arXiv 论文论证：同状态配对使 JEPA 对柏拉图表示假说的证明在部分参数区间失效
Same-State Pairs Make One JEPA Proof of the Platonic Representation Hypothesis Vacuous
AI 导读
Xin Li 在 arXiv 发文指出，JEPA 对柏拉图表示假说（PRH）的证明依赖每条观测决定世界状态及谱隙保证极小元唯一性这一前提。在同状态正样本对的硬白化目标下，世界核变为单位阵，任意居中白化状态函数都是全局极小元；当 d_z−1≥2k 时两个极小元的最佳旋转平方残差可达 2k，而 k<d_z−1 时唯一性前提不可满足，证明在此区间空洞。
正文 · 原文
Abstract: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.
| Subjects: | Machine Learning (cs.LG); Artificial Intelligence (cs.AI) |
| Cite as: | arXiv:2611.16182 [cs.LG] |
| (or arXiv:2611.16182v1 [cs.LG] for this version) | |
| https://doi.org/10.48550/arXiv.2611.16182 arXiv-issued DOI via DataCite (pending registration) |
Submission history
From: Xin Li [view email]
[v1]
Thu, 12 Nov 2026 02:12:24 UTC (43 KB)
来源：arXiv cs.AI · arxiv.org