# Structure-Unified M-Tree Coding Solver for MathWord Problem

arXiv: https://arxiv.org/abs/2210.12432 · HTML: https://mlsanity.com/paper/2210.12432/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 13 of its 34 references that are in the map.
- First posted on arXiv 22 Oct 2022.

## Builds on (most cited first, 13 of 13)

- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://mlsanity.com/paper/1810.04805/) (2018)
- [RoBERTa: A Robustly Optimized BERT Pretraining Approach](https://mlsanity.com/paper/1907.11692/) (2019)
- [Unified Language Model Pre-training for Natural Language Understanding and Generation](https://mlsanity.com/paper/1905.03197/) (2019)
- [Translating a Math Word Problem to an Expression Tree](https://mlsanity.com/paper/1811.05632/) (2018)
- [Semantically-Aligned Equation Generation for Solving and Reasoning Math Word Problems](https://mlsanity.com/paper/1811.00720/) (2018)
- [Neural-Symbolic Solver for Math Word Problems with Auxiliary Tasks](https://mlsanity.com/paper/2107.01431/) (2021)
- [Semantically-Aligned Universal Tree-Structured Solver for Math Word Problems](https://mlsanity.com/paper/2010.06823/) (2020)
- [Viable Dependency Parsing as Sequence Labeling](https://mlsanity.com/paper/1902.10505/) (2019)
- [Graph-to-Tree Neural Networks for Learning Structured Input-Output Translation with Applications to Semantic Parsing and Math Word Problem](https://mlsanity.com/paper/2004.13781/) (2020)
- [Constituent Parsing as Sequence Labeling](https://mlsanity.com/paper/1810.08994/) (2018)
- [Sequence Labeling Parsing by Learning Across Representations](https://mlsanity.com/paper/1907.01339/) (2019)
- [Discontinuous Constituent Parsing as Sequence Labeling](https://mlsanity.com/paper/2010.00633/) (2020)
- [Better, Faster, Stronger Sequence Tagging Constituent Parsers](https://mlsanity.com/paper/1902.10985/) (2019)

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

- [Non-Autoregressive Math Word Problem Solver with Unified Tree Structure](https://mlsanity.com/paper/2305.04556/) (2023)
- [An Expression Tree Decoding Strategy for Mathematical Equation Generation](https://mlsanity.com/paper/2310.09619/) (2023)
- [Foundation of Intelligence: Review of Math Word Problems from Human Cognition Perspective](https://mlsanity.com/paper/2510.21999/) (2025)
- [A Diversity-Enhanced Knowledge Distillation Model for Practical Math Word Problem Solving](https://mlsanity.com/paper/2501.03670/) (2025)

## Abstract (arXiv)

As one of the challenging NLP tasks, designing math word problem (MWP) solvers has attracted increasing research attention for the past few years. In previous work, models designed by taking into account the properties of the binary tree structure of mathematical expressions at the output side have achieved better performance. However, the expressions corresponding to a MWP are often diverse (e.g., n1+n2 × n3-n4, n3× n2-n4+n1, etc.), and so are the corresponding binary trees, which creates difficulties in model learning due to the non-deterministic output space. In this paper, we propose the Structure-Unified M-Tree Coding Solver (SUMC-Solver), which applies a tree with any M branches (M-tree) to unify the output structures. To learn the M-tree, we use a mapping to convert the M-tree into the M-tree codes, where codes store the information of the paths from tree root to leaf nodes and the information of leaf nodes themselves, and then devise a Sequence-to-Code (seq2code) model to generate the codes. Experimental results on the widely used MAWPS and Math23K datasets have demonstrated that SUMC-Solver not only outperforms several state-of-the-art models under similar experimental settings but also performs much better under low-resource conditions.