# Learning by Fixing: Solving Math Word Problems with Weak Supervision

arXiv: https://arxiv.org/abs/2012.10582 · HTML: https://mlsanity.com/paper/2012.10582/

## Key facts

- Cited by 25 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 19 Dec 2020.

## Built on by (most cited first, 25 of 25)

- [Inter-GPS: Interpretable Geometry Problem Solving with Formal Language and Symbolic Reasoning](https://mlsanity.com/paper/2105.04165/) (2021)
- [A Survey of Deep Learning for Mathematical Reasoning](https://mlsanity.com/paper/2212.10535/) (2022)
- [MultiHiertt: Numerical Reasoning over Multi Hierarchical Tabular and Textual Data](https://mlsanity.com/paper/2206.01347/) (2022)
- [From LSAT: The Progress and Challenges of Complex Reasoning](https://mlsanity.com/paper/2108.00648/) (2021)
- [CLOVA: A Closed-Loop Visual Assistant with Tool Usage and Update](https://mlsanity.com/paper/2312.10908/) (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)
- [PTR: A Benchmark for Part-based Conceptual, Relational, and Physical Reasoning](https://mlsanity.com/paper/2112.05136/) (2021)
- [A Review of Emerging Research Directions in Abstract Visual Reasoning](https://mlsanity.com/paper/2202.10284/) (2022)
- [MWP-BERT: Numeracy-Augmented Pre-training for Math Word Problem Solving](https://mlsanity.com/paper/2107.13435/) (2021)
- [Answering Numerical Reasoning Questions in Table-Text Hybrid Contents with Graph-based Encoder and Tree-based Decoder](https://mlsanity.com/paper/2209.07692/) (2022)
- [MinT: Boosting Generalization in Mathematical Reasoning via Multi-View Fine-Tuning](https://mlsanity.com/paper/2307.07951/) (2023)
- [Softened Symbol Grounding for Neuro-symbolic Systems](https://mlsanity.com/paper/2403.00323/) (2024)
- [Enhancing Mathematical Reasoning in LLMs by Stepwise Correction](https://mlsanity.com/paper/2410.12934/) (2024)
- [Towards Tractable Mathematical Reasoning: Challenges, Strategies, and Opportunities for Solving Math Word Problems](https://mlsanity.com/paper/2111.05364/) (2021)
- [Why are NLP Models Fumbling at Elementary Math? A Survey of Deep Learning based Word Problem Solvers](https://mlsanity.com/paper/2205.15683/) (2022)
- [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)
- [Survey of Natural Language Processing for Education: Taxonomy, Systematic Review, and Future Trends](https://mlsanity.com/paper/2401.07518/) (2024)
- [Fixing Malfunctional Objects With Learned Physical Simulation and Functional Prediction](https://mlsanity.com/paper/2205.02834/) (2022)
- [From Large to Tiny: Distilling and Refining Mathematical Expertise for Math Word Problems with Weakly Supervision](https://mlsanity.com/paper/2403.14390/) (2024)
- [WARM: A Weakly (+Semi) Supervised Model for Solving Math word Problems](https://mlsanity.com/paper/2104.06722/) (2021)
- [ComSearch: Equation Searching with Combinatorial Strategy for Solving Math Word Problems with Weak Supervision](https://mlsanity.com/paper/2210.07017/) (2022)
- [Foundation of Intelligence: Review of Math Word Problems from Human Cognition Perspective](https://mlsanity.com/paper/2510.21999/) (2025)
- [Advanced Weakly-Supervised Formula Exploration for Neuro-Symbolic Mathematical Reasoning](https://mlsanity.com/paper/2502.00629/) (2025)

## Abstract (arXiv)

Previous neural solvers of math word problems (MWPs) are learned with full supervision and fail to generate diverse solutions. In this paper, we address this issue by introducing a textitweakly-supervised paradigm for learning MWPs. Our method only requires the annotations of the final answers and can generate various solutions for a single problem. To boost weakly-supervised learning, we propose a novel textitlearning-by-fixing (LBF) framework, which corrects the misperceptions of the neural network via symbolic reasoning. Specifically, for an incorrect solution tree generated by the neural network, the textitfixing mechanism propagates the error from the root node to the leaf nodes and infers the most probable fix that can be executed to get the desired answer. To generate more diverse solutions, textittree regularization is applied to guide the efficient shrinkage and exploration of the solution space, and a textitmemory buffer is designed to track and save the discovered various fixes for each problem. Experimental results on the Math23K dataset show the proposed LBF framework significantly outperforms reinforcement learning baselines in weakly-supervised learning. Furthermore, it achieves comparable top-1 and much better top-3/5 answer accuracies than fully-supervised methods, demonstrating its strength in producing diverse solutions.