SSEmb: A Joint Structural and Semantic Embedding Framework for Mathematical Formula Retrieval

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 mathematical formulas. Structurally, we employ Graph Contrastive Learning to encode formulas represented as 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.