Effect of the initial configuration of weights on the training and function of artificial neural networks

TL;DR

This study investigates how the initial weight configuration influences the training dynamics and final performance of neural networks, revealing that successful training tends to keep weights close to their initial random values.

Contribution

It provides a quantitative analysis of weight deviations during training and shows the critical role of initial configurations in the optimization process.

Findings

Training keeps weights near initial values in successful cases

Abrupt increase in weight deviation correlates with overfitting

SGD's effectiveness is limited to local regions around initial weights

Abstract

The function and performance of neural networks is largely determined by the evolution of their weights and biases in the process of training, starting from the initial configuration of these parameters to one of the local minima of the loss function. We perform the quantitative statistical characterization of the deviation of the weights of two-hidden-layer ReLU networks of various sizes trained via Stochastic Gradient Descent (SGD) from their initial random configuration. We compare the evolution of the distribution function of this deviation with the evolution of the loss during training. We observed that successful training via SGD leaves the network in the close neighborhood of the initial configuration of its weights. For each initial weight of a link we measured the distribution function of the deviation from this value after training and found how the moments of this distribution and its peak depend on the initial weight. We explored the evolution of these deviations during training and observed an abrupt increase within the overfitting region. This jump occurs simultaneously with a similarly abrupt increase recorded in the evolution of the loss function. Our results suggest that SGD's ability to efficiently find local minima is restricted to the vicinity of the random initial configuration of weights.