A prism hierarchy of learning regimes in large linear autoencoders
Theoretical studies of machine learning models commonly consider different limiting regimes in which the learning dynamics of gradient descent becomes theoretically tractable. It is, however, desirable to have a systematically obtained picture of qualitatively different extreme learning regimes for a particular type of models. In this paper we propose such a picture for large weight-tied linear autoencoders characterized by input and latent dimensions, initialization magnitude, and training set size. This model is nonlinear in the weights and its gradient flow does not have a general theoretical solution. We show that at the level of the formal loss-expansion hierarchy, its extreme regime...
| Authors | Eugene Golikov, Yaroslav Gusev, Dmitry Yarotsky |
|---|---|
| Primary category | cs.LG |
| Published | 3 June 2026 |
| Last updated at source | 6 October 2026 |
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