Improved weight initialization for deep and narrow feedforward neural network

Appropriate weight initialization settings, along with the ReLU activation function, have been a cornerstone of modern deep learning, making it possible to train and deploy highly effective and efficient neural network models across diverse artificial intelligence. The problem of dying ReLU, where ReLU neurons become inactive and yield zero output, presents a significant challenge in the training of deep neural networks with ReLU activation function. Theoretical research and various methods have been introduced to address the problem. However, even with these methods and research, training remains challenging for extremely deep and narrow feedforward networks with ReLU activation function. In this paper, we propose a new weight initialization method to address this issue. We prove the properties of the proposed initial weight matrix and demonstrate how these properties facilitate the effective propagation of signal vectors. Through a series of experiments and comparisons with existing methods, we demonstrate the effectiveness of the new initialization method.