  Deep neural networks can suffer from the exploding and vanishing activation
problem, in which the networks fail to train properly because the neural
signals either amplify or attenuate across the layers and become saturated.
While other normalization methods aim to fix the stated problem, most of them
have inference speed penalties in those applications that require running
averages of the neural activations. Here we extend the unitary framework based
on Lie algebra to neural networks of any dimensionalities, overcoming the major
constraints of the prior arts that limit synaptic weights to be square
matrices. Our proposed unitary convolutional neural networks deliver up to 32%
faster inference speeds and up to 50% reduction in permanent hard disk space
while maintaining competitive prediction accuracy.
