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Self-consistent Reasoning For Solving Math Word Problems

Jing Xiong, Zhongwei Wan, Xiping Hu, Min Yang, Chengming Li

TL;DR

This work addresses spurious correlations in math word problem solving by introducing SCR, a self-consistent reasoning framework that exposes shortcuts through pruning a sub-network and aligns predictive distributions with a symmetric KL divergence. The method jointly trains a source network and a pruned sub-network, encouraging them to generate equivalent expressions that reflect the underlying problem logic rather than surface cues. Extensive experiments on Math23k and Ape210k show SCR outperforms strong baselines and demonstrates robustness via ablations and case studies, including generation of alternative yet equivalent solution expressions. The approach also highlights the importance of learnable quantity embeddings and offers directions for future work on distinguishing equivalent versus merely similar expressions.

Abstract

Math word problems (MWPs) is a task that automatically derives solution expression from a giving math problems in text. The previous studies suffer from spurious correlations between input text and output expression. To mitigate this issue, we propose a self-consistent reasoning framework called SCR, which attempts to adopt a pruning strategy to correct the output distribution shift so as to implicitly fix those spurious correlative samples. Specifically, we firstly obtain a sub-network by pruning a roberta2tree model, for the sake to use the gap on output distribution between the original roberta2tree model and the pruned sub-network to expose spurious correlative samples. Then, we calibrate the output distribution shift by applying symmetric Kullback-Leibler divergence to alleviate spurious correlations. In addition, SCR generates equivalent expressions, thereby, capturing the original text's logic rather than relying on hints from original text. Extensive experiments on two large-scale benchmarks demonstrate that our model substantially outperforms the strong baseline methods.

Self-consistent Reasoning For Solving Math Word Problems

TL;DR

This work addresses spurious correlations in math word problem solving by introducing SCR, a self-consistent reasoning framework that exposes shortcuts through pruning a sub-network and aligns predictive distributions with a symmetric KL divergence. The method jointly trains a source network and a pruned sub-network, encouraging them to generate equivalent expressions that reflect the underlying problem logic rather than surface cues. Extensive experiments on Math23k and Ape210k show SCR outperforms strong baselines and demonstrates robustness via ablations and case studies, including generation of alternative yet equivalent solution expressions. The approach also highlights the importance of learnable quantity embeddings and offers directions for future work on distinguishing equivalent versus merely similar expressions.

Abstract

Math word problems (MWPs) is a task that automatically derives solution expression from a giving math problems in text. The previous studies suffer from spurious correlations between input text and output expression. To mitigate this issue, we propose a self-consistent reasoning framework called SCR, which attempts to adopt a pruning strategy to correct the output distribution shift so as to implicitly fix those spurious correlative samples. Specifically, we firstly obtain a sub-network by pruning a roberta2tree model, for the sake to use the gap on output distribution between the original roberta2tree model and the pruned sub-network to expose spurious correlative samples. Then, we calibrate the output distribution shift by applying symmetric Kullback-Leibler divergence to alleviate spurious correlations. In addition, SCR generates equivalent expressions, thereby, capturing the original text's logic rather than relying on hints from original text. Extensive experiments on two large-scale benchmarks demonstrate that our model substantially outperforms the strong baseline methods.
Paper Structure (16 sections, 8 equations, 1 figure, 6 tables)

This paper contains 16 sections, 8 equations, 1 figure, 6 tables.

Table of Contents

  1. Introduction
  2. Methodology
  3. The Encoder-Decoder Architecture
  4. Self-consistent Reasoning
  5. Experiment
  6. Experimental Setup
  7. Datasets
  8. Implementation Details
  9. Baselines
  10. Experimental Results
  11. Main Results
  12. Ablation Study
  13. The Sensitivity Analysis of $\boldsymbol{\alpha}$
  14. The Sensitivity Analysis of Pruning Rate
  15. Case Study
  16. ...and 1 more sections

Figures (1)

  • Figure 1: Overview of the proposed framework SCR