A Closed Form Depth-Width Law for Neural Collapse in Deep Linear Networks
How depth and width of neural networks shape learned representations is usually studied only after training. We show that, in a tractable feature-learning setting, this dependence can instead be obtained in closed form. Using neural collapse as a probe of representation geometry, we express NC1--NC3 directly in terms of the learned feature kernel, extending an identity known for NC1 to the angular part of NC2 and to NC3 under a ridge readout. For deep linear networks with exchangeable class structure, the resulting kernel equations yield a geometric law, exact within the theory, for the layerwise evolution of within-class variability. At large width, the accumulated compression becomes a ...
| Authors | Pankhil Gawade, Kirsten Fischer, Guy Wolf et al. |
|---|---|
| Primary category | cs.LG |
| Published | 15 October 2026 |
| Last updated at source | 15 October 2026 |
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