# CoMAT: Chain of Mathematically Annotated Thought Improves Mathematical Reasoning

arXiv: https://arxiv.org/abs/2410.10336 · HTML: https://mlsanity.com/paper/2410.10336/

## Key facts

- Cited by 16 papers in the map (data through 14 Oct 2026).
- Placed in Mathematical reasoning, one of 17 directions in LLM reasoning.
- Builds on 47 of its 69 references that are in the map.
- First posted on arXiv 14 Oct 2024.

## Placed in

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

## Builds on (most cited first, 30 of 47)

- [GPT-4 Technical Report](https://mlsanity.com/paper/2303.08774/) (2023)
- [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)
- [Measuring Mathematical Problem Solving With the MATH Dataset](https://mlsanity.com/paper/2103.03874/) (2021)
- [Let's Verify Step by Step](https://mlsanity.com/paper/2305.20050/) (2023)
- [Qwen2 Technical Report](https://mlsanity.com/paper/2407.10671/) (2024)
- [Scaling LLM Test-Time Compute Optimally can be More Effective than Scaling Model Parameters](https://mlsanity.com/paper/2408.03314/) (2024)
- [OlympiadBench: A Challenging Benchmark for Promoting AGI with Olympiad-Level Bilingual Multimodal Scientific Problems](https://mlsanity.com/paper/2402.14008/) (2024)
- [Program of Thoughts Prompting: Disentangling Computation from Reasoning for Numerical Reasoning Tasks](https://mlsanity.com/paper/2211.12588/) (2022)
- [Gemini: A Family of Highly Capable Multimodal Models](https://mlsanity.com/paper/2312.11805/) (2023)
- [CRITIC: Large Language Models Can Self-Correct with Tool-Interactive Critiquing](https://mlsanity.com/paper/2305.11738/) (2023)
- [Automatic Chain of Thought Prompting in Large Language Models](https://mlsanity.com/paper/2210.03493/) (2022)
- [Program Induction by Rationale Generation : Learning to Solve and Explain Algebraic Word Problems](https://mlsanity.com/paper/1705.04146/) (2017)
- [Plan-and-Solve Prompting: Improving Zero-Shot Chain-of-Thought Reasoning by Large Language Models](https://mlsanity.com/paper/2305.04091/) (2023)
- [GSM-Symbolic: Understanding the Limitations of Mathematical Reasoning in Large Language Models](https://mlsanity.com/paper/2410.05229/) (2024)
- [Language Models are Multilingual Chain-of-Thought Reasoners](https://mlsanity.com/paper/2210.03057/) (2022)
- [Improve Mathematical Reasoning in Language Models by Automated Process Supervision](https://mlsanity.com/paper/2406.06592/) (2024)
- [Logic-LM: Empowering Large Language Models with Symbolic Solvers for Faithful Logical Reasoning](https://mlsanity.com/paper/2305.12295/) (2023)
- [Solving General Arithmetic Word Problems](https://mlsanity.com/paper/1608.01413/) (2016)
- [Draft, Sketch, and Prove: Guiding Formal Theorem Provers with Informal Proofs](https://mlsanity.com/paper/2210.12283/) (2022)
- [Faithful Chain-of-Thought Reasoning](https://mlsanity.com/paper/2301.13379/) (2023)
- [Large Language Models for Mathematical Reasoning: Progresses and Challenges](https://mlsanity.com/paper/2402.00157/) (2024)
- [MathPrompter: Mathematical Reasoning using Large Language Models](https://mlsanity.com/paper/2303.05398/) (2023)
- [Are We Done with MMLU?](https://mlsanity.com/paper/2406.04127/) (2024)
- [Evaluating the Performance of Large Language Models on GAOKAO Benchmark](https://mlsanity.com/paper/2305.12474/) (2023)
- [Navigate through Enigmatic Labyrinth A Survey of Chain of Thought Reasoning: Advances, Frontiers and Future](https://mlsanity.com/paper/2309.15402/) (2023)
- [LINC: A Neurosymbolic Approach for Logical Reasoning by Combining Language Models with First-Order Logic Provers](https://mlsanity.com/paper/2310.15164/) (2023)
- [Symbolic Chain-of-Thought Distillation: Small Models Can Also "Think" Step-by-Step](https://mlsanity.com/paper/2306.14050/) (2023)
- [Holistic Evaluation of Language Models](https://mlsanity.com/paper/2211.09110/) (2022)
- [Solving Math Word Problems by Combining Language Models With Symbolic Solvers](https://mlsanity.com/paper/2304.09102/) (2023)

