Implicit Greedy Rank Learning in Autoencoders via Overparameterized Linear Networks
This work addresses the challenge of controlling latent space rank in autoencoders for improved performance in machine learning applications, representing an incremental advancement.
The paper tackled the problem of implicit rank regularization in autoencoders by analyzing greedy learning of low-rank latent codes, showing that with linear autoencoders on synthetic data, the method converges stably to ground-truth latent code rank, and with nonlinear autoencoders, it converges to latent ranks optimal for downstream tasks like classification and image sampling.
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.