local-global-dissociation-after-calibration

IN premise — summaries/2026/08/24/aristotelian-2026-sR-references-chunk-3.md

Created 2026-08-24T17:10:51+00:00

After permutation calibration, local neighborhood metrics (mKNN, CKNNA, cycle-kNN) retain significant cross-modal alignment and scaling trend with model capability, while global spectral metrics (CKA linear, CKA RBF, SVCCA, RV, Procrustes) lose their scaling trend (CKA linear Pearson r drops from 0.86 to 0.45; Unbiased CKA from 0.65 to −0.01)

Summary

Once you strip out the statistical artifacts introduced by calibration, the big-picture structural alignment between modalities turns out to be mostly noise, while the fine-grained neighborhood structure remains a reliable signal of how well the model actually aligns information across inputs. This matters because it means you should trust local similarity metrics over global geometry metrics when judging whether a model has genuinely learned cross-modal correspondence, since the global picture is largely an encoding artifact that disappears under proper controls.