After correcting CKA and mutual k-NN alignment for a proven width/depth-dependent null-baseline confound (O(d/n) for global spectral metrics vs O(k/n) for local-neighborhood metrics), the Platonic Representation Hypothesis's global cross-modal convergence largely vanishes while its local-neighborhood convergence survives, across real image-text and video-language pretrained model pairs

Gröger, Wen & Brbić (2026) prove that representational-similarity metrics have a non-vanishing expected value even between statistically independent representations: global spectral metrics like CKA carry an $\mathcal{O}(d_xd_y/n)$ null baseline that grows with representation width (and, via layer-selection, depth), while local-neighborhood metrics like mutual k-NN carry a much smaller $\mathcal{O}(k/n)$ baseline. They introduce a permutation-based null-calibration framework ([[null-calibrated-representational-similarity]]) that estimates and subtracts off this baseline for any similarity metric, then re-run the Platonic Representation Hypothesis's own image-text alignment experiments (following Huh et al. 2024's setup: BLOOMZ, OpenLLaMA, base LLaMA and Gemma-2-9B-it on the language side; AugReg/MAE/DINOv2/ CLIP-LAION2B Vision Transformers on the vision side, paired via Wikipedia image-caption data) plus a new video-language extension (VideoMAE base/large/huge paired with DINOv2/CLIP-LAION2B vision-side encoders and the same language-model family) through this calibration. The result: "the apparent convergence reported by global spectral measures largely disappears after calibration, while local neighborhood similarity... retains significant agreement across different modalities" -- a genuine narrowing of the Platonic Representation Hypothesis's original claim rather than its wholesale refutation, motivating the [[aristotelian-representation-hypothesis]]. The paper's precise correlation coefficients, effect sizes and permutation p-values for each modality pairing sit in Section 6 and Appendix E.8/E.9 of the source, which could not be retrieved despite three separate full-text fetch attempts (direct fetch, plus two dedicated subagents trying arXiv HTML v1/v2, ar5iv, ar5iv.org, a Jina reader mirror, Semantic Scholar, OpenReview, and the paper's own GitHub raw source) -- all hit the same hard MathML-bloat truncation wall before reaching those sections. The qualitative finding quoted above comes from the authors' own official project-page summary (brbiclab.epfl.ch/projects/aristotelian), and the exact model list above was independently confirmed from the paper's own GitHub source code (`aristotelian/prh/prh_models.py`, `video_models.py`), not fabricated -- but no numeric correlation/p-value/effect-size figures are recorded here since none could be honestly sourced.