Bidirectionally Self-Normalizing Neural Networks
This provides a theoretical solution to a foundational training problem in deep learning, though it appears incremental as it builds on existing normalization techniques.
The paper tackles the vanishing/exploding gradients problem in neural networks by proving that with sufficient width, this issue disappears with high probability under mild conditions, using Gaussian-Poincaré normalized activation functions and orthogonal weight matrices. Experiments on synthetic and real-world data validate the theory's effectiveness on very deep networks.
The problem of vanishing and exploding gradients has been a long-standing obstacle that hinders the effective training of neural networks. Despite various tricks and techniques that have been employed to alleviate the problem in practice, there still lacks satisfactory theories or provable solutions. In this paper, we address the problem from the perspective of high-dimensional probability theory. We provide a rigorous result that shows, under mild conditions, how the vanishing/exploding gradients problem disappears with high probability if the neural networks have sufficient width. Our main idea is to constrain both forward and backward signal propagation in a nonlinear neural network through a new class of activation functions, namely Gaussian-Poincaré normalized functions, and orthogonal weight matrices. Experiments on both synthetic and real-world data validate our theory and confirm its effectiveness on very deep neural networks when applied in practice.