More Data Cannot Break a Symmetry: Identifiability by Design
Unsupervised representational alignment recovers a stimulus-by-stimulus correspondence from geometry alone, but the automorphism group of the stimulus geometry bounds what any such alignment can identify, before data exist. The obvious diagnostic for this degeneracy, the cheapest non-identity relabelling, ranks two published designs in the wrong order, because dense sampling creates near-duplicates whose transposition is nearly free. We turn this known invariance (Demetci et al., 2024) into a design-time diagnostic and intervention. In colour, where candidate geometries have closed form, we show that the failure is structural: sixty-four times the restart budget leaves a symmetric design ...
| Authors | Jing Xu, Christopher Kanan |
|---|---|
| Primary category | cs.LG |
| Published | 27 August 2026 |
| Last updated at source | 27 August 2026 |
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