prh-kernel-formal-definition
IN premise — summaries/2026/08/24/huh-2024-prh-s1-introduction.md
Created 2026-08-24T17:10:56+00:00
In the Platonic Representation Hypothesis (Huh et al., ICML 2024), the kernel is formally defined as K(xᵢ, xⱼ) = ⟨f(xᵢ), f(xⱼ)⟩, capturing the similarity/distance structure induced by a representation f: X → ℝⁿ, and it is the kernel (not raw embeddings) that is compared across models.
Summary
When comparing two neural networks to see if they "see" the world the same way, what actually gets compared is a matrix of pairwise similarity scores (the kernel), not the raw embedding vectors themselves. This means the test is about who-similar-to-whom structure, so two models can differ in dimensionality, rotation, or scaling and still be judged as sharing a common representation.