重新审视柏拉图式表征假说：一种亚里士多德式的观点
Revisiting the Platonic Representation Hypothesis: An Aristotelian View
AI总结：
针对神经网络表征收敛于统一统计模型的柏拉图式假说，本文发现现有相似性度量受网络规模混淆，提出基于置换的零校准框架，揭示全局谱收敛在校准后消失，而局部邻域相似性（非距离）仍跨模态一致，据此提出亚里士多德式表征假说。
摘要：
柏拉图式表征假说认为，神经网络的表征正在收敛到一个共同的现实统计模型。我们表明，用于测量表征相似性的现有度量受到网络规模的混淆：增加模型深度或宽度会系统性地膨胀表征相似性分数。为了纠正这些影响，我们引入了一个基于置换的零校准框架，该框架将任何表征相似性度量转化为具有统计保证的校准分数。我们使用我们的校准框架重新审视柏拉图式表征假说，这揭示了一幅微妙的图景：全局谱度量报告的明显收敛在校准后基本消失，而局部邻域相似性（而非局部距离）在不同模态之间保留了显著的一致性。基于这些发现，我们提出了亚里士多德式表征假说：神经网络中的表征正在收敛到共享的局部邻域关系。
英文摘要：
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.
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