Noise Ceilings for Representational Convergence

The Platonic Representation Hypothesis links increasing model alignment to a shared representation of the world. Yet a rising alignment score can also reflect more reproducible training outcomes. We develop a noise-ceiling analysis that separates training-seed reliability from consensus alignment. For mutual nearest-neighbor overlap and linear centered kernel alignment (CKA), normalized representation objects give an exact factorization of expected alignment, without assuming additive or isotropic noise. Across nine PolyPythia seeds at each of five scales, reliability accounts for 51.3% of the language–vision log-alignment trend; an independent OLMo suite gives 50.7%. Fixed-readout, capability-axis, and replicated-vision controls support a substantial reliability contribution. Fresh extraction of 105 training checkpoints reveals a sharper distinction: Pythia 14M raw CKA alignment rises by 89% while corrected consensus falls by 10%, and the measured training paths differ between Pythia and OLMo. Known-truth experiments expose the limits of correction with few seeds. Raw alignment also predicts held-out retrieval better than corrected alignment, distinguishing consensus from individual-model utility. The resulting protocol measures reproducibility, shared representational structure, and usefulness as separate properties, making convergence claims more precise and testable.