post-calibration-three-way-distinction-global-local-knn-distances

IN premise — summaries/2026/08/24/aristotelian-2026-s0-abstract.md

Created 2026-08-24T17:10:50+00:00

After permutation-based null-calibration, global spectral measures (CKA, CCA) lose their scaling convergence trend, local neighborhood similarity (mutual k-NN) retains significant cross-modal alignment, but local pairwise distances do not retain alignment.

Summary

Once you strip out the statistical artifacts that make modalities look more similar than they really are, the only cross-modal signal that survives is the neighborhood structure — which points cluster together — while overall alignment scores and raw pairwise distances become indistinguishable from noise. This tells the system to trust k-nearest-neighbor geometry as a valid basis for cross-modal matching and to discount global similarity metrics and raw distance comparisons as unreliable after proper calibration.