## Built on by (most cited first, 16 of 16)

- [Towards Reasoning Era: A Survey of Long Chain-of-Thought for Reasoning Large Language Models](https://mlsanity.com/paper/2503.09567/) (2025)
- [Can 1B LLM Surpass 405B LLM? Rethinking Compute-Optimal Test-Time Scaling](https://mlsanity.com/paper/2502.06703/) (2025)
- [A Comprehensive Survey on Trustworthiness in Reasoning with Large Language Models](https://mlsanity.com/paper/2509.03871/) (2025)
- [Improving Chain-of-Thought Reasoning via Quasi-Symbolic Abstractions](https://mlsanity.com/paper/2502.12616/) (2025)
- [Theorem Prover as a Judge for Synthetic Data Generation](https://mlsanity.com/paper/2502.13137/) (2025)
- [From What to Why: A Multi-Agent System for Evidence-based Chemical Reaction Condition Reasoning](https://mlsanity.com/paper/2509.23768/) (2025)
- [PiCSAR: Probabilistic Confidence Selection And Ranking for Reasoning Chains](https://mlsanity.com/paper/2508.21787/) (2025)
- [DTS: Enhancing Large Reasoning Models via Decoding Tree Sketching](https://mlsanity.com/paper/2511.00640/) (2025)
- [Pythagoras-Prover: Advancing Efficient Formal Proving via Augmented Lean Formalisation](https://mlsanity.com/paper/2606.12594/) (2026)
- [Can Large Reasoning Models Improve Accuracy on Mathematical Tasks Using Flawed Thinking?](https://mlsanity.com/paper/2512.17079/) (2025)
- [One More Question is Enough, Expert Question Decomposition (EQD) Model for Domain Quantitative Reasoning](https://mlsanity.com/paper/2510.01526/) (2025)
- [Can I Have Your Order? Monte-Carlo Tree Search for Slot Filling Ordering in Diffusion Language Models](https://mlsanity.com/paper/2602.12586/) (2026)
- [Systematic Optimization of Open Source Large Language Models for Mathematical Reasoning](https://mlsanity.com/paper/2509.07238/) (2025)
- [Value-Aware Numerical Representations for Transformer Language Models](https://mlsanity.com/paper/2601.09706/) (2026)
- [Agent-GWO: Collaborative Agents for Dynamic Prompt Optimization in Large Language Models](https://mlsanity.com/paper/2604.18612/) (2026)
- [When Tokenization is Secretly Output Supervision](https://mlsanity.com/paper/2609.01386/) (2026)

## Abstract (arXiv)

Mathematical reasoning remains a significant challenge for large language models (LLMs), despite progress in prompting techniques such as Chain-of-Thought (CoT). We present **Chain of Mathematically Annotated Thought (CoMAT)**, which enhances reasoning through two stages: *Symbolic Conversion* (converting natural language queries into symbolic form) and *Reasoning Execution* (deriving answers from symbolic representations). CoMAT operates entirely with a single LLM and without external solvers. Across four LLMs, CoMAT outperforms traditional CoT on six out of seven benchmarks, achieving gains of 4.48% on MMLU-Redux (MATH) and 4.58% on GaoKao MCQ. In addition to improved performance, CoMAT ensures faithfulness and verifiability, offering a transparent reasoning process for complex mathematical tasks