Gromov-Wasserstein Autoencoders

Learning concise data representations without supervisory signals is a fundamental challenge in machine learning. A prominent approach to this goal is likelihood-based models such as variational autoencoders (VAE) to learn latent representations based on a meta-prior, which is a general premise assumed beneficial for downstream tasks (e.g., disentanglement). However, such approaches often deviate from the original likelihood architecture to apply the introduced meta-prior, causing undesirable changes in their training. In this paper, we propose a novel representation learning method, Gromov-Wasserstein Autoencoders (GWAE), which directly matches the latent and data distributions. Instead of a likelihood-based objective, GWAE models have a trainable prior optimized by minimizing the Gromov-Wasserstein (GW) metric. The GW metric measures the distance structure-oriented discrepancy between distributions supported on incomparable spaces, e.g., with different dimensionalities. By restricting the family of the trainable prior, we can introduce meta-priors to control latent representations for downstream tasks. The empirical comparison with the existing VAE-based methods shows that GWAE models can learn representations based on meta-priors by changing the prior family without further modifying the GW objective.