Formula retrieval is a core 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 that leverages 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 \(P^\prime @10\) and \(nDCG^\prime @10\) . Furthermore, SSEmb enhances the performance of all runs of other methods and achieves state-of-the-art results when combined with Approach0.

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

  • Ruyin Li,
  • Xiaoyu Chen

摘要

Formula retrieval is a core 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 that leverages 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 \(P^\prime @10\) and \(nDCG^\prime @10\) . Furthermore, SSEmb enhances the performance of all runs of other methods and achieves state-of-the-art results when combined with Approach0.