Research On Approximation Properties Of Convolutional Neural Networks

At present,the era of artificial intelligence has arrived,and deep learning has received more and more attention.This technology of autonomous learning from data has made breakthroughs in many fields.Convolutional neural network is one of the most widely used network structures in deep learning technology.But for a better understanding of the convolutional neural network model,there is still no theoretical basis.Therefore,the current theoretical research on the mathematical model of convolutional neural network has very important theoretical significance and practical value.This paper mainly studies the promotion ability of convolutional neural networks.First,the approximation properties of convolutional neural networks are introduced from the perspective of function approximation theory,and a proof of the consistency of convolutional neural networks is given,which means that convolutional neural networks can approximate any function in the set of continuous functions with arbitrary precision.It also shows that the approximation order of the convolutional neural network is related to the input dimension d.Secondly,combining the function approximation method and statistical learning method to perform error decomposition on the convolutional neural network algorithm,and estimate the upper bounds of the sample error and the approximation error,respectively.The number of samples m and the number of adjustable parameters of the convolutional neural network w and the number of layers J are defined.The theoretical results show the consistency of the convolutional neural network under the framework of statistical learning theory.Finally,simulation experiments and real data set experiments verify the generalization ability and effective performance of convolutional neural networks.With the increase in the number of training samples m and the number of layers J,the stronger the promotion ability of the convolutional neural network and the higher the accuracy of the algorithm.The experimental results effectively validate our theoretical conclusions.