrating adaptive reasoning over multiple iterations.

Researchers are investing substantial effort in developing powerful general-purpose agents, wherein Foundation Models are used as modules within agentic systems (e.g. Chain-of-Thought, Self-Reflection, Toolformer). However, the history of machine learning teaches us that hand-designed solutions are eventually replaced by learned solutions. We formulate a new research area, Automated Design of Agentic Systems (ADAS), which aims to automatically create powerful agentic system designs, including inventing novel building blocks and/or combining them in new ways. We further demonstrate that there is an unexplored yet promising approach within ADAS where agents can be defined in code and new agents can be automatically discovered by a meta agent programming ever better ones in code. Given that programming languages are Turing Complete, this approach theoretically enables the learning of any possible agentic system: including novel prompts, tool use, control flows, and combinations thereof. We present a simple yet effective algorithm named Meta Agent Search to demonstrate this idea, where a meta agent iteratively programs interesting new agents based on an ever-growing archive of previous discoveries. Through extensive experiments across multiple domains including coding, science, and math, we show that our algorithm can progressively invent agents with novel designs that greatly outperform state-of-the-art hand-designed agents. Importantly, we consistently observe the surprising result that agents invented by Meta Agent Search maintain superior performance even when transferred across domains and models, demonstrating their robustness and generality. Provided we develop it safely, our work illustrates the potential of an exciting new research direction toward automatically designing ever-more powerful agentic systems to benefit humanity.

This paper proposes a query-level meta-agent named FlowReasoner to automate the design of query-level multi-agent systems, i.e., one system per user query. Our core idea is to incentivize a reasoning-based meta-agent via external execution feedback. Concretely, by distilling DeepSeek R1, we first endow the basic reasoning ability regarding the generation of multi-agent systems to FlowReasoner. Then, we further enhance it via reinforcement learning (RL) with external execution feedback. A multi-purpose reward is designed to guide the RL training from aspects of performance, complexity, and efficiency. In this manner, FlowReasoner is enabled to generate a personalized multi-agent system for each user query via deliberative reasoning. Experiments on both engineering and competition code benchmarks demonstrate the superiority of FlowReasoner. Remarkably, it surpasses o1-mini by 10.52% accuracy across three benchmarks. The code is available at https://github.com/sail-sg/FlowReasoner.

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

Human mathematicians are often good at recognizing modular and reusable theorems that make complex mathematical results within reach. In this paper, we propose a novel method called theoREm-from-prooF extrACTOR (REFACTOR) for training neural networks to mimic this ability in formal mathematical theorem proving. We show on a set of unseen proofs, REFACTOR is able to extract 19.6% of the theorems that humans would use to write the proofs. When applying the model to the existing Metamath library, REFACTOR extracted 16 new theorems. With newly extracted theorems, we show that the existing proofs in the MetaMath database can be refactored. The new theorems are used very frequently after refactoring, with an average usage of 733.5 times, and help shorten the proof lengths. Lastly, we demonstrate that the prover trained on the new-theorem refactored dataset proves more test theorems and outperforms state-of-the-art baselines by frequently leveraging a diverse set of newly extracted theorems. Code can be found at https://github.com/jinpz/refactor.

Open data repositories hold potential for evidence-based decision-making, yet are inaccessible to non-experts lacking expertise in dataset discovery, schema mapping, and statistical analysis. Large language models show promise for individual tasks, but end-to-end analytical workflows expose fundamental limitations: attention dilutes across growing contexts, specialized reasoning patterns interfere, and errors propagate undetected. We present PublicAgent, a multi-agent framework that addresses these limitations through decomposition into specialized agents for intent clarification, dataset discovery, analysis, and reporting. This architecture maintains focused attention within agent contexts and enables validation at each stage. Evaluation across five models and 50 queries derives five design principles for multi-agent LLM systems. First, specialization provides value independent of model strength--even the strongest model shows 97.5% agent win rates, with benefits orthogonal to model scale. Second, agents divide into universal (discovery, analysis) and conditional (report, intent) categories. Universal agents show consistent effectiveness (std dev 12.4%) while conditional agents vary by model (std dev 20.5%). Third, agents mitigate distinct failure modes--removing discovery or analysis causes catastrophic failures (243-280 instances), while removing report or intent causes quality degradation. Fourth, architectural benefits persist across task complexity with stable win rates (86-92% analysis, 84-94% discovery), indicating workflow management value rather than reasoning enhancement. Fifth, wide variance in agent effectiveness across models (42-96% for analysis) requires model-aware architecture design. These principles guide when and why specialization is necessary for complex analytical workflows while enabling broader access to public data through natural language interfaces.

Multi-agent systems (MAS) built on large language models (LLMs) offer a promising path toward solving complex, real-world tasks that single-agent systems often struggle to manage. While recent advancements in test-time scaling (TTS) have significantly improved single-agent performance on challenging reasoning tasks, how to effectively scale collaboration and reasoning in MAS remains an open question. In this work, we introduce an adaptive multi-agent framework designed to enhance collaborative reasoning through both model-level training and system-level coordination. We construct M500, a high-quality dataset containing 500 multi-agent collaborative reasoning traces, and fine-tune Qwen2.5-32B-Instruct on this dataset to produce M1-32B, a model optimized for multi-agent collaboration. To further enable adaptive reasoning, we propose a novel CEO agent that dynamically manages the discussion process, guiding agent collaboration and adjusting reasoning depth for more effective problem-solving. Evaluated in an open-source MAS across a range of tasks-including general understanding, mathematical reasoning, and coding-our system significantly outperforms strong baselines. For instance, M1-32B achieves 12% improvement on GPQA-Diamond, 41% on AIME2024, and 10% on MBPP-Sanitized, matching the performance of state-of-the-art models like DeepSeek-R1 on some tasks. These results highlight the importance of both learned collaboration and adaptive coordination in scaling multi-agent reasoning. Code is available at https://github.com/jincan333/MAS-TTS

