mlsanityData to 14 Oct 2026

ToRA: A Tool-Integrated Reasoning Agent for Mathematical Problem Solving

arXiv 2309.17452 ↗First posted 29 Sep 2023cs.CL cs.AIcited by 282

On the map: LLM reasoning → Mathematical reasoning

also in 1 more
Abstract (arXiv)

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-Code-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.

Key facts. Cited by 282 papers in the map (data through 14 Oct 2026). Placed in Mathematical reasoning, one of 17 directions in LLM reasoning. Builds on 45 of its 85 references that are in the map. First posted on arXiv 29 Sep 2023.

Builds on

45 of 85 references.

Closest ancestors · 7

Same direction, newest first

  1. 2023WizardMath: Empowering Mathematical Reasoning for Large Language Models via Reinforced Evol-Instruct18 Aug
  2. 2023Solving Challenging Math Word Problems Using GPT-4 Code Interpreter with Code-based Self-Verification15 Aug
  3. 2023Scaling Relationship on Learning Mathematical Reasoning with Large Language Models3 Aug
  4. 2023Evaluating and Improving Tool-Augmented Computation-Intensive Math Reasoning4 Jun
  5. 2022Solving Math Word Problems via Cooperative Reasoning induced Language Models28 Oct
  6. 2022Dynamic Prompt Learning via Policy Gradient for Semi-structured Mathematical Reasoning29 Sep
  7. 2020Generative Language Modeling for Automated Theorem Proving7 Sep

Other references · 38

  1. 2023LLaMA: Open and Efficient Foundation Language Modelscited by 14,132
  2. 2023Llama 2: Open Foundation and Fine-Tuned Chat Modelscited by 13,028
  3. 2022Chain-of-Thought Prompting Elicits Reasoning in Large Language Modelscited by 12,459
  4. 2015Distilling the Knowledge in a Neural Networkcited by 10,324
  5. 2021Training Verifiers to Solve Math Word Problemscited by 10,109
  6. 2022ReAct: Synergizing Reasoning and Acting in Language Modelscited by 8,695
  7. 2021Measuring Mathematical Problem Solving With the MATH Datasetcited by 5,371
  8. 2023Toolformer: Language Models Can Teach Themselves to Use Toolscited by 4,182
  9. 2023Let's Verify Step by Stepcited by 3,789
  10. 2023FlashAttention-2: Faster Attention with Better Parallelism and Work Partitioningcited by 2,598
  11. 2023Sparks of Artificial General Intelligence: Early experiments with GPT-4cited by 2,592
  12. 2023Code Llama: Open Foundation Models for Codecited by 2,139
26 more
  1. 2021WebGPT: Browser-assisted question-answering with human feedbackcited by 1,745
  2. 2022Least-to-Most Prompting Enables Complex Reasoning in Large Language Modelscited by 1,407
  3. 2021Improving language models by retrieving from trillions of tokenscited by 1,293
  4. 2023PaLM 2 Technical Reportcited by 1,162
  5. 2022Program of Thoughts Prompting: Disentangling Computation from Reasoning for Numerical Reasoning Taskscited by 1,076
  6. 2023Encouraging Divergent Thinking in Large Language Models through Multi-Agent Debatecited by 1,011
  7. 2022STaR: Bootstrapping Reasoning With Reasoningcited by 940
  8. 2021Are NLP Models really able to Solve Simple Math Word Problems?cited by 878
  9. 2023CRITIC: Large Language Models Can Self-Correct with Tool-Interactive Critiquingcited by 783
  10. 2023The RefinedWeb Dataset for Falcon LLM: Outperforming Curated Corpora with Web Data, and Web Data Onlycited by 763
  11. 2023Instruction Tuning with GPT-4cited by 686
  12. 2022Large Language Models Can Self-Improvecited by 664
  13. 2022PAL: Program-aided Language Modelscited by 652
  14. 2023MAmmoTH: Building Math Generalist Models through Hybrid Instruction Tuningcited by 487
  15. 2023Augmented Language Models: a Surveycited by 403
  16. 2023Enhancing Retrieval-Augmented Large Language Models with Iterative Retrieval-Generation Synergycited by 346
  17. 2022Large Language Models Are Reasoning Teacherscited by 329
  18. 2021A Diverse Corpus for Evaluating and Developing English Math Word Problem Solverscited by 318
  19. 2021ZeRO-Infinity: Breaking the GPU Memory Wall for Extreme Scale Deep Learningcited by 256
  20. 2023Specializing Smaller Language Models towards Multi-Step Reasoningcited by 251
  21. 2022Making Large Language Models Better Reasoners with Step-Aware Verifiercited by 233
  22. 2022TALM: Tool Augmented Language Modelscited by 197
  23. 2023ART: Automatic multi-step reasoning and tool-use for large language modelscited by 197
  24. 2023Platypus: Quick, Cheap, and Powerful Refinement of LLMscited by 150
  25. 2023Synthetic Prompting: Generating Chain-of-Thought Demonstrations for Large Language Modelscited by 61
  26. 2022Chaining Simultaneous Thoughts for Numerical Reasoningcited by 14

Built on by

Cited by year (2026 to 14 Oct)

Citing papers per year: 2023: 9; 2024: 105; 2025: 113; 2026: 55.

282 papers.

