# MetaRuleGPT: Recursive Numerical Reasoning of Language Models Trained with Simple Rules

arXiv: https://arxiv.org/abs/2412.13536 · HTML: https://mlsanity.com/paper/2412.13536/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Placed in Mathematical reasoning, one of 17 directions in LLM reasoning.
- Builds on 24 of its 31 references that are in the map.
- First posted on arXiv 18 Dec 2024.

## Placed in

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

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

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [Llama 2: Open Foundation and Fine-Tuned Chat Models](https://mlsanity.com/paper/2307.09288/) (2023)
- [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)
- [Measuring Massive Multitask Language Understanding](https://mlsanity.com/paper/2009.03300/) (2020)
- [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)
- [Model-Agnostic Meta-Learning for Fast Adaptation of Deep Networks](https://mlsanity.com/paper/1703.03400/) (2017)
- [Finetuned Language Models Are Zero-Shot Learners](https://mlsanity.com/paper/2109.01652/) (2021)
- [Qwen Technical Report](https://mlsanity.com/paper/2309.16609/) (2023)
- [PIQA: Reasoning about Physical Commonsense in Natural Language](https://mlsanity.com/paper/1911.11641/) (2019)
- [Least-to-Most Prompting Enables Complex Reasoning in Large Language Models](https://mlsanity.com/paper/2205.10625/) (2022)
- [Don't Give Me the Details, Just the Summary! Topic-Aware Convolutional Neural Networks for Extreme Summarization](https://mlsanity.com/paper/1808.08745/) (2018)
- [PaLM 2 Technical Report](https://mlsanity.com/paper/2305.10403/) (2023)
- [Teaching Machines to Read and Comprehend](https://mlsanity.com/paper/1506.03340/) (2015)
- [Math-Shepherd: Verify and Reinforce LLMs Step-by-step without Human Annotations](https://mlsanity.com/paper/2312.08935/) (2023)
- [MetaMath: Bootstrap Your Own Mathematical Questions for Large Language Models](https://mlsanity.com/paper/2309.12284/) (2023)
- [WizardMath: Empowering Mathematical Reasoning for Large Language Models via Reinforced Evol-Instruct](https://mlsanity.com/paper/2308.09583/) (2023)
- [ERNIE: Enhanced Language Representation with Informative Entities](https://mlsanity.com/paper/1905.07129/) (2019)
- [Complexity-Based Prompting for Multi-Step Reasoning](https://mlsanity.com/paper/2210.00720/) (2022)
- [Meta-Learning: A Survey](https://mlsanity.com/paper/1810.03548/) (2018)
- [Goat: Fine-tuned LLaMA Outperforms GPT-4 on Arithmetic Tasks](https://mlsanity.com/paper/2305.14201/) (2023)
- [Recursion of Thought: A Divide-and-Conquer Approach to Multi-Context Reasoning with Language Models](https://mlsanity.com/paper/2306.06891/) (2023)

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

- [NumPert: Numerical Perturbations to Probe Language Models for Veracity Prediction](https://mlsanity.com/paper/2511.09971/) (2025)

## Abstract (arXiv)

Recent studies have highlighted the limitations of large language models in mathematical reasoning, particularly their inability to capture the underlying logic. Inspired by meta-learning, we propose that models should acquire not only task-specific knowledge but also transferable problem-solving skills. We introduce MetaRuleGPT, a novel Transformer-based architecture that performs precise numerical calculations and complex logical operations by learning and combining different rules. In contrast with traditional training sets, which are heavily composed of massive raw instance data, MetaRuleGPT is pre-trained on much less abstract datasets containing basic, compound, and iterative rules for mathematical reasoning. Extensive experimental results demonstrate MetaRuleGPT can mimic human's rule-following capabilities, break down complexity, and iteratively derive accurate results for complex mathematical problems. These findings prove the potential of rule learning to enhance the numerical reasoning abilities of language models.