A Distributional Robustness Margin For Pathology Foundation Models

Pathology foundation models encode non-biological variation introduced by tissue preparation, staining and scanning, enabling shortcut learning that undermines generalisation across institutions. The Robustness Index (RI) was proposed to assess whether local representation geometry is dominated by biological or non-biological variation. However, its construction suffers from structural limitations that make cross-model comparison unreliable, calling for a more principled metric. We introduce the Cross-confounder Robustness Margin (CRoMa), a signed, per-sample margin that measures whether samples sharing the same biology but different confounder lie closer than samples sharing the same confounder but different biology. It is defined for every sample, allowing models to be compared on the same cohort and robustness to be analysed as a distribution rather than reduced to a single pooled score. We evaluated CRoMa across 20 tile-level encoders on three benchmarks. Rankings by median CRoMa were highly consistent across benchmarks (Spearman rho ~ 0.90), yet every encoder retained confounder-dominated samples, whose prevalence and severity varied markedly. Similar patterns emerged for four slide-level encoders evaluated on a separate benchmark, extending the analysis beyond tile-level representations. Higher median CRoMa was associated with smaller shortcut-induced performance losses in downstream linear probes, supporting its use as a representation-level indicator of shortcut susceptibility.