Free Energy of Bayesian Convolutional Neural Network with Skip Connection

Shuya Nagayasu, Sumio Watanabe
Proceedings of the 15th Asian Conference on Machine Learning, PMLR 222:927-942, 2024.

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.

Cite this Paper

BibTeX
@InProceedings{pmlr-v222-nagayasu24a, title = {Free Energy of {B}ayesian Convolutional Neural Network with Skip Connection}, author = {Nagayasu, Shuya and Watanabe, Sumio}, booktitle = {Proceedings of the 15th Asian Conference on Machine Learning}, pages = {927--942}, year = {2024}, editor = {Yanıkoğlu, Berrin and Buntine, Wray}, volume = {222}, series = {Proceedings of Machine Learning Research}, month = {11--14 Nov}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v222/nagayasu24a/nagayasu24a.pdf}, url = {https://proceedings.mlr.press/v222/nagayasu24a.html}, 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.} }
Endnote
%0 Conference Paper %T Free Energy of Bayesian Convolutional Neural Network with Skip Connection %A Shuya Nagayasu %A Sumio Watanabe %B Proceedings of the 15th Asian Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2024 %E Berrin Yanıkoğlu %E Wray Buntine %F pmlr-v222-nagayasu24a %I PMLR %P 927--942 %U https://proceedings.mlr.press/v222/nagayasu24a.html %V 222 %X 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.
APA
Nagayasu, S. & Watanabe, S.. (2024). Free Energy of Bayesian Convolutional Neural Network with Skip Connection. Proceedings of the 15th Asian Conference on Machine Learning, in Proceedings of Machine Learning Research 222:927-942 Available from https://proceedings.mlr.press/v222/nagayasu24a.html.

Related Material