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

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.

References in corpus (8)

• Explaining and Harnessing Adversarial Examples
• Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithms
• ZOO: Zeroth Order Optimization based Black-box Attacks to Deep Neural Networks without Training Substitute Models
• Delving into Transferable Adversarial Examples and Black-box Attacks
• Robust Adversarial Reinforcement Learning
• advertorch v0.1: An Adversarial Robustness Toolbox based on PyTorch
• Adversarial Examples, Uncertainty, and Transfer Testing Robustness in Gaussian Process Hybrid Deep Networks
• Robustness to Adversarial Examples through an Ensemble of Specialists