Exploring Dowker Homology for Sentence Similarity
2026-08-24 • Computation and Language
Computation and Language
AI summaryⓘ
The authors explored whether a mathematical tool called Dowker homology, which compares the shape of two sets of points, can measure how similar two sentences are by looking at their word embeddings. They tested this with different transformer models and found that Dowker homology does relate to sentence similarity scores. They also created simplified versions of these features to get a single number representing similarity, which worked okay but wasn't better than existing methods. Overall, their work shows Dowker homology can help understand sentence similarity but isn't clearly superior to current techniques.
Dowker homologypoint cloudssentence similarityword embeddingstransformer modelslatent spaceregressionpooling methods
Authors
Marius Huber, Juri Opitz
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.