Implicit Greedy Rank Learning in Autoencoders via Overparameterized Linear Networks

This paper was accepted at the workshop on Overparameterization: Pitfalls and Opportunities at the ICML 2021 conference.

Deep linear networks trained with gradient descent yield low rank solutions, as is typically studied in matrix factorization. In this paper, we take a step further and analyze implicit rank regularization in autoencoders. We show greedy learning of low-rank latent codes induced by a linear sub-network at the autoencoder bottleneck. We further propose orthogonal initialization and principled learning rate adjustment to mitigate sensitivity of training dynamics to spectral prior and linear depth. With linear autoencoders on synthetic data, our method converges stably to ground-truth latent code rank. With nonlinear autoencoders, our method converges to latent ranks optimal for downstream classification and image sampling.