Recent advancements in Multi-Agent Systems (MAS) powered by Large Language Models (LLMs) have demonstrated tremendous potential in diverse task scenarios. Nonetheless, existing agentic systems typically rely on predefined agent-role design spaces and static communication structures, limiting their adaptability as well as flexibility in complex interaction environments and leading to subpar performance on highly specialized and expert-level tasks. To address these issues, we introduce HALO, a multi-agent collaboration framework based on a hierarchical reasoning architecture. Specifically, we incorporate a high-level planning agent for task decomposition, mid-level role-design agents for subtask-specific agent instantiation, and low-level inference agents for subtask execution. Particularly, subtask execution is reformulated as a structured workflow search problem, where Monte Carlo Tree Search (MCTS) systematically explores the agentic action space to construct optimal reasoning trajectories. Additionally, as the majority of users lack expertise in prompt engineering, we leverage an Adaptive Prompt Refinement module to transform raw queries into task-specific prompts. Empirical evaluations on Code Generation (HumanEval), General Reasoning (MMLU), and Arithmetic Reasoning (MATH) benchmark datasets highlight the effectiveness of HALO, yielding a 14.4% average improvement over state-of-the-art baselines. Notably, HALO achieves up to 13.3% performance gain on the Moral Scenarios subject in the MMLU benchmark and up to 19.6% performance gain on the Algebra subarea in the MATH benchmark, indicating its advanced proficiency in tackling highly specialized and expert-level tasks. The code repository is available at https://github.com/23japhone/HALO.

Progress in scientific discovery is rarely the result of a single "Eureka" moment, but is rather the product of hundreds of scientists incrementally working together toward a common goal. While existing agent workflows are capable of producing research autonomously, they do so in isolation, without the ability to continuously improve upon prior research results. To address these challenges, we introduce AgentRxiv-a framework that lets LLM agent laboratories upload and retrieve reports from a shared preprint server in order to collaborate, share insights, and iteratively build on each other's research. We task agent laboratories to develop new reasoning and prompting techniques and find that agents with access to their prior research achieve higher performance improvements compared to agents operating in isolation (11.4% relative improvement over baseline on MATH-500). We find that the best performing strategy generalizes to benchmarks in other domains (improving on average by 3.3%). Multiple agent laboratories sharing research through AgentRxiv are able to work together towards a common goal, progressing more rapidly than isolated laboratories, achieving higher overall accuracy (13.7% relative improvement over baseline on MATH-500). These findings suggest that autonomous agents may play a role in designing future AI systems alongside humans. We hope that AgentRxiv allows agents to collaborate toward research goals and enables researchers to accelerate discovery.

The booming success of LLMs initiates rapid development in LLM agents. Though the foundation of an LLM agent is the generative model, it is critical to devise the optimal reasoning strategies and agent architectures. Accordingly, LLM agent research advances from the simple chain-of-thought prompting to more complex ReAct and Reflection reasoning strategy; agent architecture also evolves from single agent generation to multi-agent conversation, as well as multi-LLM multi-agent group chat. However, with the existing intricate frameworks and libraries, creating and evaluating new reasoning strategies and agent architectures has become a complex challenge, which hinders research investigation into LLM agents. Thus, we open-source a new AI agent library, AgentLite, which simplifies this process by offering a lightweight, user-friendly platform for innovating LLM agent reasoning, architectures, and applications with ease. AgentLite is a task-oriented framework designed to enhance the ability of agents to break down tasks and facilitate the development of multi-agent systems. Furthermore, we introduce multiple practical applications developed with AgentLite to demonstrate its convenience and flexibility. Get started now at: https://github.com/SalesforceAIResearch/AgentLite.

Search agents are language models (LMs) that reason and search knowledge bases (or the web) to answer questions; recent methods supervise only the final answer accuracy using reinforcement learning with verifiable rewards (RLVR). Most RLVR search agents tackle general-domain QA, which limits their relevance to technical AI systems in science, engineering, and medicine. In this work we propose training agents to search and reason over scientific papers -- this tests technical question-answering, it is directly relevant to real scientists, and the capabilities will be crucial to future AI Scientist systems. Concretely, we release a search corpus of 16 million biomedical paper abstracts and construct a challenging factoid QA dataset called PaperSearchQA with 60k samples answerable from the corpus, along with benchmarks. We train search agents in this environment to outperform non-RL retrieval baselines; we also perform further quantitative analysis and observe interesting agent behaviors like planning, reasoning, and self-verification. Our corpus, datasets, and benchmarks are usable with the popular Search-R1 codebase for RLVR training and released on https://huggingface.co/collections/jmhb/papersearchqa. Finally, our data creation methods are scalable and easily extendable to other scientific domains.

Recent advancements in large language models (LLMs) have sparked considerable interest in automated theorem proving and a prominent line of research integrates stepwise LLM-based provers into tree search. In this paper, we introduce a novel proof-state exploration approach for training data synthesis, designed to produce diverse tactics across a wide range of intermediate proof states, thereby facilitating effective one-shot fine-tuning of LLM as the policy model. We also propose an adaptive beam size strategy, which effectively takes advantage of our data synthesis method and achieves a trade-off between exploration and exploitation during tree search. Evaluations on the MiniF2F and ProofNet benchmarks demonstrate that our method outperforms strong baselines under the stringent Pass@1 metric, attaining an average pass rate of 60.74% on MiniF2F and 21.18% on ProofNet. These results underscore the impact of large-scale synthetic data in advancing automated theorem proving.

Software testing plays a critical role in ensuring that systems behave as intended. However, existing automated testing approaches struggle to match the capabilities of human engineers due to key limitations such as test locality, lack of general reliability, and business logic blindness. In this work, we propose a novel framework that leverages functional programming and type systems to translate Scala backend code into formal Lean representations. Our pipeline automatically generates theorems that specify the intended behavior of APIs and database operations, and uses LLM-based provers to verify them. When a theorem is proved, the corresponding logic is guaranteed to be correct and no further testing is needed. If the negation of a theorem is proved instead, it confirms a bug. In cases where neither can be proved, human intervention is required. We evaluate our method on realistic backend systems and find that it can formally verify over 50% of the test requirements, which suggests that half of a testing engineer's workload can be automated. Additionally, with an average cost of only $2.19 per API, LLM-based verification is significantly more cost-effective than manual testing and can be scaled easily through parallel execution. Our results indicate a promising direction for scalable, AI-powered software testing, with the potential to greatly improve engineering productivity as models continue to advance.

