Beyond Linear and Overcomplete Regimes: A Mean-Field Analysis of Bottleneck Autoencoders
Autoencoders (AEs) learn low-dimensional representations by mapping data into a latent space while minimizing reconstruction error. Despite their empirical success, theoretical understanding remains limited and largely restricted to linear models or settings without a bottleneck. In this work, we study nonlinear AEs with a fixed finite-dimensional bottleneck in the mean-field (MF) regime. We derive explicit MF learning dynamics for both encoder and decoder, providing a tractable characterization of training in the nonlinear setting. We show that, over finite time horizons, the empirical risk of finite-width networks trained with stochastic gradient descent closely tracks the MF risk traje...
| Authors | Santanu Das, Ramyak Bilas, Pascal Esser et al. |
|---|---|
| Primary category | cs.LG |
| Published | 5 June 2026 |
| Last updated at source | 22 June 2026 |
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