  Dropout-based regularization methods can be regarded as injecting random
noise with pre-defined magnitude to different parts of the neural network
during training. It was recently shown that Bayesian dropout procedure not only
improves generalization but also leads to extremely sparse neural architectures
by automatically setting the individual noise magnitude per weight. However,
this sparsity can hardly be used for acceleration since it is unstructured. In
the paper, we propose a new Bayesian model that takes into account the
computational structure of neural networks and provides structured sparsity,
e.g. removes neurons and/or convolutional channels in CNNs. To do this we
inject noise to the neurons outputs while keeping the weights unregularized. We
establish the probabilistic model with a proper truncated log-uniform prior
over the noise and truncated log-normal variational approximation that ensures
that the KL-term in the evidence lower bound is computed in closed-form. The
model leads to structured sparsity by removing elements with a low SNR from the
computation graph and provides significant acceleration on a number of deep
neural architectures. The model is easy to implement as it can be formulated as
a separate dropout-like layer.
