# Generalizing Math Word Problem Solvers via Solution Diversification

arXiv: https://arxiv.org/abs/2212.00833 · HTML: https://mlsanity.com/paper/2212.00833/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 16 of its 38 references that are in the map.
- First posted on arXiv 1 Dec 2022.

## Builds on (most cited first, 16 of 16)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Generate & Rank: A Multi-task Framework for Math Word Problems](https://mlsanity.com/paper/2109.03034/) (2021)
- [NumNet: Machine Reading Comprehension with Numerical Reasoning](https://mlsanity.com/paper/1910.06701/) (2019)
- [Translating a Math Word Problem to an Expression Tree](https://mlsanity.com/paper/1811.05632/) (2018)
- [Giving BERT a Calculator: Finding Operations and Arguments with Reading Comprehension](https://mlsanity.com/paper/1909.00109/) (2019)
- [Semantically-Aligned Equation Generation for Solving and Reasoning Math Word Problems](https://mlsanity.com/paper/1811.00720/) (2018)
- [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)
- [Seeking Patterns, Not just Memorizing Procedures: Contrastive Learning for Solving Math Word Problems](https://mlsanity.com/paper/2110.08464/) (2021)
- [Learning by Fixing: Solving Math Word Problems with Weak Supervision](https://mlsanity.com/paper/2012.10582/) (2020)
- [Measuring and Improving BERT's Mathematical Abilities by Predicting the Order of Reasoning](https://mlsanity.com/paper/2106.03921/) (2021)
- [SMART: A Situation Model for Algebra Story Problems via Attributed Grammar](https://mlsanity.com/paper/2012.14011/) (2020)
- [Text2Math: End-to-end Parsing Text into Math Expressions](https://mlsanity.com/paper/1910.06571/) (2019)
- [Recall and Learn: A Memory-augmented Solver for Math Word Problems](https://mlsanity.com/paper/2109.13112/) (2021)
- [A Meaning-based Statistical English Math Word Problem Solver](https://mlsanity.com/paper/1803.06064/) (2018)

## Built on by (most cited first, 7 of 7)

- [Fuse, Reason and Verify: Geometry Problem Solving with Parsed Clauses from Diagram](https://mlsanity.com/paper/2407.07327/) (2024)
- [Get an A in Math: Progressive Rectification Prompting](https://mlsanity.com/paper/2312.06867/) (2023)
- [From Large to Tiny: Distilling and Refining Mathematical Expertise for Math Word Problems with Weakly Supervision](https://mlsanity.com/paper/2403.14390/) (2024)
- [Foundation of Intelligence: Review of Math Word Problems from Human Cognition Perspective](https://mlsanity.com/paper/2510.21999/) (2025)
- [A Theoretical Review on Solving Algebra Problems](https://mlsanity.com/paper/2411.00031/) (2024)
- [ENTRA: Entropy-Based Redundancy Avoidance in Large Language Model Reasoning](https://mlsanity.com/paper/2601.07123/) (2026)
- [SANE: State Anomaly Neutralization for Stable Extreme-Context Delta-Rule Models](https://mlsanity.com/paper/2608.22354/) (2026)

## Abstract (arXiv)

Current math word problem (MWP) solvers are usually Seq2Seq models trained by the (one-problem; one-solution) pairs, each of which is made of a problem description and a solution showing reasoning flow to get the correct answer. However, one MWP problem naturally has multiple solution equations. The training of an MWP solver with (one-problem; one-solution) pairs excludes other correct solutions, and thus limits the generalizability of the MWP solver. One feasible solution to this limitation is to augment multiple solutions to a given problem. However, it is difficult to collect diverse and accurate augment solutions through human efforts. In this paper, we design a new training framework for an MWP solver by introducing a solution buffer and a solution discriminator. The buffer includes solutions generated by an MWP solver to encourage the training data diversity. The discriminator controls the quality of buffered solutions to participate in training. Our framework is flexibly applicable to a wide setting of fully, semi-weakly and weakly supervised training for all Seq2Seq MWP solvers. We conduct extensive experiments on a benchmark dataset Math23k and a new dataset named Weak12k, and show that our framework improves the performance of various MWP solvers under different settings by generating correct and diverse solutions.