Free Energy of Bayesian Convolutional Neural Network with Skip Connection

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 has 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. Bayesian Free Energy is the negative log marginal likelihood which is equivalent to Stochastic Complexity or Minimum Description Length (MDL) used for evaluating model complexity. 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.