# Learning by Analogy: Enhancing Few-Shot Prompting for Math Word Problem Solving with Computational Graph-Based Retrieval

arXiv: https://arxiv.org/abs/2411.16454 · HTML: https://mlsanity.com/paper/2411.16454/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 29 of its 43 references that are in the map.
- First posted on arXiv 25 Nov 2024.

## Builds on (most cited first, 29 of 29)

- [GPT-4 Technical Report](https://mlsanity.com/paper/2303.08774/) (2023)
- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [A Simple Framework for Contrastive Learning of Visual Representations](https://mlsanity.com/paper/2002.05709/) (2020)
- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [Retrieval-Augmented Generation for Knowledge-Intensive NLP Tasks](https://mlsanity.com/paper/2005.11401/) (2020)
- [Representation Learning with Contrastive Predictive Coding](https://mlsanity.com/paper/1807.03748/) (2018)
- [Momentum Contrast for Unsupervised Visual Representation Learning](https://mlsanity.com/paper/1911.05722/) (2019)
- [Retrieval-Augmented Generation for Large Language Models: A Survey](https://mlsanity.com/paper/2312.10997/) (2023)
- [Text Embeddings by Weakly-Supervised Contrastive Pre-training](https://mlsanity.com/paper/2212.03533/) (2022)
- [Qwen2.5-Math Technical Report: Toward Mathematical Expert Model via Self-Improvement](https://mlsanity.com/paper/2409.12122/) (2024)
- [MathQA: Towards Interpretable Math Word Problem Solving with Operation-Based Formalisms](https://mlsanity.com/paper/1905.13319/) (2019)
- [Program Induction by Rationale Generation : Learning to Solve and Explain Algebraic Word Problems](https://mlsanity.com/paper/1705.04146/) (2017)
- [LLM2Vec: Large Language Models Are Secretly Powerful Text Encoders](https://mlsanity.com/paper/2404.05961/) (2024)
- [BioMistral: A Collection of Open-Source Pretrained Large Language Models for Medical Domains](https://mlsanity.com/paper/2402.10373/) (2024)
- [OpenMathInstruct-2: Accelerating AI for Math with Massive Open-Source Instruction Data](https://mlsanity.com/paper/2410.01560/) (2024)
- [Are Graph Augmentations Necessary? Simple Graph Contrastive Learning for Recommendation](https://mlsanity.com/paper/2112.08679/) (2021)
- [Distilling System 2 into System 1](https://mlsanity.com/paper/2407.06023/) (2024)
- [Ape210K: A Large-Scale and Template-Rich Dataset of Math Word Problems](https://mlsanity.com/paper/2009.11506/) (2020)
- [Large Language Models Are Not Strong Abstract Reasoners](https://mlsanity.com/paper/2305.19555/) (2023)
- [Pretraining with Contrastive Sentence Objectives Improves Discourse Performance of Language Models](https://mlsanity.com/paper/2005.10389/) (2020)
- [Retrieval-augmented Generation to Improve Math Question-Answering: Trade-offs Between Groundedness and Human Preference](https://mlsanity.com/paper/2310.03184/) (2023)
- [Deceptive Semantic Shortcuts on Reasoning Chains: How Far Can Models Go without Hallucination?](https://mlsanity.com/paper/2311.09702/) (2023)
- [Cause and Effect: Can Large Language Models Truly Understand Causality?](https://mlsanity.com/paper/2402.18139/) (2024)
- [What Makes Math Word Problems Challenging for LLMs?](https://mlsanity.com/paper/2403.11369/) (2024)
- [Calc-X and Calcformers: Empowering Arithmetical Chain-of-Thought through Interaction with Symbolic Systems](https://mlsanity.com/paper/2305.15017/) (2023)
- [Can Large Language Models Reason? A Characterization via 3-SAT](https://mlsanity.com/paper/2408.07215/) (2024)
- [SuperCLUE-Math6: Graded Multi-Step Math Reasoning Benchmark for LLMs in Chinese](https://mlsanity.com/paper/2401.11819/) (2024)
- [CAMBranch: Contrastive Learning with Augmented MILPs for Branching](https://mlsanity.com/paper/2402.03647/) (2024)
- [Panacea: A foundation model for clinical trial search, summarization, design, and recruitment](https://mlsanity.com/paper/2407.11007/) (2024)

## Built on by (most cited first, 5 of 5)

- [LLMs with in-context learning for Algorithmic Theoretical Physics](https://mlsanity.com/paper/2605.08212/) (2026)
- [Learning to Reason by Analogy via Retrieval-Augmented Reinforcement Fine-Tuning](https://mlsanity.com/paper/2606.13680/) (2026)
- [SABER-Math: Automated Benchmark for Information Retrieval Evaluation in Mathematics](https://mlsanity.com/paper/2606.29894/) (2026)
- [LLM2IR: simple unsupervised contrastive learning makes long-context LLM great retriever](https://mlsanity.com/paper/2601.05262/) (2025)
- [Sparse Autoencoders Are a Shared Coordinate System for Symbolic Matching](https://mlsanity.com/paper/2610.19636/) (2026)

## Abstract (arXiv)

Large language models (LLMs) are known to struggle with complicated reasoning tasks such as math word problems (MWPs). In this paper, we present how analogy from similarly structured questions can improve LLMs' problem-solving capabilities for MWPs. Specifically, we rely on the retrieval of problems with similar computational graphs to the given question to serve as exemplars in the prompt, providing the correct reasoning path for the generation model to refer to. Empirical results across six math word problem datasets demonstrate the effectiveness of our proposed method, which achieves a significant improvement of up to 6.7 percent on average in absolute value, compared to baseline methods. These results highlight our method's potential in addressing the reasoning challenges in current LLMs.