# ChatGLM-Math: Improving Math Problem-Solving in Large Language Models with a Self-Critique Pipeline

arXiv: https://arxiv.org/abs/2404.02893 · HTML: https://mlsanity.com/paper/2404.02893/

## Key facts

- Cited by 47 papers in the map (data through 14 Oct 2026).
- Builds on 50 of its 69 references that are in the map.
- First posted on arXiv 3 Apr 2024.

## Builds on (most cited first, 30 of 50)

- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [Training language models to follow instructions with human feedback](https://mlsanity.com/paper/2203.02155/) (2022)
- [LLaMA: Open and Efficient Foundation Language Models](https://mlsanity.com/paper/2302.13971/) (2023)
- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [Judging LLM-as-a-Judge with MT-Bench and Chatbot Arena](https://mlsanity.com/paper/2306.05685/) (2023)
- [Direct Preference Optimization: Your Language Model is Secretly a Reward Model](https://mlsanity.com/paper/2305.18290/) (2023)
- [Measuring Massive Multitask Language Understanding](https://mlsanity.com/paper/2009.03300/) (2020)
- [Scaling Laws for Neural Language Models](https://mlsanity.com/paper/2001.08361/) (2020)
- [Self-Consistency Improves Chain of Thought Reasoning in Language Models](https://mlsanity.com/paper/2203.11171/) (2022)
- [Measuring Mathematical Problem Solving With the MATH Dataset](https://mlsanity.com/paper/2103.03874/) (2021)
- [PaLM: Scaling Language Modeling with Pathways](https://mlsanity.com/paper/2204.02311/) (2022)
- [Tree of Thoughts: Deliberate Problem Solving with Large Language Models](https://mlsanity.com/paper/2305.10601/) (2023)
- [Constitutional AI: Harmlessness from AI Feedback](https://mlsanity.com/paper/2212.08073/) (2022)
- [PIQA: Reasoning about Physical Commonsense in Natural Language](https://mlsanity.com/paper/1911.11641/) (2019)
- [BLOOM: A 176B-Parameter Open-Access Multilingual Language Model](https://mlsanity.com/paper/2211.05100/) (2022)
- [Challenging BIG-Bench Tasks and Whether Chain-of-Thought Can Solve Them](https://mlsanity.com/paper/2210.09261/) (2022)
- [LongBench: A Bilingual, Multitask Benchmark for Long Context Understanding](https://mlsanity.com/paper/2308.14508/) (2023)
- [Don't Give Me the Details, Just the Summary! Topic-Aware Convolutional Neural Networks for Extreme Summarization](https://mlsanity.com/paper/1808.08745/) (2018)
- [AgentBench: Evaluating LLMs as Agents](https://mlsanity.com/paper/2308.03688/) (2023)
- [A General Language Assistant as a Laboratory for Alignment](https://mlsanity.com/paper/2112.00861/) (2021)
- [Teaching Machines to Read and Comprehend](https://mlsanity.com/paper/1506.03340/) (2015)
- [GLM: General Language Model Pretraining with Autoregressive Blank Infilling](https://mlsanity.com/paper/2103.10360/) (2021)
- [Math-Shepherd: Verify and Reinforce LLMs Step-by-step without Human Annotations](https://mlsanity.com/paper/2312.08935/) (2023)
- [Graph of Thoughts: Solving Elaborate Problems with Large Language Models](https://mlsanity.com/paper/2308.09687/) (2023)
- [Large Language Models as Optimizers](https://mlsanity.com/paper/2309.03409/) (2023)
- [GLM-130B: An Open Bilingual Pre-trained Model](https://mlsanity.com/paper/2210.02414/) (2022)
- [MetaMath: Bootstrap Your Own Mathematical Questions for Large Language Models](https://mlsanity.com/paper/2309.12284/) (2023)
- [AGIEval: A Human-Centric Benchmark for Evaluating Foundation Models](https://mlsanity.com/paper/2304.06364/) (2023)
- [Program Induction by Rationale Generation : Learning to Solve and Explain Algebraic Word Problems](https://mlsanity.com/paper/1705.04146/) (2017)
- [DeepSeek LLM: Scaling Open-Source Language Models with Longtermism](https://mlsanity.com/paper/2401.02954/) (2024)

