A Study on the Uncertainty of Convolutional Layers in Deep Neural Networks

TL;DR

This paper investigates the Min-Max property in convolutional layer weights of neural networks like LeNet, linking it to uncertainty reduction and improved adversarial robustness, offering insights into convolutional interpretability.

Contribution

It reveals a Min-Max property in convolutional weights during training and connects it to uncertainty minimization and robustness, providing a new perspective for neural network design.

Findings

Convolutional weights exhibit a Min-Max property during training.

The Min-Max property correlates with reduced uncertainty in parameters.

Models with this property show increased adversarial robustness.

Abstract

This paper shows a Min-Max property existing in the connection weights of the convolutional layers in a neural network structure, i.e., the LeNet. Specifically, the Min-Max property means that, during the back propagation-based training for LeNet, the weights of the convolutional layers will become far away from their centers of intervals, i.e., decreasing to their minimum or increasing to their maximum. From the perspective of uncertainty, we demonstrate that the Min-Max property corresponds to minimizing the fuzziness of the model parameters through a simplified formulation of convolution. It is experimentally confirmed that the model with the Min-Max property has a stronger adversarial robustness, thus this property can be incorporated into the design of loss function. This paper points out a changing tendency of uncertainty in the convolutional layers of LeNet structure, and gives some insights to the interpretability of convolution.