Native Geometry vs. Linear Recoverability: How Alignment Changes Platonic Scaling

Do larger models learn increasingly similar representations of the same world?

By Hoy, Lutterbach, Chong +2Oct 15, 2026

Score███░░░░░░░3.4

VerdictWorth a reader's time today.

Abstract

Do larger models learn increasingly similar representations of the same world? The Platonic Representation Hypothesis (PRH) predicts that they should, but similar can mean native cosine geometry---nearest-neighbour structure induced by cosine similarity before any learned alignment---or linear recoverability: correspondence revealed by a supervised linear map. Using matched Legacy Survey and Hyper Suprime-Cam (HSC) embeddings across five model families, we find that Ridge alignment strengthens the relationship between model size and cross-dataset neighbourhood correspondence relative to native cosine geometry. The effect appears in all five families and persists when both representations are reduced to dimension, so it is not simply that wider embeddings give alignment more dimensions to work with. The learned maps remain far from rotations or uniform scaling, and Sparse Autoencoder (SAE) and Block-Sparse Featuriser (BSF) features give no advantage over the same alignment applied to dense embeddings. Model scale thus improves linear recoverability more clearly than native cosine-neighbourhood correspondence, without establishing convergence toward a shared native metric geometry.

Angus Hoy, Austin Lutterbach, Jasper Chong, Aman Kumar, Michael J. Smith

The editor's rubric

Heuristic review

Leverage3 / 5: A method or resource many groups across the field will adopt within a year.; 24% of this desk’s rubric
Magnitude2 / 5: Solid incremental gain on a meaningful problem.; 18% of this desk’s rubric
Evidence3 / 5: Solid: multiple benchmarks or cohorts, ablations, fair baselines, released code or data.; 14% of this desk’s rubric
Novelty3 / 5: A genuinely new approach to an open problem.; 16% of this desk’s rubric
Trajectory3 / 5: A clear path to scale.; 18% of this desk’s rubric
Stakes2 / 5: Benefits a professional community (practitioners, clinicians, engineers).; 10% of this desk’s rubric

Dimension	Level	Weight	What that level means
Leverage	███░░ 3	24%	A method or resource many groups across the field will adopt within a year.
Magnitude	██░░░ 2	18%	Solid incremental gain on a meaningful problem.
Evidence	███░░ 3	14%	Solid: multiple benchmarks or cohorts, ablations, fair baselines, released code or data.
Novelty	███░░ 3	16%	A genuinely new approach to an open problem.
Trajectory	███░░ 3	18%	A clear path to scale.
Stakes	██░░░ 2	10%	Benefits a professional community (practitioners, clinicians, engineers).

Editor’s rationale

Heuristic triage from title and abstract text only, not a reading of the paper. Cues found: method (we report); verification (multiple benchmarks); scale (scalable, larger models).

How the score was computed

rank-2026-10-18

Score███░░░░░░░3.4

Score = 10 × (65% × adjusted merit / 10 + 25% × attention + 10% × freshness)

Desks place stronger verdicts first, then use this score to order work within the same verdict.

Merit: 5.4 / 10; Weighted rubric, evidence-gated.
Adjusted merit: 4.5 / 10; Shrunk toward the desk prior by editor confidence (38%).
Attention: 0%; Citations, upvotes, points, mentions.
Freshness: 43%; Half-life decay since publication.

No attention signals recorded yet.

The record

Reviewed by heuristic-v7 on Oct 19, 2026, 01:37 UTC. Paper type: method.
Categories: cs.LG, astro-ph.IM
BRIEF, No.3 in the Physics edition of October 19, 2026.