Implicit Rank-Minimizing Autoencoder
This work addresses the challenge of controlling latent space dimensionality in autoencoders for image generation and representation learning, though it appears incremental as it builds on known gradient descent properties in linear networks.
The authors tackled the problem of minimizing the information capacity of autoencoder latent representations by implicitly reducing the rank of the covariance matrix through extra linear layers, resulting in a simple and deterministic model that learns compact latent spaces.
An important component of autoencoders is the method by which the information capacity of the latent representation is minimized or limited. In this work, the rank of the covariance matrix of the codes is implicitly minimized by relying on the fact that gradient descent learning in multi-layer linear networks leads to minimum-rank solutions. By inserting a number of extra linear layers between the encoder and the decoder, the system spontaneously learns representations with a low effective dimension. The model, dubbed Implicit Rank-Minimizing Autoencoder (IRMAE), is simple, deterministic, and learns compact latent spaces. We demonstrate the validity of the method on several image generation and representation learning tasks.