Revisiting the Platonic Representation Hypothesis: An Aristotelian View

TL;DR

This paper critically examines the Platonic Representation Hypothesis, revealing that previous similarity metrics are confounded by network scale and proposing a calibration framework that supports a revised Aristotelian view of neural representations converging locally.

Contribution

The paper introduces a permutation-based null-calibration method to correct similarity metrics and revises the hypothesis to focus on local neighborhood convergence.

Findings

Global spectral similarity largely disappears after calibration.

Local neighborhood similarity persists across modalities.

Local distances do not show significant convergence.

Abstract

The Platonic Representation Hypothesis suggests that representations from neural networks are converging to a common statistical model of reality. We show that the existing metrics used to measure representational similarity are confounded by network scale: increasing model depth or width can systematically inflate representational similarity scores. To correct these effects, we introduce a permutation-based null-calibration framework that transforms any representational similarity metric into a calibrated score with statistical guarantees. We revisit the Platonic Representation Hypothesis with our calibration framework, which reveals a nuanced picture: the apparent convergence reported by global spectral measures largely disappears after calibration, while local neighborhood similarity, but not local distances, retains significant agreement across different modalities. Based on these findings, we propose the Aristotelian Representation Hypothesis: representations in neural networks are converging to shared local neighborhood relationships.