Which Geometry on Which Layer? Measured Sign-Spectral Assignment in Mixed-Optimizer Training
Modern neural-network training uses mixed recipes, assigning AdamW-like or sign-based updates to embedding and output layers and spectral updates to hidden matrices. These assignments are usually fixed by layer type, without a clear criterion for selecting the appropriate geometry. We turn sign-versus-spectral assignment into a measurable, layerwise decision problem. For ideal memoryless steps, we derive a finite-batch ratio of conservative descent-lemma lower bounds for spectral and sign updates. Its closed form separates signal efficiency from a geometry-dependent global curvature factor. In the positive-signal regime, the same smoothness assumption gives two-sided bounds that determine...
| Authors | Hiroki Naganuma, Laura Gomezjurado, Mahdi Ghaznavi et al. |
|---|---|
| Primary category | cs.LG |
| Published | 12 October 2026 |
| Last updated at source | 12 October 2026 |
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