Disentangling Disentanglement in Variational Autoencoders

TL;DR

This paper generalizes the concept of disentanglement in VAEs by introducing a decomposition framework that encompasses various properties of latent representations, enabling richer and more controllable learned features.

Contribution

It proposes a new decomposition-based perspective on disentanglement, extending beyond independence to include properties like sparsity and hierarchy, and introduces an alternative training objective for better control.

Findings

$eta$-VAE controls latent overlap more than disentanglement

Breaking invariance with prior manipulation improves disentanglement

Different priors enable various decompositions

Abstract

We develop a generalisation of disentanglement in VAEs---decomposition of the latent representation---characterising it as the fulfilment of two factors: a) the latent encodings of the data having an appropriate level of overlap, and b) the aggregate encoding of the data conforming to a desired structure, represented through the prior. Decomposition permits disentanglement, i.e. explicit independence between latents, as a special case, but also allows for a much richer class of properties to be imposed on the learnt representation, such as sparsity, clustering, independent subspaces, or even intricate hierarchical dependency relationships. We show that the $\beta$-VAE varies from the standard VAE predominantly in its control of latent overlap and that for the standard choice of an isotropic Gaussian prior, its objective is invariant to rotations of the latent representation. Viewed from the decomposition perspective, breaking this invariance with simple manipulations of the prior can yield better disentanglement with little or no detriment to reconstructions. We further demonstrate how other choices of prior can assist in producing different decompositions and introduce an alternative training objective that allows the control of both decomposition factors in a principled manner.