Language agents perform complex tasks by using tools to execute each step precisely. However, most existing agents are based on proprietary models or designed to target specific tasks, such as mathematics or multi-hop question answering. We introduce Husky, a holistic, open-source language agent that learns to reason over a unified action space to address a diverse set of complex tasks involving numerical, tabular, and knowledge-based reasoning. Husky iterates between two stages: 1) generating the next action to take towards solving a given task and 2) executing the action using expert models and updating the current solution state. We identify a thorough ontology of actions for addressing complex tasks and curate high-quality data to train expert models for executing these actions. Our experiments show that Husky outperforms prior language agents across 14 evaluation datasets. Moreover, we introduce HuskyQA, a new evaluation set which stress tests language agents for mixed-tool reasoning, with a focus on retrieving missing knowledge and performing numerical reasoning. Despite using 7B models, Husky matches or even exceeds frontier LMs such as GPT-4 on these tasks, showcasing the efficacy of our holistic approach in addressing complex reasoning problems. Our code and models are available at https://github.com/agent-husky/Husky-v1.

Automated theorem proving (ATP) has become an appealing domain for exploring the reasoning ability of the recent successful generative language models. However, current ATP benchmarks mainly focus on symbolic inference, but rarely involve the understanding of complex number combination reasoning. In this work, we propose TRIGO, an ATP benchmark that not only requires a model to reduce a trigonometric expression with step-by-step proofs but also evaluates a generative LM's reasoning ability on formulas and its capability to manipulate, group, and factor number terms. We gather trigonometric expressions and their reduced forms from the web, annotate the simplification process manually, and translate it into the Lean formal language system. We then automatically generate additional examples from the annotated samples to expand the dataset. Furthermore, we develop an automatic generator based on Lean-Gym to create dataset splits of varying difficulties and distributions in order to thoroughly analyze the model's generalization ability. Our extensive experiments show our proposed TRIGO poses a new challenge for advanced generative LM's including GPT-4 which is pre-trained on a considerable amount of open-source formal theorem-proving language data, and provide a new tool to study the generative LM's ability on both formal and mathematical reasoning.

Language models have become increasingly powerful tools for formal mathematical reasoning. However, most existing approaches rely exclusively on either large general-purpose models or smaller specialized models, each with distinct limitations, while training specialized large models still requires significant computational resources. This paper introduces ProofCompass, a novel hybrid methodology that achieves remarkable computational efficiency by strategically guiding existing specialized prover methods, such as DeepSeek-Prover-v1.5-RL (DSP-v1.5) with a Large Language Model (LLM) without requiring additional model training. The LLM provides natural language proof strategies and analyzes failed attempts to select intermediate lemmas, enabling effective problem decomposition. On the miniF2F benchmark, ProofCompass demonstrates substantial resource efficiency: it outperforms DSP-v1.5 (54.9% rightarrow 55.3%) while using 25x fewer attempts (3200 rightarrow 128). Our synergistic approach paves the way for simultaneously improving computational efficiency and accuracy in formal theorem proving.

AI agents -- systems that combine foundation models with reasoning, planning, memory, and tool use -- are rapidly becoming a practical interface between natural-language intent and real-world computation. This survey synthesizes the emerging landscape of AI agent architectures across: (i) deliberation and reasoning (e.g., chain-of-thought-style decomposition, self-reflection and verification, and constraint-aware decision making), (ii) planning and control (from reactive policies to hierarchical and multi-step planners), and (iii) tool calling and environment interaction (retrieval, code execution, APIs, and multimodal perception). We organize prior work into a unified taxonomy spanning agent components (policy/LLM core, memory, world models, planners, tool routers, and critics), orchestration patterns (single-agent vs.\ multi-agent; centralized vs.\ decentralized coordination), and deployment settings (offline analysis vs.\ online interactive assistance; safety-critical vs.\ open-ended tasks). We discuss key design trade-offs -- latency vs.\ accuracy, autonomy vs.\ controllability, and capability vs.\ reliability -- and highlight how evaluation is complicated by non-determinism, long-horizon credit assignment, tool and environment variability, and hidden costs such as retries and context growth. Finally, we summarize measurement and benchmarking practices (task suites, human preference and utility metrics, success under constraints, robustness and security) and identify open challenges including verification and guardrails for tool actions, scalable memory and context management, interpretability of agent decisions, and reproducible evaluation under realistic workloads.

Large Language Models (LLMs) have shown impressive capabilities in multi-step reasoning and problem-solving.Recent works introduce multi-agent reflection frameworks where multiple LLM agents critique and refine each other's outputs using reinforcement learning (RL). However, these approaches often rely on single-shot responses and lack structural diversity in reasoning exploration. In this paper, we propose DRAFT-RL, a novel framework that integrates Chain-of-Draft (CoD) reasoning into multi-agent RL training. Instead of generating single responses, each agent produces multiple drafts per query, which are then evaluated by peer agents and a learned reward model to identify the most promising trajectory. These selected drafts are used to refine future reasoning strategies through actor-critic learning.DRAFT-RL enables explicit multi-path exploration, peer-guided reflection, and reward-aligned selection, resulting in more robust and interpretable LLM agent behavior. We evaluate our method on complex reasoning tasks including code synthesis, symbolic math, and knowledge-intensive QA,demonstrating that DRAFT-RL outperforms existing reflective and RL-based agents by significant margins in both accuracy and convergence speed

Multi-agent AI systems powered by large language models (LLMs) are increasingly applied to solve complex tasks. However, these systems often rely on fragile, manually designed prompts and heuristics, making optimization difficult. A key challenge in optimizing multi-agent systems is acquiring suitable training data for specialized agents. We introduce SiriuS, a self-improving, reasoning-driven optimization framework for multi-agent systems. Central to our approach is the construction of an experience library: a repository of high-quality reasoning trajectories. The library is built by retaining reasoning steps that lead to successful outcomes, providing a robust training set for optimizing multi-agent system. Additionally, we introduce a library augmentation procedure that refines unsuccessful trajectories, further enriching the library. SiriuS boosts performance by 2.86\% to 21.88\% on reasoning and biomedical QA and enhances agent negotiation in competitive settings. Our results show that SiriuS enhances multi-agent performance while generating reusable data for self-correction and self-play enhancement in the future.

