Topological quantification of ambiguity in semantic search

TL;DR

This paper explores how the topological structure of sentence embeddings encodes semantic ambiguity, using persistent homology metrics to distinguish ambiguous from unambiguous sentences in both simulated and real-world data.

Contribution

It introduces a formal topological framework for quantifying semantic ambiguity in sentence embeddings using persistent homology metrics, validated on a large corpus.

Findings

Ambiguous sentences separate from unambiguous ones in topological metrics.

Persistent homology provides a stable, model-agnostic signal of semantic discontinuities.

Results are consistent across different embedding models and data granularities.

Abstract

We studied how the local topological structure of sentence-embedding neighborhoods encodes semantic ambiguity. Extending ideas that link word-level polysemy to non-trivial persistent homology, we generalized the concept to full sentences and quantified ambiguity of a query in a semantic search process with two persistent homology metrics: the 1-Wasserstein norm of $H_{0}$ and the maximum loop lifetime of $H_{1}$. We formalized the notion of ambiguity as the relative presence of semantic domains or topics in sentences. We then used this formalism to compute "ab-initio" simulations that encode datapoints as linear combination of randomly generated single topics vectors in an arbitrary embedding space and demonstrate that ambiguous sentences separate from unambiguous ones in both metrics. Finally we validated those findings with real-world case by investigating on a fully open corpus comprising Nobel Prize Physics lectures from 1901 to 2024, segmented into contiguous, non-overlapping chunks at two granularity: $\sim\!250$ tokens and $\sim\!750$ tokens. We tested embedding with four publicly available models. Results across all models reproduce simulations and remain stable despite changes in embedding architecture. We conclude that persistent homology provides a model-agnostic signal of semantic discontinuities, suggesting practical use for ambiguity detection and semantic search recall.