When Probe Rankings Don't Transfer: The Probe Selection Tax in Sleep-EEG Foundation Models

Foundation models do not eliminate downstream model selection: they expose many plausible interfaces to a fixed representation. We ask whether source-domain validation can identify which interface will transport across institutions. Across 500 four-head probes of a pretrained sleep-EEG model evaluated in 338 participants from 3 institutions, probe rankings are substantially more concordant between source institutions than between source and held institutions (mean Spearman $0.584$ vs. $0.093$). Consequently, expanding probe search from 1 to 500 candidates raises source-validation AUROC by $+0.213$, while macro held-site AUROC rises only $+0.023$. We call the unrecovered source gain the Probe Selection Tax; here it is $+0.191$ and positive across all 100 candidate orderings. At S0001, the source-selected probe has held-site AUROC $0.422$, while another candidate in the same bank reaches $0.764$. Top-10 averaging improves this site but yields no macro held-site gain. These results show that source-consistent interface selection need not imply institutional transport and motivate reporting probe-search budget alongside held-site performance.