A new paper challenges the Platonic Representation Hypothesis — the idea that neural networks converge toward a single global representation of reality as they scale. The authors show that common similarity metrics like CKA are inflated by model width (embedding dimension) and depth (number of layer pairs), making models appear more globally aligned than they actually are. They propose a permutation-based null-calibration framework that is metric-agnostic and corrects for both sources of bias. After calibration, global convergence largely disappears, but local neighborhood structure — which objects sit near which — remains meaningfully shared across models. This 'Aristotelian' view suggests models converge on local topology and relational structure rather than a universal global geometry. The practical takeaway: always calibrate representational similarity scores against a null distribution, especially when comparing models of different scales.
