# From Topology to Retrieval: Decoding Embedding Spaces with Unified Signatures

arXiv: https://arxiv.org/abs/2511.22150 · HTML: https://mlsanity.com/paper/2511.22150/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 54 of its 92 references that are in the map.
- First posted on arXiv 27 Nov 2025.

## Builds on (most cited first, 30 of 54)

- [Retrieval-Augmented Generation for Knowledge-Intensive NLP Tasks](https://mlsanity.com/paper/2005.11401/) (2020)
- [UMAP: Uniform Manifold Approximation and Projection for Dimension Reduction](https://mlsanity.com/paper/1802.03426/) (2018)
- [HuggingFace's Transformers: State-of-the-art Natural Language Processing](https://mlsanity.com/paper/1910.03771/) (2019)
- [Similarity of Neural Network Representations Revisited](https://mlsanity.com/paper/1905.00414/) (2019)
- [MS MARCO: A Human Generated MAchine Reading COmprehension Dataset](https://mlsanity.com/paper/1611.09268/) (2016)
- [MiniLM: Deep Self-Attention Distillation for Task-Agnostic Compression of Pre-Trained Transformers](https://mlsanity.com/paper/2002.10957/) (2020)
- [Understanding Contrastive Representation Learning through Alignment and Uniformity on the Hypersphere](https://mlsanity.com/paper/2005.10242/) (2020)
- [Text Embeddings by Weakly-Supervised Contrastive Pre-training](https://mlsanity.com/paper/2212.03533/) (2022)
- [BEIR: A Heterogenous Benchmark for Zero-shot Evaluation of Information Retrieval Models](https://mlsanity.com/paper/2104.08663/) (2021)
- [Approximate Nearest Neighbor Negative Contrastive Learning for Dense Text Retrieval](https://mlsanity.com/paper/2007.00808/) (2020)
- [How Contextual are Contextualized Word Representations? Comparing the Geometry of BERT, ELMo, and GPT-2 Embeddings](https://mlsanity.com/paper/1909.00512/) (2019)
- [Towards General Text Embeddings with Multi-stage Contrastive Learning](https://mlsanity.com/paper/2308.03281/) (2023)
- [Fact or Fiction: Verifying Scientific Claims](https://mlsanity.com/paper/2004.14974/) (2020)
- [Large Dual Encoders Are Generalizable Retrievers](https://mlsanity.com/paper/2112.07899/) (2021)
- [SPECTER: Document-level Representation Learning using Citation-informed Transformers](https://mlsanity.com/paper/2004.07180/) (2020)
- [The Platonic Representation Hypothesis](https://mlsanity.com/paper/2405.07987/) (2024)
- [Multilingual E5 Text Embeddings: A Technical Report](https://mlsanity.com/paper/2402.05672/) (2024)
- [The Vendi Score: A Diversity Evaluation Metric for Machine Learning](https://mlsanity.com/paper/2210.02410/) (2022)
- [Estimating the intrinsic dimension of datasets by a minimal neighborhood information](https://mlsanity.com/paper/1803.06992/) (2018)
- [Efficiently Teaching an Effective Dense Retriever with Balanced Topic Aware Sampling](https://mlsanity.com/paper/2104.06967/) (2021)
- [Visualizing and Measuring the Geometry of BERT](https://mlsanity.com/paper/1906.02715/) (2019)
- [CLIMATE-FEVER: A Dataset for Verification of Real-World Climate Claims](https://mlsanity.com/paper/2012.00614/) (2020)
- [Getting aligned on representational alignment](https://mlsanity.com/paper/2310.13018/) (2023)
- [Dense Text Retrieval based on Pretrained Language Models: A Survey](https://mlsanity.com/paper/2211.14876/) (2022)
- [Ripser: efficient computation of Vietoris-Rips persistence barcodes](https://mlsanity.com/paper/1908.02518/) (2019)
- [On the Theoretical Limitations of Embedding-Based Retrieval](https://mlsanity.com/paper/2508.21038/) (2025)
- [Gemini Embedding: Generalizable Embeddings from Gemini](https://mlsanity.com/paper/2503.07891/) (2025)
- [Reliability of CKA as a Similarity Measure in Deep Learning](https://mlsanity.com/paper/2210.16156/) (2022)
- [Scikit-dimension: a Python package for intrinsic dimension estimation](https://mlsanity.com/paper/2109.02596/) (2021)
- [Representation Topology Divergence: A Method for Comparing Neural Network Representations](https://mlsanity.com/paper/2201.00058/) (2021)

## Built on by (most cited first, 5 of 5)

- [ABLE: Representing and Mapping LLMs via Attribution-Based Large-model Embedding](https://mlsanity.com/paper/2606.07524/) (2026)
- [Isotropy Cliffs: The Geometric Signature of Decision-Making in Large Language Models](https://mlsanity.com/paper/2608.00828/) (2026)
- [Topological Attribution Distance (TAD): Revealing Segment-Level RAG Influence on LLM Output Geometry for Incident Log Analysis](https://mlsanity.com/paper/2608.16775/) (2026)
- [Repurposing Unified Topological Signatures for Graph Representation Learning](https://mlsanity.com/paper/2609.17061/) (2026)
- [UltraBERT: Beyond the Limit of BERT Pre-Training](https://mlsanity.com/paper/2610.15028/) (2026)

## Abstract (arXiv)

Studying the shape of text embedding spaces enhances our understanding of model behavior and how geometry affects downstream task performance. While a range of topological and geometric metrics have been explored, they are typically analyzed in isolation, and the connections between them remain largely unknown. In this paper, we present Unified Topological Signatures (UTS) for characterizing the structure of embedding spaces. We evaluate our method across a wide range of text embedding models and retrieval datasets, finding that it outperforms individual metrics in downstream performance prediction. Through several experiments, we demonstrate that the signatures characterize embedding spaces more accurately, improve the prediction of model-specific properties and biases, and reveal novel insights into representational similarity that challenge the global claims of the Platonic Representation Hypothesis.