# Learning Mathematical Rules with Large Language Models

arXiv: https://arxiv.org/abs/2410.16973 · HTML: https://mlsanity.com/paper/2410.16973/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 24 of its 28 references that are in the map.
- First posted on arXiv 22 Oct 2024.

## Builds on (most cited first, 24 of 24)

- [Llama 2: Open Foundation and Fine-Tuned Chat Models](https://mlsanity.com/paper/2307.09288/) (2023)
- [DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models](https://mlsanity.com/paper/2402.03300/) (2024)
- [Measuring Massive Multitask Language Understanding](https://mlsanity.com/paper/2009.03300/) (2020)
- [Think you have Solved Question Answering? Try ARC, the AI2 Reasoning Challenge](https://mlsanity.com/paper/1803.05457/) (2018)
- [HellaSwag: Can a Machine Really Finish Your Sentence?](https://mlsanity.com/paper/1905.07830/) (2019)
- [QLoRA: Efficient Finetuning of Quantized LLMs](https://mlsanity.com/paper/2305.14314/) (2023)
- [Sparks of Artificial General Intelligence: Early experiments with GPT-4](https://mlsanity.com/paper/2303.12712/) (2023)
- [Solving Quantitative Reasoning Problems with Language Models](https://mlsanity.com/paper/2206.14858/) (2022)
- [Galactica: A Large Language Model for Science](https://mlsanity.com/paper/2211.09085/) (2022)
- [WizardMath: Empowering Mathematical Reasoning for Large Language Models via Reinforced Evol-Instruct](https://mlsanity.com/paper/2308.09583/) (2023)
- [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)
- [LeanDojo: Theorem Proving with Retrieval-Augmented Language Models](https://mlsanity.com/paper/2306.15626/) (2023)
- [Scaling Relationship on Learning Mathematical Reasoning with Large Language Models](https://mlsanity.com/paper/2308.01825/) (2023)
- [Llemma: An Open Language Model For Mathematics](https://mlsanity.com/paper/2310.10631/) (2023)
- [Orca: Progressive Learning from Complex Explanation Traces of GPT-4](https://mlsanity.com/paper/2306.02707/) (2023)
- [LoRA+: Efficient Low Rank Adaptation of Large Models](https://mlsanity.com/paper/2402.12354/) (2024)
- [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)
- [Deep Learning for Symbolic Mathematics](https://mlsanity.com/paper/1912.01412/) (2019)
- [MathPrompter: Mathematical Reasoning using Large Language Models](https://mlsanity.com/paper/2303.05398/) (2023)
- [Progressive-Hint Prompting Improves Reasoning in Large Language Models](https://mlsanity.com/paper/2304.09797/) (2023)
- [Length Generalization in Arithmetic Transformers](https://mlsanity.com/paper/2306.15400/) (2023)
- [An Empirical Study of Data Ability Boundary in LLMs' Math Reasoning](https://mlsanity.com/paper/2403.00799/) (2024)

## Built on by (most cited first, 1 of 1)

- [Unraveling Arithmetic in Large Language Models: The Role of Algebraic Structures](https://mlsanity.com/paper/2411.16260/) (2024)

## Abstract (arXiv)

In this paper, we study the ability of large language models to learn specific mathematical rules such as distributivity or simplifying equations. We present an empirical analysis of their ability to generalize these rules, as well as to reuse them in the context of word problems. For this purpose, we provide a rigorous methodology to build synthetic data incorporating such rules, and perform fine-tuning of large language models on such data. Our experiments show that our model can learn and generalize these rules to some extent, as well as suitably reuse them in the context of word problems.