A new approach to neural networks using pseudo-differential operators

Abstract

In this paper, we initially concentrate on the concept of complex convolutional neural networks, constructing the essential frameworks required for managing complex-valued inputs. We subsequently introduce a novel neural network architecture that replaces the standard convolution operator with a more general operator known as pseudo-differential operators. This unique modification ensures the effective handling of an input’s frequency information through the application of appropriate filters. To validate this approach, we conducted empirical testing on one-dimensional and two-dimensional datasets. The results affirm the convergence and efficacy of this novel architecture, indicating a potential significant advancement in the field of complex neural network development.