aiqbench analysis
This research challenges the prevailing view of model convergence by distinguishing between relational structure and metric geometry, revealing that while topological relationships stabilize across vision-language models, quantitative distance metrics show significantly weaker alignment. The study demonstrates that capacity-dependent trends in similarity measures largely vanish once these structural factors are disentangled, offering a more nuanced understanding of how large models represent data beyond simple Euclidean spaces.
What Converges in the Platonic Representation Hypothesis? Structure over Geometry
arXiv:2609.27252v1 Announce Type: new 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.
Title:What Converges in the Platonic Representation Hypothesis? Structure over Geometry
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.
Machine Learning (cs.LG); Computer Vision and Pattern Recognition (cs.CV); Algebraic Topology (math.AT)
arXiv:2609.27252 [cs.LG]
(or arXiv:2609.27252v1 [cs.LG] for this version)
https://doi.org/10.48550/arXiv.2609.27252 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
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Full text under the publisher's open licence · 313 words
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