# Improving Arithmetic Reasoning Ability of Large Language Models through Relation Tuples, Verification and Dynamic Feedback

arXiv: https://arxiv.org/abs/2406.17873 · HTML: https://mlsanity.com/paper/2406.17873/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Placed in Mathematical reasoning, one of 17 directions in LLM reasoning.
- Builds on 25 of its 28 references that are in the map.
- First posted on arXiv 25 Jun 2024.

## Placed in

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

## Builds on (most cited first, 25 of 25)

- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [GPT-4 Technical Report](https://mlsanity.com/paper/2303.08774/) (2023)
- [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)
- [Efficient Memory Management for Large Language Model Serving with PagedAttention](https://mlsanity.com/paper/2309.06180/) (2023)
- [Self-Consistency Improves Chain of Thought Reasoning in Language Models](https://mlsanity.com/paper/2203.11171/) (2022)
- [Large Language Models are Zero-Shot Reasoners](https://mlsanity.com/paper/2205.11916/) (2022)
- [Self-Refine: Iterative Refinement with Self-Feedback](https://mlsanity.com/paper/2303.17651/) (2023)
- [Show Your Work: Scratchpads for Intermediate Computation with Language Models](https://mlsanity.com/paper/2112.00114/) (2021)
- [Are NLP Models really able to Solve Simple Math Word Problems?](https://mlsanity.com/paper/2103.07191/) (2021)
- [Large Language Models Can Self-Improve](https://mlsanity.com/paper/2210.11610/) (2022)
- [A Diverse Corpus for Evaluating and Developing English Math Word Problem Solvers](https://mlsanity.com/paper/2106.15772/) (2021)
- [Think before you speak: Training Language Models With Pause Tokens](https://mlsanity.com/paper/2310.02226/) (2023)
- [Reasoning with Language Model Prompting: A Survey](https://mlsanity.com/paper/2212.09597/) (2022)
- [Solving Challenging Math Word Problems Using GPT-4 Code Interpreter with Code-based Self-Verification](https://mlsanity.com/paper/2308.07921/) (2023)
- [MathCoder: Seamless Code Integration in LLMs for Enhanced Mathematical Reasoning](https://mlsanity.com/paper/2310.03731/) (2023)
- [Faithful Logical Reasoning via Symbolic Chain-of-Thought](https://mlsanity.com/paper/2405.18357/) (2024)
- [Language Models Can Teach Themselves to Program Better](https://mlsanity.com/paper/2207.14502/) (2022)
- [Iteratively Prompt Pre-trained Language Models for Chain of Thought](https://mlsanity.com/paper/2203.08383/) (2022)
- [Don't Trust: Verify -- Grounding LLM Quantitative Reasoning with Autoformalization](https://mlsanity.com/paper/2403.18120/) (2024)
- [Automatic Model Selection with Large Language Models for Reasoning](https://mlsanity.com/paper/2305.14333/) (2023)
- [FaiRR: Faithful and Robust Deductive Reasoning over Natural Language](https://mlsanity.com/paper/2203.10261/) (2022)
- [Teaching Language Models to Self-Improve through Interactive Demonstrations](https://mlsanity.com/paper/2310.13522/) (2023)
- [ERA-CoT: Improving Chain-of-Thought through Entity Relationship Analysis](https://mlsanity.com/paper/2403.06932/) (2024)
- [Calc-X and Calcformers: Empowering Arithmetical Chain-of-Thought through Interaction with Symbolic Systems](https://mlsanity.com/paper/2305.15017/) (2023)

## Built on by (most cited first, 4 of 4)

- [Improving LLM Reasoning through Scaling Inference Computation with Collaborative Verification](https://mlsanity.com/paper/2410.05318/) (2024)
- [ActionVOS: Actions as Prompts for Video Object Segmentation](https://mlsanity.com/paper/2407.07402/) (2024)
- [Direct Quantized Training of Language Models with Stochastic Rounding](https://mlsanity.com/paper/2412.04787/) (2024)
- [GRC: Unifying Reasoning-Driven Generation, Retrieval and Compression](https://mlsanity.com/paper/2605.09100/) (2026)

## Abstract (arXiv)

Current representations used in reasoning steps of large language models can mostly be categorized into two main types: (1) natural language, which is difficult to verify; and (2) non-natural language, usually programming code, which is difficult for people who are unfamiliar with coding to read. In this paper, we propose to use a semi-structured form to represent reasoning steps of large language models. Specifically, we use relation tuples, which are not only human-readable but also machine-friendly and easier to verify than natural language. We implement a framework that includes three main components: (1) introducing relation tuples into the reasoning steps of large language models; (2) implementing an automatic verification process of reasoning steps with a local code interpreter based on relation tuples; and (3) integrating a simple and effective dynamic feedback mechanism, which we found helpful for self-improvement of large language models. The experimental results on various arithmetic datasets demonstrate the effectiveness of our method in improving the arithmetic reasoning ability of large language models. The source code is available at https://github.com/gpgg/art.