Deep Information Propagation
This addresses the problem of training deep neural networks by identifying fundamental depth limits based on signal propagation, which is foundational for ML/AI researchers designing network architectures.
The paper investigates how signal propagation depth in untrained random neural networks limits trainable depth, showing that networks can only be trained when information travels through them and that arbitrarily deep training is possible only near criticality, with dropout destroying this critical point and limiting trainable depth.
We study the behavior of untrained neural networks whose weights and biases are randomly distributed using mean field theory. We show the existence of depth scales that naturally limit the maximum depth of signal propagation through these random networks. Our main practical result is to show that random networks may be trained precisely when information can travel through them. Thus, the depth scales that we identify provide bounds on how deep a network may be trained for a specific choice of hyperparameters. As a corollary to this, we argue that in networks at the edge of chaos, one of these depth scales diverges. Thus arbitrarily deep networks may be trained only sufficiently close to criticality. We show that the presence of dropout destroys the order-to-chaos critical point and therefore strongly limits the maximum trainable depth for random networks. Finally, we develop a mean field theory for backpropagation and we show that the ordered and chaotic phases correspond to regions of vanishing and exploding gradient respectively.