@article{Guo2023, 
author = {Pei-Chang Guo},
title = {New regularization methods for convolutional kernel tensors},
year = {2023},
journal = {AIMS Mathematics},
volume = {8},
number = {11},
pages = {26188-26198},
keywords = {regularization, singular values, doubly blocked banded Toeplitz matrices, convolutional kernel tensor},
url = {https://www.sciopen.com/article/10.3934/math.20231335},
doi = {10.3934/math.20231335},
abstract = {Convolution is a very basic and important operation for convolutional neural networks. For neural network training, how to bound the convolutional layers is a currently popular research topic. Each convolutional layer is represented by a tensor, which corresponds to a structured transformation matrix. The objective is to ensure that the singular values of each transformation matrix are bounded around 1 by changing the entries of the tensor. We propose three new regularization terms for a convolutional kernel tensor and derive the gradient descent algorithm for each penalty function. Numerical examples are presented to demonstrate the effectiveness of the algorithms.}
}