Scale-Regularized Filter Learning

TL;DR

This paper introduces a scale regularization method for training high-dimensional linear neurons in convolutional neural networks, combining variational techniques for efficient learning and improved regularization.

Contribution

It proposes a novel scale regularization approach for high-dimensional filter learning, solved efficiently via variational methods, addressing a gap in scale handling in neural network training.

Findings

Effective learning of high-dimensional filters demonstrated

Scale regularization improves training stability

Variational methods enable efficient optimization

Abstract

We start out by demonstrating that an elementary learning task, corresponding to the training of a single linear neuron in a convolutional neural network, can be solved for feature spaces of very high dimensionality. In a second step, acknowledging that such high-dimensional learning tasks typically benefit from some form of regularization and arguing that the problem of scale has not been taken care of in a very satisfactory manner, we come to a combined resolution of both of these shortcomings by proposing a form of scale regularization. Moreover, using variational method, this regularization problem can also be solved rather efficiently and we demonstrate, on an artificial filter learning problem, the capabilities of our basic linear neuron. From a more general standpoint, we see this work as prime example of how learning and variational methods could, or even should work to their mutual benefit.