  Modern deep neural networks require a tremendous amount of data to train,
often needing hundreds or thousands of labeled examples to learn an effective
representation. For these networks to work with less data, more structure must
be built into their architectures or learned from previous experience. The
learned weights of convolutional neural networks (CNNs) trained on large
datasets for object recognition contain a substantial amount of structure.
These representations have parallels to simple cells in the primary visual
cortex, where receptive fields are smooth and contain many regularities.
Incorporating smoothness constraints over the kernel weights of modern CNN
architectures is a promising way to improve their sample complexity. We propose
a smooth kernel regularizer that encourages spatial correlations in convolution
kernel weights. The correlation parameters of this regularizer are learned from
previous experience, yielding a method with a hierarchical Bayesian
interpretation. We show that our correlated regularizer can help constrain
models for visual recognition, improving over an L2 regularization baseline.
