  Learning a generative model of visual information with sparse and
compositional features has been a challenge for both theoretical neuroscience
and machine learning communities. Sparse coding models have achieved great
success in explaining the receptive fields of mammalian primary visual cortex
with sparsely activated latent representation. In this paper, we focus on a
recently proposed model, sparse coding variational autoencoder (SVAE) (Barello
et al., 2018), and show that the end-to-end training scheme of SVAE leads to a
large group of decoding filters not fully optimized with noise-like receptive
fields. We propose a few heuristics to improve the training of SVAE and show
that a unit $L_2$ norm constraint on the decoder is critical to produce sparse
coding filters. Such normalization can be considered as local lateral
inhibition in the cortex. We verify this claim empirically on both natural
image patches and MNIST dataset and show that projection of the filters onto
unit norm drastically increases the number of active filters. Our results
highlight the importance of weight normalization for learning sparse
representation from data and suggest a new way of reducing the number of
inactive latent components in VAE learning.
