Be a Goldfish: Forgetting Bad Conditioning in Sparse Linear Regression via Variational Autoencoders

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 original sparse coding model suffered from two key limitations; however: (1) computing the neural response to an image patch required minimizing a nonlinear objective function via recurrent dynamics and (2) fitting relied on approximate inference methods that ignored uncertainty. Although subsequent work has developed several methods to overcome these obstacles, we propose a novel solution inspired by the variational autoencoder (VAE) framework. We introduce the sparse coding variational autoencoder (SVAE), which augments the sparse coding model with a probabilistic recognition model parameterized by a deep neural network. This recognition model provides a neurally plausible feedforward 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 Victor Geadah and Gabriel Barello contributed equally.