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From Topology to Retrieval: Decoding Embedding Spaces with Unified Signatures

NeurIPS 2026 · Label-efficient and robust learning › Recognition and long-tail · approach: Correspondence and causal representation learning · 0 citations (OpenAlex)

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Introduces Unified Topological Signatures (UTS), a vector of 15 topological/geometric descriptors computed per embedding space (global) or per neighborhood (local), used to fingerprint 27 text embedding models, predict retrieval effectiveness and document retrievability, and test the Platonic Representation Hypothesis.

Problem

Text embedding geometry and topology are studied in isolation, with unclear connections between metrics and little understanding of how they relate to model identity, retrieval effectiveness, and retrievability bias in dense retrieval.

Approach

Combine many topological, intrinsic-dimension, diversity, density, isotropy and clustering descriptors into a normalized, PCA-reduced signature vector for whole embedding spaces (and k-NN neighborhoods for individual documents), enabling prediction tasks and a unified similarity measure between models.

Key results

• Top four principal components capture over 91% of variance across the 15 UTS descriptors.
• UTS identifies the specific embedding model for unseen datasets with balanced accuracy 0.55 ± 0.21 versus 0.04 baseline across 27 classes.
• Local UTS predicts document retrievability with average accuracy 0.77, outperforming single-feature baselines such as local intrinsic dimension and density.

Surprising findings

• Model family, not model size, dominates representational similarity; large and small models from the same family cluster together, challenging the Platonic Representation Hypothesis's convergence assumption.
• Predicting retrieval performance from global topology gives only moderate correlations (Spearman about 0.6), indicating topology alone cannot fully explain retrieval effectiveness.

Limitations

• Analysis limited to retrieval datasets; effects on clustering or classification untested.
• Global topology yields only moderate predictive power for retrieval metrics (R2 about 0.34-0.37).
• Descriptors require subsampling for tractability, so some measures may not fully converge on large corpora.

Experimental setup

Datasets: MS MARCO ArguAna Touche2020 NFCorpus TREC-COVID SciFact SCIDOCS ClimateFEVER CQADupstack QuoraRetrieval FiQA2018

Benchmarks: MTEB retrieval datasets (11)

Metrics: balanced accuracy R2 Spearman rho accuracy Gini coefficient Recall MAP NDCG

Baselines: Centered Kernel Alignment local intrinsic dimension mean pairwise similarity word count raw embeddings

Builds on: Platonic Representation Hypothesis Centered Kernel Alignment retrievability

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