cka-width-inflation-gap-exact
IN premise — summaries/2026/08/24/aristotelian-2026-sR-references-chunk-2.md
Created 2026-08-24T17:10:50+00:00
For fixed sample size n, the sample centered linear CKA converges to 1 almost surely as width d→∞, with the inflation gap equal to exactly 1−ρ² where ρ² is the true population alignment
Summary
In very high dimensions, the sample CKA measure will always read as perfect alignment (driving toward 1), no matter what the true relationship between the two representations actually is, and the overestimation is exactly 1−ρ². This means CKA cannot be trusted as a diagnostic in wide architectures, because it will systematically confirm alignment even when there is none, fooling any decision pipeline that relies on it.