Transforming Rank: How Architecture Navigates the Spectral Pathologies of Depth
We investigate how each component of the Transformer feedforward block architecture design determines how much rank survives across depth at initialization. We reinterpret skip connections and normalization, long understood as controlling magnitude, as mechanisms for preserving gradient rank across depth, since the very matrix multiplications and nonlinear activations that make the network expressive also reduce the rank. We show that skip connections trade off rank collapse against ensemble-like behavior, controlled by the relative scales of the branch and the skip: skip connections route the gradient around the residual branch, where rank is lost, rather than along the long gradient pat...
| Authors | Katie Everett |
|---|---|
| Primary category | cs.LG |
| Published | 15 July 2026 |
| Last updated at source | 15 July 2026 |
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