New regularization methods for convolutional kernel tensors

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.