Topological Metric for Unsupervised Embedding Quality Evaluation
Abstract
Modern representation learning increasingly relies on unsupervised and self-supervised methods trained on large-scale unlabeled data. While these approaches achieve impressive generalization across tasks and domains, evaluating embedding quality without labels remains an open challenge. In this work, we propose Persistence, a topology-aware metric based on persistent homology that quantifies the geometric structure and topological richness of embedding spaces in a fully unsupervised manner. Unlike metrics that assume linear separability or rely on covariance structure, Persistence captures global and multi-scale organization. Empirical results across diverse domains show that Persistence consistently achieves top-tier correlations with downstream performance, outperforming existing unsupervised metrics and enabling reliable model and hyperparameter selection.
Cite
@article{arxiv.2512.15285,
title = {Topological Metric for Unsupervised Embedding Quality Evaluation},
author = {Aleksei Shestov and Anton Klenitskiy and Daria Denisova and Amurkhan Dzagkoev and Daniil Petrovich and Andrey Savchenko and Maksim Makarenko},
journal= {arXiv preprint arXiv:2512.15285},
year = {2025}
}