# Gap-Filling Prompting Enhances Code-Assisted Mathematical Reasoning

arXiv: https://arxiv.org/abs/2411.05407 · HTML: https://mlsanity.com/paper/2411.05407/

## 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 10 of its 23 references that are in the map.
- First posted on arXiv 8 Nov 2024.

## Placed in

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

## Builds on (most cited first, 10 of 10)

- [Llama 2: Open Foundation and Fine-Tuned Chat Models](https://mlsanity.com/paper/2307.09288/) (2023)
- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [Code Llama: Open Foundation Models for Code](https://mlsanity.com/paper/2308.12950/) (2023)
- [Least-to-Most Prompting Enables Complex Reasoning in Large Language Models](https://mlsanity.com/paper/2205.10625/) (2022)
- [Program of Thoughts Prompting: Disentangling Computation from Reasoning for Numerical Reasoning Tasks](https://mlsanity.com/paper/2211.12588/) (2022)
- [Platypus: Quick, Cheap, and Powerful Refinement of LLMs](https://mlsanity.com/paper/2308.07317/) (2023)
- [Progressive-Hint Prompting Improves Reasoning in Large Language Models](https://mlsanity.com/paper/2304.09797/) (2023)
- [Achieving >97% on GSM8K: Deeply Understanding the Problems Makes LLMs Better Solvers for Math Word Problems](https://mlsanity.com/paper/2404.14963/) (2024)
- [Hint-before-Solving Prompting: Guiding LLMs to Effectively Utilize Encoded Knowledge](https://mlsanity.com/paper/2402.14310/) (2024)
- [Key-Point-Driven Mathematical Reasoning Distillation of Large Language Model](https://mlsanity.com/paper/2407.10167/) (2024)

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

- [Dynamic Policy Induction for Adaptive Prompt Optimization: Bridging the Efficiency-Accuracy Gap via Lightweight Reinforcement Learning](https://mlsanity.com/paper/2509.25267/) (2025)

## Abstract (arXiv)

Despite the strong performance of large language models (LLMs) in tasks like mathematical reasoning, their practical use is limited by high computational demands and proprietary restrictions. Chain-of-thought (CoT) and program-of-thought (PoT) fine-tuning are common methods to transfer LLM knowledge to small language models (SLMs). However, CoT often leads to calculation errors in SLMs, while PoT has shown more promise. While most PoT-based approaches focus on direct problem-to-code conversion or extracting only the key information from questions and then providing code solution for it, this work emphasizes filling the gaps in the question to clearly illustrate the solution path, which can be challenging for an SLM to understand when such information is not explicitly provided. Therefore, this paper introduces Gap-Filling Prompting (GFP), a novel two-step prompting strategy designed to enhance the problem-solving process for SLMs. The first step identifies these gaps and provides hints for filling them, while the second step adds the hints to the question to generate a final code solution. Experimental results on two benchmark datasets demonstrate that GFP significantly improves the mathematical reasoning abilities of SLMs.