An axiomatized PDE model of deep neural networks

arXiv:2307.12333v2 Announce Type: replace
Abstract: Inspired by the relation between deep neural network (DNN) and partial differential equations (PDEs), we study the general form of the PDE models of deep neural networks. To achieve this goal, we formulate DNN as an evolution operator from a simple base model. Based on several reasonable assumptions, we prove that the evolution operator is actually determined by convection-diffusion equation. This convection-diffusion equation model gives mathematical explanation for several effective networks. Moreover, we show that …

abstract arxiv cs.lg deep neural network differential dnn evolution form general network networks neural network neural networks simple study type