mlsanityData to 14 Oct 2026

Solving Math Word Problems via Cooperative Reasoning induced Language Models

arXiv 2210.16257 ↗First posted 28 Oct 2022cs.CLcited by 77

On the map: LLM reasoning → Mathematical reasoning

Abstract (arXiv)

Large-scale pre-trained language models (PLMs) bring new opportunities to challenging problems, especially those that need high-level intelligence, such as the math word problem (MWPs). However, directly applying existing PLMs to MWPs can fail as the generation process lacks sufficient supervision and thus lacks fast adaptivity as humans. We notice that human reasoning has a dual reasoning framework that consists of an immediate reaction system (system 1) and a delicate reasoning system (system 2), where the entire reasoning is determined by their interaction. This inspires us to develop a cooperative reasoning-induced PLM for solving MWPs, called Cooperative Reasoning (CoRe), resulting in a human-like reasoning architecture with system 1 as the generator and system 2 as the verifier. In our approach, the generator is responsible for generating reasoning paths, and the verifiers are used to supervise the evaluation in order to obtain reliable feedback for the generator. We evaluate our CoRe framework on several mathematical reasoning datasets and achieve decent improvement over state-of-the-art methods, up to 9.6% increase over best baselines. Our codes are available at https://github.com/TianHongZXY/CoRe

Key facts. Cited by 77 papers in the map (data through 14 Oct 2026). Placed in Mathematical reasoning, one of 17 directions in LLM reasoning. Builds on 19 of its 41 references that are in the map. First posted on arXiv 28 Oct 2022.

Builds on

19 of 41 references.

References · 19

  1. 2020Language Models are Few-Shot Learnerscited by 32,419
  2. 2022Chain-of-Thought Prompting Elicits Reasoning in Large Language Modelscited by 12,459
  3. 2021Training Verifiers to Solve Math Word Problemscited by 10,109
  4. 2022Self-Consistency Improves Chain of Thought Reasoning in Language Modelscited by 5,708
  5. 2022PaLM: Scaling Language Modeling with Pathwayscited by 5,326
  6. 2022Large Language Models are Zero-Shot Reasonerscited by 4,374
  7. 2021Finetuned Language Models Are Zero-Shot Learnerscited by 3,780
  8. 2022Emergent Abilities of Large Language Modelscited by 2,512
  9. 2020DeBERTa: Decoding-enhanced BERT with Disentangled Attentioncited by 2,181
  10. 2021Multitask Prompted Training Enables Zero-Shot Task Generalizationcited by 1,470
  11. 2022LaMDA: Language Models for Dialog Applicationscited by 1,220
  12. 2021Show Your Work: Scratchpads for Intermediate Computation with Language Modelscited by 886
7 more
  1. 2016Solving General Arithmetic Word Problemscited by 360
  2. 2021A Diverse Corpus for Evaluating and Developing English Math Word Problem Solverscited by 318
  3. 2021Improving Coherence and Consistency in Neural Sequence Models with Dual-System, Neuro-Symbolic Reasoningcited by 85
  4. 2021MWPToolkit: An Open-Source Framework for Deep Learning-Based Math Word Problem Solverscited by 39
  5. 2016Unit Dependency Graph and its Application to Arithmetic Word Problem Solvingcited by 25
  6. 2021To Beam Or Not To Beam: That is a Question of Cooperation for Language GANscited by 14
  7. 2022A Disability Lens towards Biases in GPT-3 Generated Open-Ended Languagescited by 3

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2023: 16; 2024: 33; 2025: 24; 2026: 4.

77 papers.

