Multi-View Reasoning: Consistent Contrastive Learning for Math Word Problem

TL;DR

This paper introduces a multi-view contrastive learning approach for math word problem solving, aligning top-down and bottom-up reasoning views to improve accuracy and diversity in equation generation.

Contribution

It proposes a novel multi-view consistent contrastive learning framework that aligns two reasoning perspectives for better semantics-to-equation mapping.

Findings

Significantly outperforms baselines on multiple datasets.

Improves handling of complex math problems.

Enhances diversity and correctness of generated equations.

Abstract

Math word problem solver requires both precise relation reasoning about quantities in the text and reliable generation for the diverse equation. Current sequence-to-tree or relation extraction methods regard this only from a fixed view, struggling to simultaneously handle complex semantics and diverse equations. However, human solving naturally involves two consistent reasoning views: top-down and bottom-up, just as math equations also can be expressed in multiple equivalent forms: pre-order and post-order. We propose a multi-view consistent contrastive learning for a more complete semantics-to-equation mapping. The entire process is decoupled into two independent but consistent views: top-down decomposition and bottom-up construction, and the two reasoning views are aligned in multi-granularity for consistency, enhancing global generation and precise reasoning. Experiments on multiple datasets across two languages show our approach significantly outperforms the existing baselines, especially on complex problems. We also show after consistent alignment, multi-view can absorb the merits of both views and generate more diverse results consistent with the mathematical laws.