Free energy of Bayesian Convolutional Neural Network with Skip Connection

TL;DR

This paper investigates the Bayesian free energy of CNNs with skip connections, revealing that their generalization performance's upper bound is independent of overparametrization, unlike traditional CNNs.

Contribution

It demonstrates that Bayesian CNNs with skip connections have an upper bound on free energy unaffected by overparametrization, providing new insights into their generalization properties.

Findings

Upper bound of free energy independent of overparametrization

Bayesian CNNs with skip connections have similar generalization error properties

Insights into the role of skip connections in Bayesian CNNs

Abstract

Since the success of Residual Network(ResNet), many of architectures of Convolutional Neural Networks(CNNs) have adopted skip connection. While the generalization performance of CNN with skip connection has been explained within the framework of Ensemble Learning, the dependency on the number of parameters have not been revealed. In this paper, we show that Bayesian free energy of Convolutional Neural Network both with and without skip connection in Bayesian learning. The upper bound of free energy of Bayesian CNN with skip connection does not depend on the oveparametrization and, the generalization error of Bayesian CNN has similar property.