From Topology to Retrieval: Decoding Embedding Spaces with Unified Signatures

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Main Authors: Rottach, Florian, Rudman, William, Rieck, Bastian, Scells, Harrisen, Eickhoff, Carsten
Format: Preprint
Published: 2025
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author Rottach, Florian
Rudman, William
Rieck, Bastian
Scells, Harrisen
Eickhoff, Carsten
author_facet Rottach, Florian
Rudman, William
Rieck, Bastian
Scells, Harrisen
Eickhoff, Carsten
contents Studying how embeddings are organized in space not only enhances model interpretability but also uncovers factors that drive downstream task performance. In this paper, we present a comprehensive analysis of topological and geometric measures across a wide set of text embedding models and datasets. We find a high degree of redundancy among these measures and observe that individual metrics often fail to sufficiently differentiate embedding spaces. Building on these insights, we introduce Unified Topological Signatures (UTS), a holistic framework for characterizing embedding spaces. We show that UTS can predict model-specific properties and reveal similarities driven by model architecture. Further, we demonstrate the utility of our method by linking topological structure to ranking effectiveness and accurately predicting document retrievability. We find that a holistic, multi-attribute perspective is essential to understanding and leveraging the geometry of text embeddings.
format Preprint
id arxiv_https___arxiv_org_abs_2511_22150
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle From Topology to Retrieval: Decoding Embedding Spaces with Unified Signatures
Rottach, Florian
Rudman, William
Rieck, Bastian
Scells, Harrisen
Eickhoff, Carsten
Machine Learning
Computation and Language
Information Retrieval
Studying how embeddings are organized in space not only enhances model interpretability but also uncovers factors that drive downstream task performance. In this paper, we present a comprehensive analysis of topological and geometric measures across a wide set of text embedding models and datasets. We find a high degree of redundancy among these measures and observe that individual metrics often fail to sufficiently differentiate embedding spaces. Building on these insights, we introduce Unified Topological Signatures (UTS), a holistic framework for characterizing embedding spaces. We show that UTS can predict model-specific properties and reveal similarities driven by model architecture. Further, we demonstrate the utility of our method by linking topological structure to ranking effectiveness and accurately predicting document retrievability. We find that a holistic, multi-attribute perspective is essential to understanding and leveraging the geometry of text embeddings.
title From Topology to Retrieval: Decoding Embedding Spaces with Unified Signatures
topic Machine Learning
Computation and Language
Information Retrieval
url https://arxiv.org/abs/2511.22150