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  1. 2024DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Modelscited by 9,379
  2. 2024Tulu 3: Pushing Frontiers in Open Language Model Post-Trainingcited by 1,053
  3. 2023Math-Shepherd: Verify and Reinforce LLMs Step-by-step without Human Annotationscited by 928
  4. 2024DeepSeek LLM: Scaling Open-Source Language Models with Longtermismcited by 642
  5. 2024A Survey on the Memory Mechanism of Large Language Model based Agentscited by 634
  6. 2025Towards Reasoning Era: A Survey of Long Chain-of-Thought for Reasoning Large Language Modelscited by 384
  7. 2025ToolRL: Reward is All Tool Learning Needscited by 362
  8. 2025rStar-Math: Small LLMs Can Master Math Reasoning with Self-Evolved Deep Thinkingcited by 313
  9. 2024A Survey on Knowledge Distillation of Large Language Modelscited by 284
  10. 2024Step-DPO: Step-wise Preference Optimization for Long-chain Reasoning of LLMscited by 273
  11. 2024Continual Learning of Large Language Models: A Comprehensive Surveycited by 234
  12. 2024Data Interpreter: An LLM Agent For Data Sciencecited by 225
38 more
  1. 2024Tool Learning with Large Language Models: A Surveycited by 223
  2. 2025UI-TARS-2 Technical Report: Advancing GUI Agent with Multi-Turn Reinforcement Learningcited by 215
  3. 2024OpenMathInstruct-2: Accelerating AI for Math with Massive Open-Source Instruction Datacited by 200
  4. 2025WebDancer: Towards Autonomous Information Seeking Agencycited by 188
  5. 2025Agentic Reinforced Policy Optimizationcited by 172
  6. 2024AlphaMath Almost Zero: Process Supervision without Processcited by 162
  7. 2024GSM-Plus: A Comprehensive Benchmark for Evaluating the Robustness of LLMs as Mathematical Problem Solverscited by 158
  8. 2024Orca-Math: Unlocking the potential of SLMs in Grade School Mathcited by 151
  9. 2025A Minimalist Approach to LLM Reasoning: from Rejection Sampling to Reinforcecited by 145
  10. 2024MathScale: Scaling Instruction Tuning for Mathematical Reasoningcited by 144
  11. 2024OpenMathInstruct-1: A 1.8 Million Math Instruction Tuning Datasetcited by 143
  12. 2024Mutual Reasoning Makes Smaller LLMs Stronger Problem-Solverscited by 138
  13. 2023OpenAgents: An Open Platform for Language Agents in the Wildcited by 137
  14. 2024Rho-1: Not All Tokens Are What You Needcited by 133
  15. 2024Toward Self-Improvement of LLMs via Imagination, Searching, and Criticizingcited by 125
  16. 2024MAVIS: Mathematical Visual Instruction Tuning with an Automatic Data Enginecited by 113
  17. 2025Agentic Reasoning and Tool Integration for LLMs via Reinforcement Learningcited by 110
  18. 2024Common 7B Language Models Already Possess Strong Math Capabilitiescited by 109
  19. 2024Agent-FLAN: Designing Data and Methods of Effective Agent Tuning for Large Language Modelscited by 100
  20. 2024Easy-to-Hard Generalization: Scalable Alignment Beyond Human Supervisioncited by 96
  21. 2025VerlTool: Towards Holistic Agentic Reinforcement Learning with Tool Usecited by 96
  22. 2024DART-Math: Difficulty-Aware Rejection Tuning for Mathematical Problem-Solvingcited by 95
  23. 2024Small LLMs Are Weak Tool Learners: A Multi-LLM Agentcited by 93
  24. 2024MARIO: MAth Reasoning with code Interpreter Output -- A Reproducible Pipelinecited by 81
  25. 2024SPA-Bench: A Comprehensive Benchmark for SmartPhone Agent Evaluationcited by 81
  26. 2024Formal Mathematical Reasoning: A New Frontier in AIcited by 81
  27. 2025Acting Less is Reasoning More! Teaching Model to Act Efficientlycited by 80
  28. 2025Reinforcing Multi-Turn Reasoning in LLM Agents via Fine-Grained Reward Structure and Credit Assignmentcited by 79
  29. 2025PyVision: Agentic Vision with Dynamic Toolingcited by 79
  30. 2025From AI for Science to Agentic Science: A Survey on Autonomous Scientific Discoverycited by 77
  31. 2023Igniting Language Intelligence: The Hitchhiker's Guide From Chain-of-Thought Reasoning to Language Agentscited by 72
  32. 2024MathGenie: Generating Synthetic Data with Question Back-translation for Enhancing Mathematical Reasoning of LLMscited by 72
  33. 2024Step-level Value Preference Optimization for Mathematical Reasoningcited by 72
  34. 2025ACEBench: Who Wins the Match Point in Tool Usage?cited by 71
  35. 2023TinyGSM: achieving >80% on GSM8k with small language modelscited by 70
  36. 2025Self-rewarding correction for mathematical reasoningcited by 70
  37. 2025Ego-R1: Chain-of-Tool-Thought for Ultra-Long Egocentric Video Reasoningcited by 68
  38. 2024MindSearch: Mimicking Human Minds Elicits Deep AI Searchercited by 66

50 most cited of 282 All 282 (JSON)

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  1. 2024MATHSENSEI: A Tool-Augmented Large Language Model for Mathematical Reasoning
  2. 2026Artificial Intelligence for Mathematical Reasoning: An Integrated Survey of Language Models, Neuro-symbolic Systems, and Verified Discovery
  3. 2025A Toolbox, Not a Hammer -- Multi-TAG: Scaling Math Reasoning with Multi-Tool Aggregation
  4. 2026Mathematical Reasoning in Large Language Models: Benchmarks, Architectures, Evaluation, and Open Challenges
  5. 2026M2A: Synergizing Mathematical and Agentic Reasoning in Large Language Models
  6. 2024DotaMath: Decomposition of Thought with Code Assistance and Self-correction for Mathematical Reasoning
  7. 2026RMA: an Agentic System for Research-Level Mathematical Problems
  8. 2025MathMist: A Parallel Multilingual Benchmark Dataset for Mathematical Problem Solving and Reasoning