# Topological quantification of ambiguity in semantic search

arXiv: https://arxiv.org/abs/2406.07990 · HTML: https://mlsanity.com/paper/2406.07990/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 11 of its 23 references that are in the map.
- First posted on arXiv 12 Jun 2024.

## Builds on (most cited first, 11 of 11)

- [BERTopic: Neural topic modeling with a class-based TF-IDF procedure](https://mlsanity.com/paper/2203.05794/) (2022)
- [ColBERTv2: Effective and Efficient Retrieval via Lightweight Late Interaction](https://mlsanity.com/paper/2112.01488/) (2021)
- [Not All Language Model Features Are One-Dimensionally Linear](https://mlsanity.com/paper/2405.14860/) (2024)
- [SPLADE v2: Sparse Lexical and Expansion Model for Information Retrieval](https://mlsanity.com/paper/2109.10086/) (2021)
- [Is Cosine-Similarity of Embeddings Really About Similarity?](https://mlsanity.com/paper/2403.05440/) (2024)
- [giotto-tda: A Topological Data Analysis Toolkit for Machine Learning and Data Exploration](https://mlsanity.com/paper/2004.02551/) (2020)
- [Problems with Cosine as a Measure of Embedding Similarity for High Frequency Words](https://mlsanity.com/paper/2205.05092/) (2022)
- [Geometry Helps to Compare Persistence Diagrams](https://mlsanity.com/paper/1606.03357/) (2016)
- [Topology of Word Embeddings: Singularities Reflect Polysemy](https://mlsanity.com/paper/2011.09413/) (2020)
- [Solving Cosine Similarity Underestimation between High Frequency Words by L2 Norm Discounting](https://mlsanity.com/paper/2305.10610/) (2023)
- [Unsupervised Sentence-embeddings by Manifold Approximation and Projection](https://mlsanity.com/paper/2102.03795/) (2021)

## Abstract (arXiv)

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 H0 and the maximum loop lifetime of H1. 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: ~!250 tokens and ~!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.