Sparse Coding Variational Auto Encoders
The sparse coding model posits that the visual system has evolved to efficiently code natural stimuli using a sparse set of features from an overcomplete dictionary. The classic sparse coding model suffers from two key limitations, however: (1) computing the neural response to an image patch requires minimizing a nonlinear objective function, which was initially not easily mapped onto a neurally plausible feedforward mechanism and (2) fitting the model to data relied on an approximate inference method that ignores uncertainty. Here we address these two shortcomings by formulating a variational inference method for the sparse coding model inspired by the variational auto encoder (VAE) framework. The sparse coding variational auto encoder (SVAE) augments the classic sparse coding model with a probabilistic recognition model, parametrized by a deep neural network. This recognition model provides a neurally plausible implementation for the mapping from image patches to neural activities, and enables a principled method for fitting the sparse coding model to data via maximization of the evidence lower bound (ELBO) The SVAE differs from the traditional VAE in three important ways: the generative model is the sparse coding model instead of a deep network; the latent representation is overcomplete, with more latent dimensions than image pixels; and the prior over latent variables is a sparse or heavy tailed instead of Gaussian. We fit the SVAE to natural image data under different assumed prior distributions, and show that it obtains higher test performance than previous fitting methods. Finally, we examine the response properties of the recognition network and show that it captures important nonlinear properties of neurons in the early visual pathway.