Learning by Fixing: Solving Math Word Problems with Weak Supervision

By Yining Hong, Qing Li, Daniel Ciao, Siyuan Huang, Song-Chun Zhu. 2020

65 citations recorded by the source corpus.

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 weakly-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 learning-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 fixing 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, tree regularization is applied to guide the efficient shrinkage and exploration of the solution space, and a memory 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.

Subfields: Artificial Intelligence, Natural Language Processing

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Artificial Intelligence

1. Xiangliang Zhang
2. Zhenwen Liang
3. Jipeng Zhang
4. Chuang Gan
5. Josh Tenenbaum
6. Lei Wang
7. Antonio Torralba
8. Jie Shao

In Natural Language Processing

1. Zhenwen Liang
2. Xiangliang Zhang
3. Jipeng Zhang
4. Lei Wang
5. Jie Shao
6. Bing Tian Dai
7. Ee-Peng Lim
8. Yan Wang

Citations in the corpus

• MWPToolkit: An Open-Source Framework for Deep Learning-Based Math Word Problem Solvers (2021, background): “In addition, weakly supervised learning for MWP solving (Hong et al., 2021; Chatterjee et al., 2021) and supervised learning for geometric problem solving (Lu et al.”
• PTR: A Benchmark for Part-based Conceptual, Relational, and Physical Reasoning (2021, background): “Also, while previous datasets emphasize reasoning based on spatial relationships, humans possess diverse reasoning abilities, including analogy [62], geometry[48, 40], arithmetic[63, 20, 21], and physics [13].”
• MWP-BERT: A Strong Baseline for Math Word Problems (2021, background): “, 2020a), weak supervision (Hong et al., 2021a), and situation model (Hong et al.”
• Neural-Symbolic Solver for Math Word Problems with Auxiliary Tasks (2021, unknown): “…2017; Liang et al., 2018a), to deep learning meth-ods (Ling et al., 2017; Wang et al., 2017, 2018b; Huang et al., 2018; Wang et al., 2018a; Xie and Sun, 2019; Wang et al., 2019; Zhang et al., 2020a,b; Qin et al., 2020; Shen and Jin, 2020; Wu et al., 2020; Chen et al., 2021; Hong et al., 2021a,b).”
• A Survey of Deep Learning for Mathematical Reasoning (2022, unknown): “, 2021) MWP Generation Seq2Tree GRU Tree 4 A word-clause-problem encoder LBF (Hong et al., 2021a) MWP Generation Seq2Tree BiGRU Tree 4 A learning-by-fixing (LBF) framework Seq2DAG (Cao et al.”