# Translating a Math Word Problem to an Expression Tree

arXiv: https://arxiv.org/abs/1811.05632 · HTML: https://mlsanity.com/paper/1811.05632/

## Key facts

- Cited by 57 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 14 Nov 2018.

## Built on by (most cited first, 30 of 57)

- [Inter-GPS: Interpretable Geometry Problem Solving with Formal Language and Symbolic Reasoning](https://mlsanity.com/paper/2105.04165/) (2021)
- [Large Language Models are Better Reasoners with Self-Verification](https://mlsanity.com/paper/2212.09561/) (2022)
- [GeoQA: A Geometric Question Answering Benchmark Towards Multimodal Numerical Reasoning](https://mlsanity.com/paper/2105.14517/) (2021)
- [A Survey of Deep Learning for Mathematical Reasoning](https://mlsanity.com/paper/2212.10535/) (2022)
- [Generate & Rank: A Multi-task Framework for Math Word Problems](https://mlsanity.com/paper/2109.03034/) (2021)
- [Towards Complex Document Understanding By Discrete Reasoning](https://mlsanity.com/paper/2207.11871/) (2022)
- [Logic-Driven Context Extension and Data Augmentation for Logical Reasoning of Text](https://mlsanity.com/paper/2105.03659/) (2021)
- [From LSAT: The Progress and Challenges of Complex Reasoning](https://mlsanity.com/paper/2108.00648/) (2021)
- [MWPToolkit: An Open-Source Framework for Deep Learning-Based Math Word Problem Solvers](https://mlsanity.com/paper/2109.00799/) (2021)
- [Neural-Symbolic Solver for Math Word Problems with Auxiliary Tasks](https://mlsanity.com/paper/2107.01431/) (2021)
- [Towards Data-and Knowledge-Driven Artificial Intelligence: A Survey on Neuro-Symbolic Computing](https://mlsanity.com/paper/2210.15889/) (2022)
- [MWP-BERT: Numeracy-Augmented Pre-training for Math Word Problem Solving](https://mlsanity.com/paper/2107.13435/) (2021)
- [Let GPT be a Math Tutor: Teaching Math Word Problem Solvers with Customized Exercise Generation](https://mlsanity.com/paper/2305.14386/) (2023)
- [Math Word Problem Generation with Mathematical Consistency and Problem Context Constraints](https://mlsanity.com/paper/2109.04546/) (2021)
- [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)
- [Can neural networks do arithmetic? A survey on the elementary numerical skills of state-of-the-art deep learning models](https://mlsanity.com/paper/2303.07735/) (2023)
- [Interpretable Math Word Problem Solution Generation Via Step-by-step Planning](https://mlsanity.com/paper/2306.00784/) (2023)
- [MinT: Boosting Generalization in Mathematical Reasoning via Multi-View Fine-Tuning](https://mlsanity.com/paper/2307.07951/) (2023)
- [Using Large Language Model to Solve and Explain Physics Word Problems Approaching Human Level](https://mlsanity.com/paper/2309.08182/) (2023)
- [NOAHQA: Numerical Reasoning with Interpretable Graph Question Answering Dataset](https://mlsanity.com/paper/2109.10604/) (2021)
- [ELASTIC: Numerical Reasoning with Adaptive Symbolic Compiler](https://mlsanity.com/paper/2210.10105/) (2022)
- [Recall and Learn: A Memory-augmented Solver for Math Word Problems](https://mlsanity.com/paper/2109.13112/) (2021)
- [Self-consistent Reasoning For Solving Math Word Problems](https://mlsanity.com/paper/2210.15373/) (2022)
- [Unbiased Math Word Problems Benchmark for Mitigating Solving Bias](https://mlsanity.com/paper/2205.08108/) (2022)
- [From Blind Solvers to Logical Thinkers: Benchmarking LLMs' Logical Integrity on Faulty Mathematical Problems](https://mlsanity.com/paper/2410.18921/) (2024)
- [Leveraging Large Language Models for Bengali Math Word Problem Solving with Chain of Thought Reasoning](https://mlsanity.com/paper/2505.21354/) (2025)
- [Generalizing Math Word Problem Solvers via Solution Diversification](https://mlsanity.com/paper/2212.00833/) (2022)
- [Math Word Problem Solving by Generating Linguistic Variants of Problem Statements](https://mlsanity.com/paper/2306.13899/) (2023)
- [Solving Math Word Problem with Problem Type Classification](https://mlsanity.com/paper/2308.13844/) (2023)

## Abstract (arXiv)

Sequence-to-sequence (SEQ2SEQ) models have been successfully applied to automatic math word problem solving. Despite its simplicity, a drawback still remains: a math word problem can be correctly solved by more than one equations. This non-deterministic transduction harms the performance of maximum likelihood estimation. In this paper, by considering the uniqueness of expression tree, we propose an equation normalization method to normalize the duplicated equations. Moreover, we analyze the performance of three popular SEQ2SEQ models on the math word problem solving. We find that each model has its own specialty in solving problems, consequently an ensemble model is then proposed to combine their advantages. Experiments on dataset Math23K show that the ensemble model with equation normalization significantly outperforms the previous state-of-the-art methods.