There are two main barriers to using large language models (LLMs) in clinical reasoning. Firstly, while LLMs exhibit significant promise in Natural Language Processing (NLP) tasks, their performance in complex reasoning and planning falls short of expectations. Secondly, LLMs use uninterpretable methods to make clinical decisions that are fundamentally different from the clinician's cognitive processes. This leads to user distrust. In this paper, we present a multi-agent framework called ArgMed-Agents, which aims to enable LLM-based agents to make explainable clinical decision reasoning through interaction. ArgMed-Agents performs self-argumentation iterations via Argumentation Scheme for Clinical Discussion (a reasoning mechanism for modeling cognitive processes in clinical reasoning), and then constructs the argumentation process as a directed graph representing conflicting relationships. Ultimately, use symbolic solver to identify a series of rational and coherent arguments to support decision. We construct a formal model of ArgMed-Agents and present conjectures for theoretical guarantees. ArgMed-Agents enables LLMs to mimic the process of clinical argumentative reasoning by generating explanations of reasoning in a self-directed manner. The setup experiments show that ArgMed-Agents not only improves accuracy in complex clinical decision reasoning problems compared to other prompt methods, but more importantly, it provides users with decision explanations that increase their confidence.

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

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

AI web agents use Internet resources at far greater speed, scale, and complexity -- changing how users and services interact. Deployed maliciously or erroneously, these agents could overload content providers. At the same time, web agents can bypass CAPTCHAs and other defenses by mimicking user behavior or flood authentication systems with fake accounts. Yet providers must protect their services and content from denial-of-service attacks and scraping by web agents. In this paper, we design a framework that imposes tunable costs on agents before providing access to resources; we call this Web Agent Throttling. We start by formalizing Throttling Gates as challenges issued to an agent that are asymmetric, scalable, robust, and compatible with any agent. Focusing on a common component -- the language model -- we require the agent to solve reasoning puzzles, thereby incurring excessive token-generation costs. However, we find that using existing puzzles, e.g., coding or math, as throttling gates fails to satisfy our properties. To address this, we introduce rebus-based Reasoning Gates, synthetic text puzzles that require multi-hop reasoning over world knowledge (thereby throttling an agent's model). We design a scalable generation and verification protocol for such reasoning gates. Our framework achieves computational asymmetry, i.e., the response-generation cost is 9.2x higher than the generation cost for SOTA models. We further deploy reasoning gates on a custom website and Model Context Protocol (MCP) servers and evaluate with real-world web agents. Finally, we discuss the limitations and environmental impact of real-world deployment of our framework.

Recent advances in large language models (LLMs) and multi-agent systems have demonstrated remarkable capabilities in complex problem-solving tasks such as deep research, vibe coding, and mathematical reasoning. However, most existing multi-agent systems are built upon manual prompt/workflow engineering with sophisticated agent frameworks, making them computationally inefficient, less capable, and can not benefit from data-centric learning. In this work, we introduce Chain-of-Agents (CoA), a novel paradigm of LLM reasoning that enables native end-to-end complex problem-solving in the same way as a multi-agent system (i.e., multi-turn problem solving with multiple tools and multiple agents) within one model. In chain-of-agents problem-solving, the model dynamically activates different tool agents and role-playing agents to simulate multi-agent collaboration in an end-to-end fashion. To elicit end-to-end chain-of-agents problem-solving abilities in LLMs, we introduce a multi-agent distillation framework to distill state-of-the-art multi-agent systems into chain-of-agents trajectories for agentic supervised fine-tuning. We then use agentic reinforcement learning on verifiable agentic tasks to further improve the models' capabilities on chain-of-agents problem solving. We call the resulting models Agent Foundation Models (AFMs). Our empirical studies demonstrate that AFM establishes new state-of-the-art performance across diverse benchmarks in both web agent and code agent settings. We make the entire research, including the model weights, code for training and evaluation, and the training data, fully open-sourced, which offers a solid starting point for future research on agent models and agentic RL.

Existing Tool-Integrated Reasoning (TIR) models have effectively extended the question-answering capabilities of LLMs by incorporating external tools. However, real-world scenarios present numerous open-ended problems where fixed tools often fail to meet task requirements. Furthermore, the lack of self-optimization mechanisms means that erroneous tool outputs can mislead the LLM's responses. Additionally, the construction of existing tools entails significant manual effort, which consequently constrains their applicability. Recognizing that the reasoning traces of LLMs encapsulate implicit problem-solving capabilities, we propose UCT, a novel training-free framework that transforms agents from tool users to tool creators. This approach harvests reasoning experiences and distills them into reusable assets. This method transforms the agent from a mere tool user into a tool creator, enabling adaptive tool creation and self-updating during the inference process. We also introduce a memory consolidation mechanism to maintain the tool library, ensuring high reusability of retained experiential memory for subsequent reasoning tasks. This novel automated tool construction paradigm continuously improves tool quality during reasoning, allowing the overall agent system to progress without additional training. Extensive experiments demonstrate that our method serves as a novel paradigm for enhancing the capabilities of TIR models. In particular, the significant performance gains achieved +20.86%uparrow and +23.04%uparrow on benchmarks across multi-domain mathematical and scientific reasoning tasks validate the self-evolving capability of the agent.

