Abstract Summary
Formula retrieval is an important topic in Mathematical Information Retrieval. We propose SSEmb, a novel embedding framework capable of capturing both structural and semantic features of formulas. Structurally, we employ Graph Contrastive Learning to encode formulas represented as Shared-substructure Operator Graphs. To enhance structural diversity while preserving mathematical validity of these formula graphs, we introduce a novel graph data augmentation approach through a substitution strategy. Semantically, we utilize Sentence-BERT to encode the surrounding text of formulas. Finally, for each query and its candidates, structural and semantic similarities are calculated separately and then fused through a weighted scheme. In the ARQMath-3 Formula Retrieval Task, SSEmb outperforms existing embedding-based methods by over 5 percentage points on P'@10 and nDCG'@10. Furthermore, SSEmb enhances the performance of all runs of other methods and achieves state-of-the-art results when combined with Approach0.
