Bidirectionally self-normalizing neural networks

doi:10.1016/j.neunet.2023.08.017

Bidirectionally self-normalizing neural networks

2023-10-01

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Thalaiyasingam Ajanthan

DOI：10.1016/j.neunet.2023.08.017

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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-Poincare 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.(c) 2023 Elsevier Ltd. All rights reserved.

Keyword:

Neural networks

Vanishing/exploding gradient problem

Training

Optimization

Bidirectionally self-normalizing neural networks

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