{"ID":2827975,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2512.15285","arxiv_id":"2512.15285","title":"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.","short_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 Persist...","url_abs":"https://arxiv.org/abs/2512.15285","url_pdf":"https://arxiv.org/pdf/2512.15285v1","authors":"[\"Aleksei Shestov\",\"Anton Klenitskiy\",\"Daria Denisova\",\"Amurkhan Dzagkoev\",\"Daniil Petrovich\",\"Andrey Savchenko\",\"Maksim Makarenko\"]","published":"2025-12-17T10:38:38Z","proceeding":"cs.LG","tasks":"[\"cs.LG\",\"cs.IR\"]","methods":"[\"Generative Adversarial Network\"]","has_code":false}