用拓扑方法无监督评估嵌入质量，更准地预测模型性能。
Topological Metric for Unsupervised Embedding Quality Evaluation
- 基于持久同调分析嵌入空间的全局结构
- 在多个领域上与下游任务表现相关性领先
- 适合无标签数据下模型选型与调参
现代表示学习越来越多依赖大规模无标签数据上的无监督和自监督方法。尽管这些方法在跨任务和跨领域上表现出色，但缺乏标签时评估嵌入质量仍是未解难题。本文提出Persistence，一种基于持久同调的拓扑感知度量，可完全无监督地量化嵌入空间的几何结构与拓扑丰富度。不同于假设线性可分或依赖协方差结构的指标，Persistence能捕捉全局与多尺度组织特征。在多个领域的实证结果表明，Persistence与下游性能具有极强相关性，显著优于现有无监督度量，可实现可靠的模型与超参数选择。
原文摘要 · Abstract (English)
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.
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