Hypothesis Spaces for Deep Learning

arXiv:2403.03353v1 Announce Type: cross
Abstract: This paper introduces a hypothesis space for deep learning that employs deep neural networks (DNNs). By treating a DNN as a function of two variables, the physical variable and parameter variable, we consider the primitive set of the DNNs for the parameter variable located in a set of the weight matrices and biases determined by a prescribed depth and widths of the DNNs. We then complete the linear span of the primitive DNN set in …

abstract arxiv cs.lg deep learning dnn function hypothesis math.fa networks neural networks paper set space spaces stat.ml type variables