发表机构
KAIST; POSTECH（韩国科学技术院; 浦项科技大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究挑战柏拉图式表征假说的局部收敛解释，提出结构尺度与比较对象的混淆，构建2×2框架评估关系结构与度量几何，发现关系结构在局部和全局尺度均稳健收敛，而度量几何收敛显著较弱。
AI 中文摘要
柏拉图式表征假说认为，能力日益增强的模型会趋向于共享的表征。近期研究将此论断缩小至共享的局部邻域关系，并发现若干全局相似性度量中依赖于能力的趋势在校准后大多消失。我们对此解释提出挑战，指出先前的局部-全局比较混淆了结构尺度（局部与全局）与比较对象：关系结构（由哪些样本相关来定义）与度量几何（以距离、相似度或相关性等定量关系为特征）。为厘清这些因素，我们构建了一个受控的2×2框架，在局部和全局尺度上同时评估关系结构和度量几何。我们引入H0骨架重叠作为互k近邻的全局对应物，并配以匹配的距离感知变体。在视觉-语言模型中，关系结构在校准后于两个尺度均展现出稳健的表征收敛，而日益严格的距离一致性则显著削弱对齐，并逐渐使依赖于能力的趋势趋于平坦。我们进一步将分析扩展到环境欧几里得几何之外，通过黎曼度量近似评估距离一致性，并重现了相同的结构-几何模式。该模式在视频-文本表征中也得以复现。综合来看，这些结果表明关系收敛从局部邻域延伸至全局跨越结构，而度量几何则表现出显著较弱的收敛。
英文摘要
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.
Comments33 pages, 12 figures, 6 tables
