Scaling up deep neural networks: a capacity allocation perspective
This work addresses the scaling challenges in deep learning for researchers and practitioners, providing theoretical guidelines to stabilize training in very deep networks, though it is incremental as it builds on prior capacity allocation concepts.
The paper tackles the problem of avoiding shattering in deep neural networks by analyzing capacity propagation through layers in the infinite-depth limit, deriving scaling relations for weights and biases in various architectures, such as inverse square root scaling for deep residual networks and recurrent networks.
Following the recent work on capacity allocation, we formulate the conjecture that the shattering problem in deep neural networks can only be avoided if the capacity propagation through layers has a non-degenerate continuous limit when the number of layers tends to infinity. This allows us to study a number of commonly used architectures and determine which scaling relations should be enforced in practice as the number of layers grows large. In particular, we recover the conditions of Xavier initialization in the multi-channel case, and we find that weights and biases should be scaled down as the inverse square root of the number of layers for deep residual networks and as the inverse square root of the desired memory length for recurrent networks.