Exploring Dowker Homology for Sentence Similarity

2026-08-24

AI Summary

研究使用Dowker同调分析句子相似性，通过将句子对的词嵌入视为潜空间中的点云，并从预训练和微调模型中提取特征来解决问题。

Abstract

Dowker homology is a topological tool that may be used to analyze the relative position of two point clouds living in a common space. We investigate whether Dowker homology captures sentence similarity information by treating the embeddings of the tokens that constitute a sentence pair as a pair of point clouds in the latent space of a transformer model, using both models that have and have not been fine-tuned for sentence similarity. We find that Dowker homology captures sentence similarity information, as measured by regressing Dowker homology features onto ground-truth similarity scores, and that it can be used for visual inspection of similarity data and models. In an attempt to make Dowker homology readily applicable, we derive from it single-number summaries that we expect to capture sentence similarity directly. These turn out to work reasonably well, but without outperforming standard sentence similarity measures based on established pooling methods.

Problem

• Dowker homology
• sentence similarity
• point clouds
• transformer model

Innovation

• Dowker homology
• sentence similarity
• point clouds
• transformer model