Structure-Preserving Graph Contrastive Learning for Mathematical Information Retrieval

2026-03-09

AI Summary

This work addresses the limitation of generic graph augmentation strategies in standard graph contrastive learning, which often disrupt the semantic structure of mathematical expression graphs—particularly for small-scale, structurally compact formulas. To mitigate this issue, the authors propose a domain-specific augmentation technique tailored for mathematical information retrieval: Variable Substitution. This approach preserves the core algebraic structure and semantic meaning of formulas within a graph contrastive learning framework. Notably, it introduces, for the first time, a structure-preserving variable substitution mechanism into graph contrastive learning, effectively alleviating semantic distortion. Experimental results demonstrate that the proposed method significantly outperforms conventional augmentation strategies when integrated into established graph contrastive retrieval models, yielding substantial improvements in mathematical formula retrieval performance.

Technology Category

• Machine Learning: Graph-based Machine Learning
• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories
• Data Mining & Knowledge Management: Graph Mining, Social Network Analysis & Community

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs
• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs

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}.

Problem

• Graph Contrastive Learning
• Mathematical Information Retrieval
• Graph Augmentation
• Formula Structure
• Semantic Preservation

Innovation

• Variable Substitution
• Graph Contrastive Learning
• Mathematical Information Retrieval
• Structure-Preserving Augmentation
• Formula Retrieval