prh-mnn-alignment-metric-definition
IN premise — summaries/2026/08/24/huh-2024-prh-s6-counterexamples-and-limitations.md
Created 2026-08-24T17:10:56+00:00
The mutual nearest-neighbor (MNN) alignment metric used in the Platonic Representation Hypothesis paper is defined as the mean intersection of k-NN sets induced by two kernels, normalized by k, and achieves approximately 0.16 in cross-model experiments on a scale where the maximum is 1.0.
Summary
This defines the yardstick the system uses to judge how much two different models agree on which data points sit near each other in their internal representations, by measuring the overlap of their nearest-neighbor groups. In practice, cross-model tests land around 0.16 out of 1.0, meaning models share only about a sixth of their neighborhood structure, which is the baseline the system will use when assessing whether representations are converging toward a common "Platonic" space or still drifting apart.