Formal proofs are challenging to write even for experienced experts. Recent progress in Neural Theorem Proving (NTP) shows promise in expediting this process. However, the formal corpora available on the Internet are limited compared to the general text, posing a significant data scarcity challenge for NTP. To address this issue, this work proposes Alchemy, a general framework for data synthesis that constructs formal theorems through symbolic mutation. Specifically, for each candidate theorem in Mathlib, we identify all invocable theorems that can be used to rewrite or apply to it. Subsequently, we mutate the candidate theorem by replacing the corresponding term in the statement with its equivalent form or antecedent. As a result, our method increases the number of theorems in Mathlib by an order of magnitude, from 110k to 6M. Furthermore, we perform continual pretraining and supervised finetuning on this augmented corpus for large language models. Experimental results demonstrate the effectiveness of our approach, achieving a 5% absolute performance improvement on Leandojo benchmark. Additionally, our synthetic data achieve a 2.5% absolute performance gain on the out-of-distribution miniF2F benchmark. To provide further insights, we conduct a comprehensive analysis of synthetic data composition and the training paradigm, offering valuable guidance for developing a strong theorem prover.

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,

Large language model (LLM) agents have shown remarkable reasoning abilities. However, existing multi-agent frameworks often rely on fixed roles or centralized control, limiting scalability and adaptability in long-horizon reasoning. We introduce SwarmSys, a closed-loop framework for distributed multi-agent reasoning inspired by swarm intelligence. Coordination in SwarmSys emerges through iterative interactions among three specialized roles, Explorers, Workers, and Validators, that continuously cycle through exploration, exploitation, and validation. To enable scalable and adaptive collaboration, we integrate adaptive agent and event profiles, embedding-based probabilistic matching, and a pheromone-inspired reinforcement mechanism, supporting dynamic task allocation and self-organizing convergence without global supervision. Across symbolic reasoning, research synthesis, and scientific programming tasks, SwarmSys consistently outperforms baselines, improving both accuracy and reasoning stability. These findings highlight swarm-inspired coordination as a promising paradigm for scalable, robust, and adaptive multi-agent reasoning, suggesting that coordination scaling may rival model scaling in advancing LLM intelligence.

Large language models have made significant progress in mathematical reasoning, which serves as an important testbed for AI and could impact scientific research if further advanced. By scaling reasoning with reinforcement learning that rewards correct final answers, LLMs have improved from poor performance to saturating quantitative reasoning competitions like AIME and HMMT in one year. However, this approach faces fundamental limitations. Pursuing higher final answer accuracy doesn't address a key issue: correct answers don't guarantee correct reasoning. Moreover, many mathematical tasks like theorem proving require rigorous step-by-step derivation rather than numerical answers, making final answer rewards inapplicable. To push the limits of deep reasoning, we believe it is necessary to verify the comprehensiveness and rigor of mathematical reasoning. Self-verification is particularly important for scaling test-time compute, especially for open problems without known solutions. Towards self-verifiable mathematical reasoning, we investigate how to train an accurate and faithful LLM-based verifier for theorem proving. We then train a proof generator using the verifier as the reward model, and incentivize the generator to identify and resolve as many issues as possible in their own proofs before finalizing them. To maintain the generation-verification gap as the generator becomes stronger, we propose to scale verification compute to automatically label new hard-to-verify proofs, creating training data to further improve the verifier. Our resulting model, DeepSeekMath-V2, demonstrates strong theorem-proving capabilities, achieving gold-level scores on IMO 2025 and CMO 2024 and a near-perfect 118/120 on Putnam 2024 with scaled test-time compute.

AlphaEvolve is a generic evolutionary coding agent that combines the generative capabilities of LLMs with automated evaluation in an iterative evolutionary framework that proposes, tests, and refines algorithmic solutions to challenging scientific and practical problems. In this paper we showcase AlphaEvolve as a tool for autonomously discovering novel mathematical constructions and advancing our understanding of long-standing open problems. To demonstrate its breadth, we considered a list of 67 problems spanning mathematical analysis, combinatorics, geometry, and number theory. The system rediscovered the best known solutions in most of the cases and discovered improved solutions in several. In some instances, AlphaEvolve is also able to generalize results for a finite number of input values into a formula valid for all input values. Furthermore, we are able to combine this methodology with Deep Think and AlphaProof in a broader framework where the additional proof-assistants and reasoning systems provide automated proof generation and further mathematical insights. These results demonstrate that large language model-guided evolutionary search can autonomously discover mathematical constructions that complement human intuition, at times matching or even improving the best known results, highlighting the potential for significant new ways of interaction between mathematicians and AI systems. We present AlphaEvolve as a powerful new tool for mathematical discovery, capable of exploring vast search spaces to solve complex optimization problems at scale, often with significantly reduced requirements on preparation and computation time.

The AI community has been exploring a pathway to artificial general intelligence (AGI) by developing "language agents", which are complex large language models (LLMs) pipelines involving both prompting techniques and tool usage methods. While language agents have demonstrated impressive capabilities for many real-world tasks, a fundamental limitation of current language agents research is that they are model-centric, or engineering-centric. That's to say, the progress on prompts, tools, and pipelines of language agents requires substantial manual engineering efforts from human experts rather than automatically learning from data. We believe the transition from model-centric, or engineering-centric, to data-centric, i.e., the ability of language agents to autonomously learn and evolve in environments, is the key for them to possibly achieve AGI. In this work, we introduce agent symbolic learning, a systematic framework that enables language agents to optimize themselves on their own in a data-centric way using symbolic optimizers. Specifically, we consider agents as symbolic networks where learnable weights are defined by prompts, tools, and the way they are stacked together. Agent symbolic learning is designed to optimize the symbolic network within language agents by mimicking two fundamental algorithms in connectionist learning: back-propagation and gradient descent. Instead of dealing with numeric weights, agent symbolic learning works with natural language simulacrums of weights, loss, and gradients. We conduct proof-of-concept experiments on both standard benchmarks and complex real-world tasks and show that agent symbolic learning enables language agents to update themselves after being created and deployed in the wild, resulting in "self-evolving agents".

