# Analogical Math Word Problems Solving with Enhanced Problem-Solution Association

arXiv: https://arxiv.org/abs/2212.00837 · HTML: https://mlsanity.com/paper/2212.00837/

## 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 51 references that are in the map.
- First posted on arXiv 1 Dec 2022.

## Placed in

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

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

- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://mlsanity.com/paper/1810.04805/) (2018)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Learning Phrase Representations using RNN Encoder-Decoder for Statistical Machine Translation](https://mlsanity.com/paper/1406.1078/) (2014)
- [Towards Evaluating the Robustness of Neural Networks](https://mlsanity.com/paper/1608.04644/) (2016)
- [Empirical Evaluation of Gated Recurrent Neural Networks on Sequence Modeling](https://mlsanity.com/paper/1412.3555/) (2014)
- [MathQA: Towards Interpretable Math Word Problem Solving with Operation-Based Formalisms](https://mlsanity.com/paper/1905.13319/) (2019)
- [Revisiting Pre-Trained Models for Chinese Natural Language Processing](https://mlsanity.com/paper/2004.13922/) (2020)
- [Nearest Neighbor Machine Translation](https://mlsanity.com/paper/2010.00710/) (2020)
- [A Survey on Retrieval-Augmented Text Generation](https://mlsanity.com/paper/2202.01110/) (2022)
- [Birds have four legs?! NumerSense: Probing Numerical Commonsense Knowledge of Pre-trained Language Models](https://mlsanity.com/paper/2005.00683/) (2020)
- [Efficient Nearest Neighbor Language Models](https://mlsanity.com/paper/2109.04212/) (2021)
- [Generate & Rank: A Multi-task Framework for Math Word Problems](https://mlsanity.com/paper/2109.03034/) (2021)
- [Translating a Math Word Problem to an Expression Tree](https://mlsanity.com/paper/1811.05632/) (2018)
- [Learning to Reason Deductively: Math Word Problem Solving as Complex Relation Extraction](https://mlsanity.com/paper/2203.10316/) (2022)
- [Neural-Symbolic Solver for Math Word Problems with Auxiliary Tasks](https://mlsanity.com/paper/2107.01431/) (2021)
- [MWP-BERT: Numeracy-Augmented Pre-training for Math Word Problem Solving](https://mlsanity.com/paper/2107.13435/) (2021)
- [The Gap of Semantic Parsing: A Survey on Automatic Math Word Problem Solvers](https://mlsanity.com/paper/1808.07290/) (2018)
- [Seeking Patterns, Not just Memorizing Procedures: Contrastive Learning for Solving Math Word Problems](https://mlsanity.com/paper/2110.08464/) (2021)
- [Learning Kernel-Smoothed Machine Translation with Retrieved Examples](https://mlsanity.com/paper/2109.09991/) (2021)
- [Relational Memory Augmented Language Models](https://mlsanity.com/paper/2201.09680/) (2022)
- [LogicSolver: Towards Interpretable Math Word Problem Solving with Logical Prompt-enhanced Learning](https://mlsanity.com/paper/2205.08232/) (2022)
- [Investigating Math Word Problems using Pretrained Multilingual Language Models](https://mlsanity.com/paper/2105.08928/) (2021)
- [SMART: A Situation Model for Algebra Story Problems via Attributed Grammar](https://mlsanity.com/paper/2012.14011/) (2020)
- [Recall and Learn: A Memory-augmented Solver for Math Word Problems](https://mlsanity.com/paper/2109.13112/) (2021)
- [Towards Tractable Mathematical Reasoning: Challenges, Strategies, and Opportunities for Solving Math Word Problems](https://mlsanity.com/paper/2111.05364/) (2021)

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

- [Let GPT be a Math Tutor: Teaching Math Word Problem Solvers with Customized Exercise Generation](https://mlsanity.com/paper/2305.14386/) (2023)
- [MinT: Boosting Generalization in Mathematical Reasoning via Multi-View Fine-Tuning](https://mlsanity.com/paper/2307.07951/) (2023)
- [An Expression Tree Decoding Strategy for Mathematical Equation Generation](https://mlsanity.com/paper/2310.09619/) (2023)
- [From Large to Tiny: Distilling and Refining Mathematical Expertise for Math Word Problems with Weakly Supervision](https://mlsanity.com/paper/2403.14390/) (2024)

## Abstract (arXiv)

Math word problem (MWP) solving is an important task in question answering which requires human-like reasoning ability. Analogical reasoning has long been used in mathematical education, as it enables students to apply common relational structures of mathematical situations to solve new problems. In this paper, we propose to build a novel MWP solver by leveraging analogical MWPs, which advance the solver's generalization ability across different kinds of MWPs. The key idea, named analogy identification, is to associate the analogical MWP pairs in a latent space, i.e., encoding an MWP close to another analogical MWP, while moving away from the non-analogical ones. Moreover, a solution discriminator is integrated into the MWP solver to enhance the association between the representations of MWPs and their true solutions. The evaluation results verify that our proposed analogical learning strategy promotes the performance of MWP-BERT on Math23k over the state-of-the-art model Generate2Rank, with 5 times fewer parameters in the encoder. We also find that our model has a stronger generalization ability in solving difficult MWPs due to the analogical learning from easy MWPs.