CloudSplat: Distributional Contrastive Learning for Tabular Data

Evaluating whether a learned encoder separates classes well currently requires training a downstream classifier, an expensive, protocol-dependent step that conflates representation quality with classifier choice. We propose the CloudSplat Separability Index (CSSI), a differentiable two-sample test statistic that answers this question directly: it tests whether the distributions of within-class and between-class embedding distances are separable. CSSI sorts both distance collections and compares them position-by-position via a penalized 1D Wasserstein distance with a generalized p-mean: at p=1 it reduces to a standard average-difference test (analogous to a t-statistic on sorted distances), while p→∞ focuses on the single worst-separated quantile position (the W∞ distance on sorted distances). Unlike kNN accuracy or silhouette (which are non-differentiable), CSSI is differentiable, enabling its direct use as a training loss. We demonstrate this bridge in two roles: (a) As a training loss: plugging CSSI into a contrastive learning framework (CloudSplat) yields state-of-the-art tabular embeddings, winning on 6/7 datasets at 5% labels against five loss baselines, 7/11 benchmarks against SCARF, and achieving rank 1.9 among six SSL methods, all with a frozen encoder; (b) As a probe-free diagnostic: CSSI achieves Spearman ρ ∈ [+0.73, +0.92] with linear-probe accuracy across three foundation-model architectures on 19 datasets, correctly identifies separability on non-convex geometries where centroid-based metrics fail, and (unlike all competing diagnostics) can be directly optimized. The p parameter provides explicit sensitivity control: low p tests average separation, high p tests worst-case separation, enabling practitioners to tune the test's power profile to their application.