Disentangling Disentanglement in Variational Autoencoders
This work addresses the challenge of learning interpretable and structured representations in unsupervised learning, offering a more flexible framework for VAEs, though it is incremental in building upon existing methods.
The authors tackled the problem of disentangling latent representations in variational autoencoders by generalizing disentanglement to a broader concept called decomposition, which includes factors like latent overlap and prior structure. They showed that simple prior manipulations can improve disentanglement without harming reconstruction quality.
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 $β$-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.