arXiv:2611.16182 · v1

Same-State Pairs Make One JEPA Proof of the Platonic Representation Hypothesis Vacuous

首次提交 2026-11-12 10:12

版本更新 2026-11-12 10:12

雷达观测 2026-11-13 14:16

摘要

In a Joint-Embedding Predictive Architecture (JEPA), the JEPA proof of the Platonic Representation Hypothesis (PRH) assumes that every observation determines the world state and that a spectral gap makes minimizers unique up to rotation. Under the hard-whitening population objective, same-state positive pairs make the induced world kernel the identity: every centered whitened state function is a global minimizer, and, when $d_z-1\ge 2k$, two minimizers can have best-rotation squared residual $2k$. The uniqueness claim is conditional; for $k<d_z-1$, where $d_z$ is the number of world states, this limit makes its premise unsatisfiable, so the claim has no content there. The experiments that motivate it leave the assumption: a caption sees only part of an image, and the paper states no experiment meets its hypotheses exactly. The theorem does not reach those experiments, and for $k<d_z-1$ its idealized same-state limit is vacuous. One of the paper's four quantitative results survives: a gap-free lower bound. Its bound vanishes only at perfect scene-explained fraction; it bounds alignment error but cannot certify good-view alignment. A canonical frame is determined only up to a rotation and a latent permutation. Paired samples fix the relative frame at effective rank $k$; a global rotation remains. Component semantics fix the relative permutation only up to signs; value anchors fix it once the mixing frame is pinned. A resource--gauge ledger records which resource fixes which gauge.