  This paper studies how neural network architecture affects the speed of
training. We introduce a simple concept called gradient confusion to help
formally analyze this. When gradient confusion is high, stochastic gradients
produced by different data samples may be negatively correlated, slowing down
convergence. But when gradient confusion is low, data samples interact
harmoniously, and training proceeds quickly. Through theoretical and
experimental results, we demonstrate how the neural network architecture
affects gradient confusion, and thus the efficiency of training. Our results
show that, for popular initialization techniques, increasing the width of
neural networks leads to lower gradient confusion, and thus faster model
training. On the other hand, increasing the depth of neural networks has the
opposite effect. Our results indicate that alternate initialization techniques
or networks using both batch normalization and skip connections help reduce the
training burden of very deep networks.
