Variational auto-encoders
 (VAEs) offer a tractable approach when performing approximate inference in otherwise intractable generative models. However, standard VAEs often produce latent codes that are disperse and lack interpretability, thus making the resulting representations unsuitable for auxiliary tasks (e.g. classiﬁcation) and human interpretation. We address these issues by merging ideas from variational auto-encoders and sparse coding, and propose to explicitly model sparsity in the latent space of a VAE with a Spike and Slab prior distribution. We derive the evidence lower bound using a discrete mixture recognition function thereby making approximate posterior inference as computational efﬁcient as in the standard VAE case. With the new approach, we are able to infer truly sparse representations with generally intractable non-linear probabilistic models. We show that these sparse representations are advantageous over standard VAE representations on two benchmark classiﬁcation tasks (MNIST and Fashion-MNIST) by demonstrating improved classiﬁcation accuracy and signiﬁcantly increased robustness to the number of latent dimensions. Furthermore, we demonstrate qualitatively that the sparse elements capture subjectively understandable sources of variation.
We explore the intersection of VAEs and sparse coding. This paper proposes an extension of VAEs with sparse priors and posteriors to learn sparse interpretable representations.