From Topology to Retrieval: Decoding Embedding Spaces with Unified Signatures
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arXiv
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| Main Authors: | , , , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866914175714852864 |
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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 |