# Solving Math Word Problems via Cooperative Reasoning induced Language Models

arXiv: https://arxiv.org/abs/2210.16257 · HTML: https://mlsanity.com/paper/2210.16257/

## 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.

## Placed in

- LLM reasoning / [Mathematical reasoning](https://mlsanity.com/lr/mathematical-reasoning/)

## Builds on (most cited first, 19 of 19)

- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [Chain-of-Thought Prompting Elicits Reasoning in Large Language Models](https://mlsanity.com/paper/2201.11903/) (2022)
- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [Self-Consistency Improves Chain of Thought Reasoning in Language Models](https://mlsanity.com/paper/2203.11171/) (2022)
- [PaLM: Scaling Language Modeling with Pathways](https://mlsanity.com/paper/2204.02311/) (2022)
- [Large Language Models are Zero-Shot Reasoners](https://mlsanity.com/paper/2205.11916/) (2022)
- [Finetuned Language Models Are Zero-Shot Learners](https://mlsanity.com/paper/2109.01652/) (2021)
- [Emergent Abilities of Large Language Models](https://mlsanity.com/paper/2206.07682/) (2022)
- [DeBERTa: Decoding-enhanced BERT with Disentangled Attention](https://mlsanity.com/paper/2006.03654/) (2020)
- [Multitask Prompted Training Enables Zero-Shot Task Generalization](https://mlsanity.com/paper/2110.08207/) (2021)
- [LaMDA: Language Models for Dialog Applications](https://mlsanity.com/paper/2201.08239/) (2022)
- [Show Your Work: Scratchpads for Intermediate Computation with Language Models](https://mlsanity.com/paper/2112.00114/) (2021)
- [Solving General Arithmetic Word Problems](https://mlsanity.com/paper/1608.01413/) (2016)
- [A Diverse Corpus for Evaluating and Developing English Math Word Problem Solvers](https://mlsanity.com/paper/2106.15772/) (2021)
- [Improving Coherence and Consistency in Neural Sequence Models with Dual-System, Neuro-Symbolic Reasoning](https://mlsanity.com/paper/2107.02794/) (2021)
- [MWPToolkit: An Open-Source Framework for Deep Learning-Based Math Word Problem Solvers](https://mlsanity.com/paper/2109.00799/) (2021)
- [Unit Dependency Graph and its Application to Arithmetic Word Problem Solving](https://mlsanity.com/paper/1612.00969/) (2016)
- [To Beam Or Not To Beam: That is a Question of Cooperation for Language GANs](https://mlsanity.com/paper/2106.06363/) (2021)
- [A Disability Lens towards Biases in GPT-3 Generated Open-Ended Languages](https://mlsanity.com/paper/2206.11993/) (2022)

## Built on by (most cited first, 30 of 77)

- [Encouraging Divergent Thinking in Large Language Models through Multi-Agent Debate](https://mlsanity.com/paper/2305.19118/) (2023)
- [Math-Shepherd: Verify and Reinforce LLMs Step-by-step without Human Annotations](https://mlsanity.com/paper/2312.08935/) (2023)
- [WizardMath: Empowering Mathematical Reasoning for Large Language Models via Reinforced Evol-Instruct](https://mlsanity.com/paper/2308.09583/) (2023)
- [From System 1 to System 2: A Survey of Reasoning Large Language Models](https://mlsanity.com/paper/2502.17419/) (2025)
- [Alphazero-like Tree-Search can Guide Large Language Model Decoding and Training](https://mlsanity.com/paper/2309.17179/) (2023)
- [Large Language Models for Mathematical Reasoning: Progresses and Challenges](https://mlsanity.com/paper/2402.00157/) (2024)
- [ToRA: A Tool-Integrated Reasoning Agent for Mathematical Problem Solving](https://mlsanity.com/paper/2309.17452/) (2023)
- [Monte Carlo Tree Search Boosts Reasoning via Iterative Preference Learning](https://mlsanity.com/paper/2405.00451/) (2024)
- [Automatically Correcting Large Language Models: Surveying the landscape of diverse self-correction strategies](https://mlsanity.com/paper/2308.03188/) (2023)
- [V-STaR: Training Verifiers for Self-Taught Reasoners](https://mlsanity.com/paper/2402.06457/) (2024)
- [Agent AI: Surveying the Horizons of Multimodal Interaction](https://mlsanity.com/paper/2401.03568/) (2024)
- [AlphaMath Almost Zero: Process Supervision without Process](https://mlsanity.com/paper/2405.03553/) (2024)
- [The Surprising Effectiveness of Negative Reinforcement in LLM Reasoning](https://mlsanity.com/paper/2506.01347/) (2025)
- [Teaching Large Language Models to Reason with Reinforcement Learning](https://mlsanity.com/paper/2403.04642/) (2024)
- [InternLM-Math: Open Math Large Language Models Toward Verifiable Reasoning](https://mlsanity.com/paper/2402.06332/) (2024)
- [ToolChain*: Efficient Action Space Navigation in Large Language Models with A* Search](https://mlsanity.com/paper/2310.13227/) (2023)
- [ZoomEye: Enhancing Multimodal LLMs with Human-Like Zooming Capabilities through Tree-Based Image Exploration](https://mlsanity.com/paper/2411.16044/) (2024)
- [OVM, Outcome-supervised Value Models for Planning in Mathematical Reasoning](https://mlsanity.com/paper/2311.09724/) (2023)
- [Cognitive Mirage: A Review of Hallucinations in Large Language Models](https://mlsanity.com/paper/2309.06794/) (2023)
- [Self-Contrast: Better Reflection Through Inconsistent Solving Perspectives](https://mlsanity.com/paper/2401.02009/) (2024)
- [Corex: Pushing the Boundaries of Complex Reasoning through Multi-Model Collaboration](https://mlsanity.com/paper/2310.00280/) (2023)
- [LLM Reasoners: New Evaluation, Library, and Analysis of Step-by-Step Reasoning with Large Language Models](https://mlsanity.com/paper/2404.05221/) (2024)
- [Self-rewarding correction for mathematical reasoning](https://mlsanity.com/paper/2502.19613/) (2025)
- [Building Math Agents with Multi-Turn Iterative Preference Learning](https://mlsanity.com/paper/2409.02392/) (2024)
- [A Survey of Mathematical Reasoning in the Era of Multimodal Large Language Model: Benchmark, Method & Challenges](https://mlsanity.com/paper/2412.11936/) (2024)
- [Visual Agents as Fast and Slow Thinkers](https://mlsanity.com/paper/2408.08862/) (2024)
- [When is Tree Search Useful for LLM Planning? It Depends on the Discriminator](https://mlsanity.com/paper/2402.10890/) (2024)
- [Enhancing Large Language Models in Coding Through Multi-Perspective Self-Consistency](https://mlsanity.com/paper/2309.17272/) (2023)
- [xCoT: Cross-lingual Instruction Tuning for Cross-lingual Chain-of-Thought Reasoning](https://mlsanity.com/paper/2401.07037/) (2024)
- [MuggleMath: Assessing the Impact of Query and Response Augmentation on Math Reasoning](https://mlsanity.com/paper/2310.05506/) (2023)

## 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