Stochastic Gradient Descent in the Saddle-to-Saddle Regime of Deep Linear Networks
Deep linear networks (DLNs) are used as an analytically tractable model of the training dynamics of deep neural networks. While gradient descent in DLNs is known to exhibit saddle-to-saddle dynamics, the impact of stochastic gradient descent (SGD) noise on this regime remains poorly understood. We investigate the dynamics of SGD during training of DLNs in the saddle-to-saddle regime. We model the training dynamics as stochastic Langevin dynamics with anisotropic, state-dependent noise. Under the assumption of aligned and balanced weights, we derive an exact decomposition of the dynamics into a system of one-dimensional per-mode stochastic differential equations. This establishes that the ...
| Authors | Guillaume Corlouer, Avi Semler, Alexander Strang et al. |
|---|---|
| Primary category | cs.LG |
| Published | 7 April 2026 |
| Last updated at source | 7 April 2026 |
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