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Structure-Preserving Graph Contrastive Learning for Mathematical Information Retrieval

Chun-Hsi Ku, Hung-Hsuan Chen

TL;DR

Variable Substitution is introduced as a domain-specific graph augmentation technique for graph contrastive learning (GCL) in the context of searching for mathematical formulas and significantly improves retrieval performance compared to generic augmentation strategies.

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}.

Structure-Preserving Graph Contrastive Learning for Mathematical Information Retrieval

TL;DR

Variable Substitution is introduced as a domain-specific graph augmentation technique for graph contrastive learning (GCL) in the context of searching for mathematical formulas and significantly improves retrieval performance compared to generic augmentation strategies.

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}.
Paper Structure (13 sections, 3 figures)

This paper contains 13 sections, 3 figures.

Table of Contents

  1. Introduction
  2. Related Work
  3. Method
  4. Graph Structure Generator
  5. Token Embedding Generator
  6. Graph Contrastive Learning with Variable Substitution
  7. Online Query Module
  8. Experiments
  9. NTCIR-12 MathIR Dataset
  10. Evaluation Metrics: Bpref and Full vs. Partial Match
  11. Compared methods
  12. Results
  13. Discussion

Figures (3)

  • Figure 1: The online and offline processing of the entire framework; we focus on Graph Contrastive Learning with Variable Substitution in this paper.
  • Figure 2: The bpref scores using the SLT layout
  • Figure 3: The bpref scores using the OPT layout