Deep Convolutional Neural Networks with Unitary Weights

While normalizations aim to fix the exploding and vanishing gradient problem in deep neural networks, they have drawbacks in speed or accuracy because of their dependency on the data set statistics. This work is a comprehensive study of a novel method based on unitary synaptic weights derived from Lie Group to construct intrinsically stable neural systems. Here we show that unitary convolutional neural networks deliver up to 32% faster inference speeds while maintaining competitive prediction accuracy. Unlike prior arts restricted to square synaptic weights, we expand the unitary networks to weights of any size and dimension.

A Projection Algorithm for the Unitary Weights

Unitary neural networks are promising alternatives for solving the exploding and vanishing activation/gradient problem without the need for explicit normalization that reduces the inference speed. However, they often require longer training time due to the additional unitary constraints on their weight matrices. Here we show a novel algorithm using a backpropagation technique with Lie algebra for computing approximated unitary weights from their pre-trained, non-unitary counterparts. The unitary networks initialized with these approximations can reach the desired accuracies much faster, mitigating their training time penalties while maintaining inference speedups. Our approach will be instrumental in the adaptation of unitary networks, especially for those neural architectures where pre-trained weights are freely available.