A Weight Initialization Based on the Linear Product Structure for Neural Networks

TL;DR

This paper introduces a novel weight initialization method for neural networks based on the linear product structure, aiming to improve training stability and reduce issues like dying ReLU in deep networks.

Contribution

The paper proposes a new initialization strategy derived from polynomial approximation and algebraic geometry, addressing limitations of existing methods in deep neural networks.

Findings

LPS initialization reduces the probability of dying ReLU.

It demonstrates improved training stability on various neural network architectures.

The method is efficient and robust on public datasets.

Abstract

Weight initialization plays an important role in training neural networks and also affects tremendous deep learning applications. Various weight initialization strategies have already been developed for different activation functions with different neural networks. These initialization algorithms are based on minimizing the variance of the parameters between layers and might still fail when neural networks are deep, e.g., dying ReLU. To address this challenge, we study neural networks from a nonlinear computation point of view and propose a novel weight initialization strategy that is based on the linear product structure (LPS) of neural networks. The proposed strategy is derived from the polynomial approximation of activation functions by using theories of numerical algebraic geometry to guarantee to find all the local minima. We also provide a theoretical analysis that the LPS initialization has a lower probability of dying ReLU comparing to other existing initialization strategies. Finally, we test the LPS initialization algorithm on both fully connected neural networks and convolutional neural networks to show its feasibility, efficiency, and robustness on public datasets.