A study on optimal generalizing learning schema for neural networks based on theories of image processing filters

A theory for neural network learning which is very effective for analyzing the generalization ability and the overlearning problem is developed。This theory is based on the image restoration theories proposed by the head investigator of this project。Although the problems of generalization and image restoration seem to have nothing in common，we have shown that both problems can be dealt with under the same methodology if we formalize them as a kind of inverse problem.This novel approach provides an analytical and quantitative method for the problems of generalization and over-learning which have been so far treated qualitatively。Followings are the major results obtained in this project.·A new framework of generalization which can extract general structures among training samples is developed based on the image restoration theories。·We analyze the generalization ability of the back-propagation using the framework。·We provide a way of choosing，training samples which does not cause the over-learning problem and gives an optimal generalizing ability。·Above theoretical results are examined by some computer simulations.

A theory for neural network learning which is very effective for analyzing the generalization ability and the overlearning problem is developed. This theory is based on the image restoration theories proposed by the head investigator of this project. Although the problems of generalization and image restoration seem to have nothing in common, we have shown that both problems can be dealt with under the same methodology if we formalize them as a kind of inverse problem. This novel approach provides an analytical and quantitative method for the problems of generalization and over-learning which have been so far treated qualitatively. Followings are the major results obtained in this project.・A new framework of generalization which can extract general structures among training samples is developed based on the image restoration theories.・We analyze the generalization ability of the back-propagation using the framework.・We provide a way of choosing, training samples which does not cause the over-learning problem and gives an optimal generalizing ability.・Above theoretical results are examined by some computer simulations.