  Neurons in the visual cortex are correlated in their variability. The
presence of correlation impacts cortical processing because noise cannot be
averaged out over many neurons. In an effort to understand the functional
purpose of correlated variability, we implement and evaluate correlated noise
models in deep convolutional neural networks. Inspired by the cortex,
correlation is defined as a function of the distance between neurons and their
selectivity. We show how to sample from high-dimensional correlated
distributions while keeping the procedure differentiable, so that
back-propagation can proceed as usual. The impact of correlated variability is
evaluated on the classification of occluded and non-occluded images with and
without the presence of other regularization techniques, such as dropout. More
work is needed to understand the effects of correlations in various conditions,
however in 10/12 of the cases we studied, the best performance on occluded
images was obtained from a model with correlated noise.
