# Topological Metric for Unsupervised Embedding Quality Evaluation

arXiv: https://arxiv.org/abs/2512.15285 · HTML: https://mlsanity.com/paper/2512.15285/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 15 of its 30 references that are in the map.
- First posted on arXiv 17 Dec 2025.

## Builds on (most cited first, 15 of 15)

- [Learning Transferable Visual Models From Natural Language Supervision](https://mlsanity.com/paper/2103.00020/) (2021)
- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [A Simple Framework for Contrastive Learning of Visual Representations](https://mlsanity.com/paper/2002.05709/) (2020)
- [Momentum Contrast for Unsupervised Visual Representation Learning](https://mlsanity.com/paper/1911.05722/) (2019)
- [Masked Autoencoders Are Scalable Vision Learners](https://mlsanity.com/paper/2111.06377/) (2021)
- [Bootstrap your own latent: A new approach to self-supervised Learning](https://mlsanity.com/paper/2006.07733/) (2020)
- [Scaling Up Visual and Vision-Language Representation Learning With Noisy Text Supervision](https://mlsanity.com/paper/2102.05918/) (2021)
- [Self-supervised Visual Feature Learning with Deep Neural Networks: A Survey](https://mlsanity.com/paper/1902.06162/) (2019)
- [A Survey on Self-supervised Learning: Algorithms, Applications, and Future Trends](https://mlsanity.com/paper/2301.05712/) (2023)
- [RankMe: Assessing the downstream performance of pretrained self-supervised representations by their rank](https://mlsanity.com/paper/2210.02885/) (2022)
- [A roadmap for the computation of persistent homology](https://mlsanity.com/paper/1506.08903/) (2015)
- [CoLES: Contrastive Learning for Event Sequences with Self-Supervision](https://mlsanity.com/paper/2002.08232/) (2020)
- [Cliques and Cavities in the Human Connectome](https://mlsanity.com/paper/1608.03520/) (2016)
- [Unsupervised Embedding Quality Evaluation](https://mlsanity.com/paper/2305.16562/) (2023)
- [Encode Me If You Can: Learning Universal User Representations via Event Sequence Autoencoding](https://mlsanity.com/paper/2508.07748/) (2025)

## Built on by (most cited first, 2 of 2)

- [Embedding-Aware Feature Discovery: Bridging Latent Representations and Interpretable Features in Event Sequences](https://mlsanity.com/paper/2603.15713/) (2026)
- [User-Centric Modeling of Transactional Sequences with Explainable State Space Models](https://mlsanity.com/paper/2607.20228/) (2026)

## Abstract (arXiv)

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.