What Converges in the Platonic Representation Hypothesis? Structure over Geometry

2026-09-22

AI Summary

本文探讨了模型能力与表示收敛性关系，通过构建一个2x2框架区分结构和几何在局部和全局尺度上的表现，揭示了关系结构比度量几何展现出更强的收敛性。

Abstract

The Platonic Representation Hypothesis suggests that increasingly capable models converge toward shared representations. Recent work narrows this claim to shared local neighborhood relationships, finding that capacity-dependent trends in several global similarity measures largely disappear after calibration. We challenge this interpretation by showing that prior local-global comparisons confound structural scale (local versus global) with what is compared: relational structure, defined by which samples are related, versus metric geometry, characterized by quantitative relations such as distances, similarities, or correlations. To disentangle these factors, we construct a controlled $2\times2$ framework that evaluates both relational structure and metric geometry at local and global scales. We introduce $H_0$ skeleton overlap as a global counterpart to mutual $k$-nearest neighbors, together with matched distance-aware variants. Across vision-language models, relational structure exhibits robust representational convergence at both scales after calibration, whereas increasingly stringent distance agreement substantially weakens alignment and progressively flattens the capacity-dependent trend. We further extend the analysis beyond ambient Euclidean geometry by evaluating distance agreement under a Riemannian metric approximation and recover the same structure-geometry pattern. The pattern is also reproduced in video-text representations. Together, these results show that relational convergence extends beyond local neighborhoods to global spanning structure, whereas metric geometry exhibits substantially weaker convergence.

Problem

• Platonic Representation Hypothesis
• relational structure
• metric geometry
• local-global scales

Innovation

• relational structure
• metric geometry
• representational convergence
• Riemannian metric approximation
• vision-language models