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

Recent advances in large language models (LLMs) have enabled agents to autonomously perform complex, open-ended tasks. However, many existing frameworks depend heavily on manually predefined tools and workflows, which hinder their adaptability, scalability, and generalization across domains. In this work, we introduce Alita--a generalist agent designed with the principle of "Simplicity is the ultimate sophistication," enabling scalable agentic reasoning through minimal predefinition and maximal self-evolution. For minimal predefinition, Alita is equipped with only one component for direct problem-solving, making it much simpler and neater than previous approaches that relied heavily on hand-crafted, elaborate tools and workflows. This clean design enhances its potential to generalize to challenging questions, without being limited by tools. For Maximal self-evolution, we enable the creativity of Alita by providing a suite of general-purpose components to autonomously construct, refine, and reuse external capabilities by generating task-related model context protocols (MCPs) from open source, which contributes to scalable agentic reasoning. Notably, Alita achieves 75.15% pass@1 and 87.27% pass@3 accuracy, which is top-ranking among general-purpose agents, on the GAIA benchmark validation dataset, 74.00% and 52.00% pass@1, respectively, on Mathvista and PathVQA, outperforming many agent systems with far greater complexity. More details will be updated at https://github.com/CharlesQ9/Alita{https://github.com/CharlesQ9/Alita}.

The trajectory of AI development suggests that we will increasingly rely on agent-based systems composed of independently developed agents with different information, privileges, and tools. The success of these systems will critically depend on effective collaboration among these heterogeneous agents, even under partial observability. Despite intense interest, few empirical studies have evaluated such agent-agent collaboration at scale. We propose a collaborative maze-solving benchmark that (i) isolates collaborative capabilities, (ii) modulates problem complexity, (iii) enables scalable automated grading, and (iv) imposes no output-format constraints, preserving ecological plausibility. Using this framework, we evaluate 32 leading open- and closed-source models in solo, homogeneous, and heterogeneous pairings. Our results reveal a "collaboration gap": models that perform well solo often degrade substantially when required to collaborate. Collaboration can break down dramatically; for instance, small distilled models that solve mazes well alone may fail almost completely in certain pairings. We find that starting with the stronger agent often improves outcomes, motivating a "relay inference" approach where the stronger agent leads before handing off to the weaker one, closing much of the gap. Our findings argue for (1) collaboration-aware evaluation, (2) training strategies developed to enhance collaborative capabilities, and (3) interaction design that reliably elicits agents' latent skills, guidance that applies to AI-AI and human-AI collaboration.

Existing agents based on large language models (LLMs) demonstrate robust problem-solving capabilities by integrating LLMs' inherent knowledge, strong in-context learning and zero-shot capabilities, and the use of tools combined with intricately designed LLM invocation workflows by humans. However, these agents still exhibit shortcomings in long-term reasoning and under-use the potential of existing tools, leading to noticeable deficiencies in complex real-world reasoning scenarios. To address these limitations, we introduce Sibyl, a simple yet powerful LLM-based agent framework designed to tackle complex reasoning tasks by efficiently leveraging a minimal set of tools. Drawing inspiration from Global Workspace Theory, Sibyl incorporates a global workspace to enhance the management and sharing of knowledge and conversation history throughout the system. Furthermore, guided by Society of Mind Theory, Sibyl implements a multi-agent debate-based jury to self-refine the final answers, ensuring a comprehensive and balanced approach. This approach aims to reduce system complexity while expanding the scope of problems solvable-from matters typically resolved by humans in minutes to those requiring hours or even days, thus facilitating a shift from System-1 to System-2 thinking. Sibyl has been designed with a focus on scalability and ease of debugging by incorporating the concept of reentrancy from functional programming from its inception, with the aim of seamless and low effort integration in other LLM applications to improve capabilities. Our experimental results on the GAIA benchmark test set reveal that the Sibyl agent instantiated with GPT-4 achieves state-of-the-art performance with an average score of 34.55%, compared to other agents based on GPT-4. We hope that Sibyl can inspire more reliable and reusable LLM-based agent solutions to address complex real-world reasoning tasks.

Extending the capabilities of Large Language Models (LLMs) with functions or tools for environment interaction has led to the emergence of the agent paradigm. In industry, training an LLM is not always feasible because of the scarcity of domain data, legal holds on proprietary customer data, rapidly changing business requirements, and the need to prototype new assistants. Agents provide an elegant solution to the above by relying on the zero-shot reasoning abilities of the underlying LLM and utilizing tools to explore and reason over customer data and respond to user requests. However, there are two concerns here: (I) acquiring large scale customer queries for agent testing is time-consuming, and (II) high reliance on the tool call sequence (or trajectory) followed by the agent to respond to user queries may lead to unexpected or incorrect behavior. To address this, we propose MAG-V, a multi-agent framework to first generate a dataset of questions that mimic customer queries; and second, reverse-engineer alternate questions from the responses for trajectory verification. Initial results indicate that our synthetic data can improve agent performance on actual customer queries. Furthermore, our trajectory verification methodology, inspired by distant supervision and using traditional machine learning (ML) models, outperforms a GPT-4o judge baseline by 11% accuracy and matches the performance of a GPT-4 judge on our constructed dataset. Overall, our approach is a step towards unifying diverse task agents into a cohesive framework for achieving an aligned objective.

We propose a many-sorted modal logic for reasoning about knowledge in multi-agent systems. Our logic introduces a clear distinction between participating agents and the environment. This allows to express local properties of agents and global properties of worlds in a uniform way, as well as to talk about the presence or absence of agents in a world. The logic subsumes the standard epistemic logic and is a conservative extension of it. The semantics is given in chromatic hypergraphs, a generalization of chromatic simplicial complexes, which were recently used to model knowledge in distributed systems. We show that the logic is sound and complete with respect to the intended semantics. We also show a further connection of chromatic hypergraphs with neighborhood frames.

