How to Start Training: The Effect of Initialization and Architecture

We investigate the effects of initialization and architecture on the start of training in deep ReLU nets. We identify two common failure modes for early training in which the mean and variance of activations are poorly behaved. For each failure mode, we give a rigorous proof of when it occurs at initialization and how to avoid it. The first failure mode, exploding/vanishing mean activation length, can be avoided by initializing weights from a symmetric distribution with variance 2/fan-in. The second failure mode, exponentially large variance of activation length, can be avoided by keeping constant the sum of the reciprocals of layer widths. We demonstrate empirically the effectiveness of our theoretical results in predicting when networks are able to start training. In particular, we note that many popular initializations fail our criteria, whereas correct initialization and architecture allows much deeper networks to be trained.