aggregation-aware-calibration-requires-same-permutation-across-layers
IN premise — summaries/2026/08/24/aristotelian-2026-s5-representational-similarity-calibration.md
Created 2026-08-24T17:10:50+00:00
Aggregation-aware null-calibration requires applying the same row permutation π_k to all layers of one model (S^{(k)}_{ℓ,ℓ'} = s(X_ℓ^A, π_k(Y_{ℓ'}^B))) to preserve the joint dependence structure exploited by the selection operator, rather than calibrating each layer independently and then aggregating.
Summary
When calibrating a multi-layer model using a method that accounts for how layers are combined, the row ordering must stay consistent across all layers of that model. Calibrating each layer on its own with independent shuffles and then gluing the results together destroys the correlation between layers that the aggregation step depends on, producing miscalibrated outputs.