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[2406.07990] Topological quantification of ambiguity in semantic search
Summary
This article explores the topological quantification of ambiguity in semantic search, linking sentence-embedding neighborhoods to semantic domains through persistent homology metrics.
Why It Matters
Understanding ambiguity in semantic search is crucial for improving information retrieval systems. This research provides a novel approach using topological methods, which can enhance the accuracy and efficiency of semantic search applications across various domains, including AI and natural language processing.
Key Takeaways
- The study introduces persistent homology as a method to quantify semantic ambiguity.
- Two metrics, the 1-Wasserstein norm and maximum loop lifetime, are used to analyze sentence embeddings.
- Real-world validation was conducted using Nobel Prize Physics lectures, confirming the model's effectiveness.
- The findings suggest practical applications for ambiguity detection in semantic search.
- This research contributes to the intersection of topology and machine learning, offering new insights into semantic understanding.
Computer Science > Machine Learning arXiv:2406.07990 (cs) [Submitted on 12 Jun 2024 (v1), last revised 17 Feb 2026 (this version, v2)] Title:Topological quantification of ambiguity in semantic search Authors:Thomas Roland Barillot, Alex De Castro View a PDF of the paper titled Topological quantification of ambiguity in semantic search, by Thomas Roland Barillot and Alex De Castro View PDF HTML (experimental) 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 ...