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  1. 2023Encouraging Divergent Thinking in Large Language Models through Multi-Agent Debatecited by 1,011
  2. 2023Math-Shepherd: Verify and Reinforce LLMs Step-by-step without Human Annotationscited by 928
  3. 2023WizardMath: Empowering Mathematical Reasoning for Large Language Models via Reinforced Evol-Instructcited by 625
  4. 2025From System 1 to System 2: A Survey of Reasoning Large Language Modelscited by 320
  5. 2023Alphazero-like Tree-Search can Guide Large Language Model Decoding and Trainingcited by 295
  6. 2024Large Language Models for Mathematical Reasoning: Progresses and Challengescited by 284
  7. 2023ToRA: A Tool-Integrated Reasoning Agent for Mathematical Problem Solvingcited by 282
  8. 2024Monte Carlo Tree Search Boosts Reasoning via Iterative Preference Learningcited by 241
  9. 2023Automatically Correcting Large Language Models: Surveying the landscape of diverse self-correction strategiescited by 238
  10. 2024V-STaR: Training Verifiers for Self-Taught Reasonerscited by 217
  11. 2024Agent AI: Surveying the Horizons of Multimodal Interactioncited by 170
  12. 2024AlphaMath Almost Zero: Process Supervision without Processcited by 162
38 more
  1. 2025The Surprising Effectiveness of Negative Reinforcement in LLM Reasoningcited by 162
  2. 2024Teaching Large Language Models to Reason with Reinforcement Learningcited by 160
  3. 2024InternLM-Math: Open Math Large Language Models Toward Verifiable Reasoningcited by 119
  4. 2023ToolChain*: Efficient Action Space Navigation in Large Language Models with A* Searchcited by 105
  5. 2024ZoomEye: Enhancing Multimodal LLMs with Human-Like Zooming Capabilities through Tree-Based Image Explorationcited by 103
  6. 2023OVM, Outcome-supervised Value Models for Planning in Mathematical Reasoningcited by 85
  7. 2023Cognitive Mirage: A Review of Hallucinations in Large Language Modelscited by 84
  8. 2024Self-Contrast: Better Reflection Through Inconsistent Solving Perspectivescited by 71
  9. 2023Corex: Pushing the Boundaries of Complex Reasoning through Multi-Model Collaborationcited by 70
  10. 2024LLM Reasoners: New Evaluation, Library, and Analysis of Step-by-Step Reasoning with Large Language Modelscited by 70
  11. 2025Self-rewarding correction for mathematical reasoningcited by 70
  12. 2024Building Math Agents with Multi-Turn Iterative Preference Learningcited by 66
  13. 2024A Survey of Mathematical Reasoning in the Era of Multimodal Large Language Model: Benchmark, Method & Challengescited by 55
  14. 2024Visual Agents as Fast and Slow Thinkerscited by 53
  15. 2024When is Tree Search Useful for LLM Planning? It Depends on the Discriminatorcited by 47
  16. 2023Enhancing Large Language Models in Coding Through Multi-Perspective Self-Consistencycited by 46
  17. 2024xCoT: Cross-lingual Instruction Tuning for Cross-lingual Chain-of-Thought Reasoningcited by 46
  18. 2023MuggleMath: Assessing the Impact of Query and Response Augmentation on Math Reasoningcited by 45
  19. 2024LLM Critics Help Catch Bugs in Mathematics: Towards a Better Mathematical Verifier with Natural Language Feedbackcited by 41
  20. 2024RAG-Star: Enhancing Deliberative Reasoning with Retrieval Augmented Verification and Refinementcited by 40
  21. 2024Entropy-Regularized Process Reward Modelcited by 38
  22. 2024Flow of Reasoning: Training LLMs for Divergent Reasoning with Minimal Examplescited by 30
  23. 2025Chain-of-Reasoning: Towards Unified Mathematical Reasoning in Large Language Models via a Multi-Paradigm Perspectivecited by 29
  24. 2025Thinking Machines: A Survey of LLM based Reasoning Strategiescited by 25
  25. 2023Mathematical Language Models: A Surveycited by 24
  26. 2025BoostStep: Boosting mathematical capability of Large Language Models via improved single-step reasoningcited by 21
  27. 2023No Train Still Gain. Unleash Mathematical Reasoning of Large Language Models with Monte Carlo Tree Search Guided by Energy Functioncited by 20
  28. 2025STaR-SQL: Self-Taught Reasoner for Text-to-SQLcited by 17
  29. 2024Advancing Process Verification for Large Language Models via Tree-Based Preference Learningcited by 16
  30. 2024Learning Evolving Tools for Large Language Modelscited by 16
  31. 2025CondAmbigQA: A Benchmark and Dataset for Conditional Ambiguous Question Answeringcited by 15
  32. 2023Question Answering as Programming for Solving Time-Sensitive Questionscited by 14
  33. 2025HyperTree Planning: Enhancing LLM Reasoning via Hierarchical Thinkingcited by 14
  34. 2025Sailing by the Stars: A Survey on Reward Models and Learning Strategies for Learning from Rewardscited by 14
  35. 2024Exploring the Mystery of Influential Data for Mathematical Reasoningcited by 13
  36. 2024Enhancing Financial Question Answering with a Multi-Agent Reflection Frameworkcited by 12
  37. 2025A Survey on Mathematical Reasoning and Optimization with Large Language Modelscited by 12
  38. 2025ROC-n-reroll: How verifier imperfection affects test-time scalingcited by 12

50 most cited of 77 All 77 (JSON)

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  1. 2025A Survey on Large Language Models for Mathematical Reasoning
  2. 2023Reasoning in Large Language Models Through Symbolic Math Word Problems
  3. 2023Learning Multi-Step Reasoning by Solving Arithmetic Tasks
  4. 2026Mathematical Reasoning in Large Language Models: Benchmarks, Architectures, Evaluation, and Open Challenges
  5. 2024Multi-Step Reasoning with Large Language Models, a Survey
  6. 2026HintMR: Eliciting Stronger Mathematical Reasoning in Small Language Models
  7. 2025Large Language Models and Mathematical Reasoning Failures
  8. 2024Can Language Models Rival Mathematics Students? Evaluating Mathematical Reasoning through Textual Manipulation and Human Experiments