Structure-Preserving Graph Contrastive Learning for Mathematical Information Retrieval

TL;DR

This paper proposes Variable Substitution, a domain-specific graph augmentation for contrastive learning that preserves mathematical formula semantics, significantly enhancing retrieval accuracy in mathematical information retrieval tasks.

Contribution

It introduces Variable Substitution as a novel augmentation technique that maintains algebraic structure, improving graph contrastive learning for mathematical formula retrieval.

Findings

Variable Substitution outperforms generic augmentation methods.

Significant improvement in retrieval performance.

Code released on GitHub for reproducibility.

Abstract

This paper introduces Variable Substitution as a domain-specific graph augmentation technique for graph contrastive learning (GCL) in the context of searching for mathematical formulas. Standard GCL augmentation techniques often distort the semantic meaning of mathematical formulas, particularly for small and highly structured graphs. Variable Substitution, on the other hand, preserves the core algebraic relationships and formula structure. To demonstrate the effectiveness of our technique, we apply it to a classic GCL-based retrieval model. Experiments show that this straightforward approach significantly improves retrieval performance compared to generic augmentation strategies. We release the code on GitHub.\footnote{https://github.com/lazywulf/formula_ret_aug}.