# Semantically-Aligned Universal Tree-Structured Solver for Math Word Problems

arXiv: https://arxiv.org/abs/2010.06823 · HTML: https://mlsanity.com/paper/2010.06823/

## Key facts

- Cited by 35 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 14 Oct 2020.

## Built on by (most cited first, 30 of 35)

- [Are NLP Models really able to Solve Simple Math Word Problems?](https://mlsanity.com/paper/2103.07191/) (2021)
- [Inter-GPS: Interpretable Geometry Problem Solving with Formal Language and Symbolic Reasoning](https://mlsanity.com/paper/2105.04165/) (2021)
- [UniGeo: Unifying Geometry Logical Reasoning via Reformulating Mathematical Expression](https://mlsanity.com/paper/2212.02746/) (2022)
- [A Survey of Deep Learning for Mathematical Reasoning](https://mlsanity.com/paper/2212.10535/) (2022)
- [A Neural Network Solves, Explains, and Generates University Math Problems by Program Synthesis and Few-Shot Learning at Human Level](https://mlsanity.com/paper/2112.15594/) (2021)
- [Unleashing the potential of prompt engineering for large language models](https://mlsanity.com/paper/2310.14735/) (2023)
- [A Survey of Reasoning with Foundation Models](https://mlsanity.com/paper/2312.11562/) (2023)
- [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)
- [MWP-BERT: Numeracy-Augmented Pre-training for Math Word Problem Solving](https://mlsanity.com/paper/2107.13435/) (2021)
- [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)
- [Mathematical Language Models: A Survey](https://mlsanity.com/paper/2312.07622/) (2023)
- [Investigating Math Word Problems using Pretrained Multilingual Language Models](https://mlsanity.com/paper/2105.08928/) (2021)
- [Interpretable Math Word Problem Solution Generation Via Step-by-step Planning](https://mlsanity.com/paper/2306.00784/) (2023)
- [NOAHQA: Numerical Reasoning with Interpretable Graph Question Answering Dataset](https://mlsanity.com/paper/2109.10604/) (2021)
- [Solving Linear Algebra by Program Synthesis](https://mlsanity.com/paper/2111.08171/) (2021)
- [ELASTIC: Numerical Reasoning with Adaptive Symbolic Compiler](https://mlsanity.com/paper/2210.10105/) (2022)
- [Towards Tractable Mathematical Reasoning: Challenges, Strategies, and Opportunities for Solving Math Word Problems](https://mlsanity.com/paper/2111.05364/) (2021)
- [A Survey on Mathematical Reasoning and Optimization with Large Language Models](https://mlsanity.com/paper/2503.17726/) (2025)
- [A Survey in Mathematical Language Processing](https://mlsanity.com/paper/2205.15231/) (2022)
- [Why are NLP Models Fumbling at Elementary Math? A Survey of Deep Learning based Word Problem Solvers](https://mlsanity.com/paper/2205.15683/) (2022)
- [Math Operation Embeddings for Open-ended Solution Analysis and Feedback](https://mlsanity.com/paper/2104.12047/) (2021)
- [Unbiased Math Word Problems Benchmark for Mitigating Solving Bias](https://mlsanity.com/paper/2205.08108/) (2022)
- [Non-Autoregressive Math Word Problem Solver with Unified Tree Structure](https://mlsanity.com/paper/2305.04556/) (2023)
- [Towards Robust Numerical Question Answering: Diagnosing Numerical Capabilities of NLP Systems](https://mlsanity.com/paper/2211.07455/) (2022)
- [Solving Machine Learning Problems](https://mlsanity.com/paper/2107.01238/) (2021)
- [Structure-Unified M-Tree Coding Solver for MathWord Problem](https://mlsanity.com/paper/2210.12432/) (2022)
- [Expression Syntax Information Bottleneck for Math Word Problems](https://mlsanity.com/paper/2310.15664/) (2023)
- [Seeking Diverse Reasoning Logic: Controlled Equation Expression Generation for Solving Math Word Problems](https://mlsanity.com/paper/2209.10310/) (2022)

## Abstract (arXiv)

A practical automatic textual math word problems (MWPs) solver should be able to solve various textual MWPs while most existing works only focused on one-unknown linear MWPs. Herein, we propose a simple but efficient method called Universal Expression Tree (UET) to make the first attempt to represent the equations of various MWPs uniformly. Then a semantically-aligned universal tree-structured solver (SAU-Solver) based on an encoder-decoder framework is proposed to resolve multiple types of MWPs in a unified model, benefiting from our UET representation. Our SAU-Solver generates a universal expression tree explicitly by deciding which symbol to generate according to the generated symbols' semantic meanings like human solving MWPs. Besides, our SAU-Solver also includes a novel subtree-level semanticallyaligned regularization to further enforce the semantic constraints and rationality of the generated expression tree by aligning with the contextual information. Finally, to validate the universality of our solver and extend the research boundary of MWPs, we introduce a new challenging Hybrid Math Word Problems dataset (HMWP), consisting of three types of MWPs. Experimental results on several MWPs datasets show that our model can solve universal types of MWPs and outperforms several state-of-the-art models.