Recent research on Reasoning of Large Language Models (LLMs) has sought to further enhance their performance by integrating meta-thinking -- enabling models to monitor, evaluate, and control their reasoning processes for more adaptive and effective problem-solving. However, current single-agent work lacks a specialized design for acquiring meta-thinking, resulting in low efficacy. To address this challenge, we introduce Reinforced Meta-thinking Agents (ReMA), a novel framework that leverages Multi-Agent Reinforcement Learning (MARL) to elicit meta-thinking behaviors, encouraging LLMs to think about thinking. ReMA decouples the reasoning process into two hierarchical agents: a high-level meta-thinking agent responsible for generating strategic oversight and plans, and a low-level reasoning agent for detailed executions. Through iterative reinforcement learning with aligned objectives, these agents explore and learn collaboration, leading to improved generalization and robustness. Experimental results demonstrate that ReMA outperforms single-agent RL baselines on complex reasoning tasks, including competitive-level mathematical benchmarks and LLM-as-a-Judge benchmarks. Comprehensive ablation studies further illustrate the evolving dynamics of each distinct agent, providing valuable insights into how the meta-thinking reasoning process enhances the reasoning capabilities of LLMs.

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

Large language models (LLMs) excel in natural language generation but often confidently produce incorrect responses, especially in tasks like mathematical reasoning. Chain-of-thought prompting, self-verification, and multi-agent debate are among the strategies proposed to improve the reasoning and factual accuracy of LLMs. Building on Du et al.'s multi-agent debate framework, we find that multi-agent debate helps at any model scale, and that diversity of thought elicits stronger reasoning in debating LLMs. Across various model sizes, performance on mathematical reasoning tasks benefits most when diverse trained models are used. Remarkably, after 4 rounds of debate, a diverse set of medium-capacity models (Gemini-Pro, Mixtral 7BX8, and PaLM 2-M) outperforms GPT-4 on the GSM-8K benchmark, scoring 91% accuracy. By comparison, when 3 instances of Gemini-Pro are used, performance only reaches 82%. Finally, this diverse set of medium-capacity models sets a new state-of-the-art performance on the ASDiv benchmark (94%). These results underscore the idea that the future of AI is agentic, with diverse cooperating agents yielding emergent capabilities beyond even the most powerful individual models.

Agentic search leverages LLMs to solve complex user information needs by executing a multi-step process of planning, searching, and synthesizing information to provide answers. This paradigm introduces unique challenges for LLMs' agentic reasoning capabilities when interacting with search systems. In this paper, we propose an LLM-based pipeline to study effective reasoning behavior patterns in agentic search by analyzing agentic search trajectories. Using this pipeline, we identify four beneficial reasoning behaviors: Information Verification, Authority Evaluation, Adaptive Search, and Error Recovery. Based on these findings, we propose a technique called Behavior Priming to train agentic search models. It synthesizes trajectories that exhibit these four behaviors and integrates them into the agentic search model through SFT, followed by standard reinforcement learning. Experiments on Qwen3-1.7B and Llama3.2-3B-Instruct across three web benchmarks and seven multi-hop QA benchmarks demonstrate that behavior priming 1) yields significant performance gains compared to training with direct RL, and 2) outperforms other SFT-then-RL baselines, such as those SFT on randomly selected trajectories or on trajectories with merely correct outcomes. Crucially, we demonstrate that the reasoning behaviors, rather than the correctness of the final answer, is the critical factor for achieving strong performance in RL: SFT on trajectories with reasoning behaviors but incorrect answers leads to comparable performance with SFT on those with reasoning behaviors and correct answers. Our analysis further reveals that the introduced reasoning behaviors endow models with more effective exploration (higher pass@k and entropy) and test-time scaling (longer trajectories) capabilities, providing a strong foundation for RL. Our code are avalible at https://github.com/cxcscmu/Behavior_Priming_For_Agentic_Search.

The demand for synthetic data in mathematical reasoning has increased due to its potential to enhance the mathematical capabilities of large language models (LLMs). However, ensuring the validity of intermediate reasoning steps remains a significant challenge, affecting data quality. While formal verification via theorem provers effectively validates LLM reasoning, the autoformalisation of mathematical proofs remains error-prone. In response, we introduce iterative autoformalisation, an approach that iteratively refines theorem prover formalisation to mitigate errors, thereby increasing the execution rate on the Lean prover from 60% to 87%. Building upon that, we introduce Theorem Prover as a Judge (TP-as-a-Judge), a method that employs theorem prover formalisation to rigorously assess LLM intermediate reasoning, effectively integrating autoformalisation with synthetic data generation. Finally, we present Reinforcement Learning from Theorem Prover Feedback (RLTPF), a framework that replaces human annotation with theorem prover feedback in Reinforcement Learning from Human Feedback (RLHF). Across multiple LLMs, applying TP-as-a-Judge and RLTPF improves benchmarks with only 3,508 samples, achieving 5.56% accuracy gain on Mistral-7B for MultiArith, 6.00% on Llama-2-7B for SVAMP, and 3.55% on Llama-3.1-8B for AQUA.

The creation of high-quality datasets to improve Large Language Model (LLM) reasoning remains a significant challenge, as current methods often suffer from generating low-quality/incorrect answers and limited information richness from available data sources. To address this, we propose AgenticMath, a novel agentic pipeline for generating high-quality mathematical question-answer pairs to enhance the supervised fine-tuning of LLMs. Our method operates through four stages: (1) Seed Question Filter that selects questions with high information richness, complexity, and clarity; (2) an Agentic Question Rephrase step that employs a multi-agent system to generate diverse, logically consistent paraphrases; (3) an Answer Augment step where rewrite answers using chain-of-thought reasoning to enhance numerical and logical correctness, without reliance on human-provided labels; and (4) a final Question and Answer Evaluation that retains only the most superior pairs. Extensive experiments demonstrate that, fine-tuning 3B-8B parameter LLMs on AgenticMath generated datasets (comprising only 30-60K math samples) achieves competitive or superior performance on diverse in domain and out-of-domain mathematical reasoning benchmarks compared to baselines trained on much more data (e.g., 400K or 2.3M samples). Our work demonstrates that targeted, high-quality data generation is a more efficient path to improving mathematical reasoning in LLMs than large-scale, low-quality alternatives.