## Built on by (most cited first, 30 of 47)

- [Step-DPO: Step-wise Preference Optimization for Long-chain Reasoning of LLMs](https://mlsanity.com/paper/2406.18629/) (2024)
- [RLHF Workflow: From Reward Modeling to Online RLHF](https://mlsanity.com/paper/2405.07863/) (2024)
- [VisuLogic: A Benchmark for Evaluating Visual Reasoning in Multi-modal Large Language Models](https://mlsanity.com/paper/2504.15279/) (2025)
- [DART-Math: Difficulty-Aware Rejection Tuning for Mathematical Problem-Solving](https://mlsanity.com/paper/2407.13690/) (2024)
- [Lifelong Learning of Large Language Model based Agents: A Roadmap](https://mlsanity.com/paper/2501.07278/) (2025)
- [Self-Evolving Multi-Agent Collaboration Networks for Software Development](https://mlsanity.com/paper/2410.16946/) (2024)
- [A Survey of Mathematical Reasoning in the Era of Multimodal Large Language Model: Benchmark, Method & Challenges](https://mlsanity.com/paper/2412.11936/) (2024)
- [Internal Consistency and Self-Feedback in Large Language Models: A Survey](https://mlsanity.com/paper/2407.14507/) (2024)
- [JiuZhang3.0: Efficiently Improving Mathematical Reasoning by Training Small Data Synthesis Models](https://mlsanity.com/paper/2405.14365/) (2024)
- [MathCoder2: Better Math Reasoning from Continued Pretraining on Model-translated Mathematical Code](https://mlsanity.com/paper/2410.08196/) (2024)
- [Step-Controlled DPO: Leveraging Stepwise Error for Enhanced Mathematical Reasoning](https://mlsanity.com/paper/2407.00782/) (2024)
- [InternLM2.5-StepProver: Advancing Automated Theorem Proving via Critic-Guided Search](https://mlsanity.com/paper/2410.15700/) (2024)
- [Weak-to-Strong Reasoning](https://mlsanity.com/paper/2407.13647/) (2024)
- [Position: Multimodal Large Language Models Can Significantly Advance Scientific Reasoning](https://mlsanity.com/paper/2502.02871/) (2025)
- [Diving into Self-Evolving Training for Multimodal Reasoning](https://mlsanity.com/paper/2412.17451/) (2024)
- [3D-Properties: Identifying Challenges in DPO and Charting a Path Forward](https://mlsanity.com/paper/2406.07327/) (2024)
- [Skywork-Math: Data Scaling Laws for Mathematical Reasoning in Large Language Models -- The Story Goes On](https://mlsanity.com/paper/2407.08348/) (2024)
- [BoostStep: Boosting mathematical capability of Large Language Models via improved single-step reasoning](https://mlsanity.com/paper/2501.03226/) (2025)
- [LEMMA: Learning from Errors for MatheMatical Advancement in LLMs](https://mlsanity.com/paper/2503.17439/) (2025)
- [Multilingual Large Language Models: A Systematic Survey](https://mlsanity.com/paper/2411.11072/) (2024)
- [Self-Tuning: Instructing LLMs to Effectively Acquire New Knowledge through Self-Teaching](https://mlsanity.com/paper/2406.06326/) (2024)
- [Training Language Models to Critique With Multi-agent Feedback](https://mlsanity.com/paper/2410.15287/) (2024)
- [Full-Step-DPO: Self-Supervised Preference Optimization with Step-wise Rewards for Mathematical Reasoning](https://mlsanity.com/paper/2502.14356/) (2025)
- [APT: Improving Specialist LLM Performance with Weakness Case Acquisition and Iterative Preference Training](https://mlsanity.com/paper/2506.03483/) (2025)
- [HiPlan: Hierarchical Planning for LLM-Based Agents with Adaptive Global-Local Guidance](https://mlsanity.com/paper/2508.19076/) (2025)
- [System-2 Mathematical Reasoning via Enriched Instruction Tuning](https://mlsanity.com/paper/2412.16964/) (2024)
- [SIaM: Self-Improving Code-Assisted Mathematical Reasoning of Large Language Models](https://mlsanity.com/paper/2408.15565/) (2024)
- [GanitLLM: Difficulty-Aware Bengali Mathematical Reasoning through Curriculum-GRPO](https://mlsanity.com/paper/2601.06767/) (2026)
- [SED: Self-Evaluation Decoding Enhances Large Language Models for Better Generation](https://mlsanity.com/paper/2405.16552/) (2024)
- [Leveraging Web-Crawled Data for High-Quality Fine-Tuning](https://mlsanity.com/paper/2408.08003/) (2024)

## Abstract (arXiv)

Large language models (LLMs) have shown excellent mastering of human language, but still struggle in real-world applications that require mathematical problem-solving. While many strategies and datasets to enhance LLMs' mathematics are developed, it remains a challenge to simultaneously maintain and improve both language and mathematical capabilities in deployed LLM systems.In this work, we tailor the Self-Critique pipeline, which addresses the challenge in the feedback learning stage of LLM alignment. We first train a general Math-Critique model from the LLM itself to provide feedback signals. Then, we sequentially employ rejective fine-tuning and direct preference optimization over the LLM's own generations for data collection. Based on ChatGLM3-32B, we conduct a series of experiments on both academic and our newly created challenging dataset, MathUserEval. Results show that our pipeline significantly enhances the LLM's mathematical problem-solving while still improving its language ability, outperforming LLMs that could be two times larger. Related techniques have been deployed to ChatGLMfootnoteurlhttps://chatglm.cn, an online serving LLM. Related evaluation dataset and scripts are released at urlhttps://github.com/THUDM/ChatGLM-Math.