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A Statistical Difference between Single-Layer Learning and Hierarchical Learning in Wide Neural Networks
Sumio Watanabe
Hierarchical neural networks are widely used in artificial intelligence, yet their mathematical properties remain incompletely understood. In the infinite-width limit, two differen…
Free energy of Bayesian Convolutional Neural Network with Skip Connection
Shuya Nagayasu, Sumio Watanabe
Since the success of Residual Network(ResNet), many of architectures of Convolutional Neural Networks(CNNs) have adopted skip connection. While the generalization performance of CN…
Bayesian Free Energy of Deep ReLU Neural Network in Overparametrized Cases
Shuya Nagayasu, Sumio Watanabe
In many research fields in artificial intelligence, it has been shown that deep neural networks are useful to estimate unknown functions on high dimensional input spaces. However,…
Upper Bound of Real Log Canonical Threshold of Tensor Decomposition and its Application to Bayesian Inference
Naoki Yoshida, Sumio Watanabe
Tensor decomposition is now being used for data analysis, information compression, and knowledge recovery. However, the mathematical property of tensor decomposition is not yet ful…
Mathematical Theory of Bayesian Statistics for Unknown Information Source
Sumio Watanabe
In statistical inference, uncertainty is unknown and all models are wrong. That is to say, a person who makes a statistical model and a prior distribution is simultaneously aware t…
Asymptotic Behavior of Bayesian Generalization Error in Multinomial Mixtures
Takumi Watanabe, Sumio Watanabe
Multinomial mixtures are widely used in the information engineering field, however, their mathematical properties are not yet clarified because they are singular learning models. I…