While large language models (LLMs) have been thoroughly evaluated for deductive and inductive reasoning, their proficiency in abductive reasoning and holistic rule learning in interactive environments remains less explored. This work introduces RULEARN, a novel benchmark specifically designed to assess the rule-learning ability of LLMs in interactive settings. In RULEARN, agents interact with the environment to gather observations and discern patterns, using these insights to solve problems. To further enhance the rule-learning capabilities of LLM agents within this benchmark, we propose IDEA agent, which integrates Induction, Deduction, and Abduction processes. IDEA agent refines this approach by leveraging a structured reasoning sequence: generating hypotheses through abduction, testing them via deduction, and refining them based on feedback from induction. This sequence enables agents to dynamically establish and apply rules, mimicking human-like reasoning processes. Our evaluation of five representative LLMs indicates that while these models can generate plausible initial hypotheses, they often struggle with strategic interaction within the environment, effective incorporation of feedback, and adaptive refinement of their hypotheses. IDEA agent demonstrates significantly improved performance on the RULEARN benchmark, offering valuable insights for the development of agents capable of human-like rule-learning in real-world scenarios. We will release our code and data.

General AI Agents are increasingly recognized as foundational frameworks for the next generation of artificial intelligence, enabling complex reasoning, web interaction, coding, and autonomous research capabilities. However, current agent systems are either closed-source or heavily reliant on a variety of paid APIs and proprietary tools, limiting accessibility and reproducibility for the research community. In this work, we present Cognitive Kernel-Pro, a fully open-source and (to the maximum extent) free multi-module agent framework designed to democratize the development and evaluation of advanced AI agents. Within Cognitive Kernel-Pro, we systematically investigate the curation of high-quality training data for Agent Foundation Models, focusing on the construction of queries, trajectories, and verifiable answers across four key domains: web, file, code, and general reasoning. Furthermore, we explore novel strategies for agent test-time reflection and voting to enhance agent robustness and performance. We evaluate Cognitive Kernel-Pro on GAIA, achieving state-of-the-art results among open-source and free agents. Notably, our 8B-parameter open-source model surpasses previous leading systems such as WebDancer and WebSailor, establishing a new performance standard for accessible, high-capability AI agents. Code is available at https://github.com/Tencent/CognitiveKernel-Pro

Despite significant advancements in general-purpose AI agents, several challenges still hinder their practical application in real-world scenarios. First, the limited planning capabilities of Large Language Models (LLM) restrict AI agents from effectively solving complex tasks that require long-horizon planning. Second, general-purpose AI agents struggle to efficiently utilize domain-specific knowledge and human expertise. In this paper, we introduce the Standard Operational Procedure-guided Agent (SOP-agent), a novel framework for constructing domain-specific agents through pseudocode-style Standard Operational Procedures (SOPs) written in natural language. Formally, we represent a SOP as a decision graph, which is traversed to guide the agent in completing tasks specified by the SOP. We conduct extensive experiments across tasks in multiple domains, including decision-making, search and reasoning, code generation, data cleaning, and grounded customer service. The SOP-agent demonstrates excellent versatility, achieving performance superior to general-purpose agent frameworks and comparable to domain-specific agent systems. Additionally, we introduce the Grounded Customer Service Benchmark, the first benchmark designed to evaluate the grounded decision-making capabilities of AI agents in customer service scenarios based on SOPs.

Leveraging mathematical Large Language Models (LLMs) for proof generation is a fundamental topic in LLMs research. We argue that the ability of current LLMs to prove statements largely depends on whether they have encountered the relevant proof process during training. This reliance limits their deeper understanding of mathematical theorems and related concepts. Inspired by the pedagogical method of "proof by counterexamples" commonly used in human mathematics education, our work aims to enhance LLMs' ability to conduct mathematical reasoning and proof through counterexamples. Specifically, we manually create a high-quality, university-level mathematical benchmark, CounterMATH, which requires LLMs to prove mathematical statements by providing counterexamples, thereby assessing their grasp of mathematical concepts. Additionally, we develop a data engineering framework to automatically obtain training data for further model improvement. Extensive experiments and detailed analyses demonstrate that CounterMATH is challenging, indicating that LLMs, such as OpenAI o1, have insufficient counterexample-driven proof capabilities. Moreover, our exploration into model training reveals that strengthening LLMs' counterexample-driven conceptual reasoning abilities is crucial for improving their overall mathematical capabilities. We believe that our work offers new perspectives on the community of mathematical LLMs.

Recent large language models (LLMs) have witnessed significant advancement in various tasks, including mathematical reasoning and theorem proving. As these two tasks require strict and formal multi-step inference, they are appealing domains for exploring the reasoning ability of LLMs but still face important challenges. Previous studies such as Chain-of-Thought (CoT) have revealed the effectiveness of intermediate steps guidance. However, such step-wise annotation requires heavy labor, leading to insufficient training steps for current benchmarks. To fill this gap, this work introduces MUSTARD, a data generation framework that masters uniform synthesis of theorem and proof data of high quality and diversity. MUSTARD synthesizes data in three stages: (1) It samples a few mathematical concept seeds as the problem category. (2) Then, it prompts a generative language model with the sampled concepts to obtain both the problems and their step-wise formal solutions. (3) Lastly, the framework utilizes a proof assistant (e.g., Lean Prover) to filter the valid proofs. With the proposed MUSTARD, we present a theorem-and-proof benchmark MUSTARDSAUCE with 5,866 valid data points. Each data point contains an informal statement, an informal proof, and a translated formal proof that passes the prover validation. We perform extensive analysis and demonstrate that MUSTARD generates validated high-quality step-by-step data. We further apply the MUSTARDSAUCE for fine-tuning smaller language models. The fine-tuned Llama 2-7B achieves a 15.41% average relative performance gain in automated theorem proving, and 8.18% in math word problems. Codes and data are available at https://github.com/Eleanor-H/MUSTARD.