On regularization for a convolutional kernel in neural networks
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Convolutional neural network is a very important model of deep learning. It can help avoid the exploding/vanishing gradient problem and improve the generalizability of a neural network if the singular values of the Jacobian of a layer are bounded around 1 in the training process. We propose a new penalty function for a convolutional kernel to let the singular values of the corresponding transformation matrix are bounded around 1. We show how to carry out the gradient type methods. The penalty is about the transformation matrix corresponding to a kernel, not directly about the kernel, which is different from results in existing papers. This provides a new regularization method about the weights of convolutional layers. Other penalty functions about a kernel can be devised following this idea in future.
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