The Degree of Best Downsampled Convolutional Neural Network Approximation in Terms of Orlicz Modulus of Smoothness

It is essential to study approximation theoretical foundations of deep convolutional neural networks, because of its interesting developments in vital domains.In spite of its dependence upon approximation substantially.The aim is to study approximation abilities of deep convolution neural network produced by downsampling operators in Orlicz spaces to reduce high dimensions that causes overfitting implementation.The degree of best approximation of Orlicz functions are estimated in terms of high order modulus of smoothness.Moreover, direct and inverse theorems are proved here to get finally both bounds of degree of approximation, with upper and lower bounds to restrict the degree of approximation with modulus of smoothness.The concluded degree of approximation by our CNN vanishes theoretically faster than the classical ones due to its dependence on modulus of smoothness.