Theory of neuromorphic computing by waves: machine learning by rogue waves, dispersive shocks, and solitons

TL;DR

This paper explores how nonlinear waves such as solitons, rogue waves, and shocks can be used as a physical basis for neural network computation, enabling new machine learning paradigms across various physical systems.

Contribution

It introduces a wave-based neural network model utilizing nonlinear wave dynamics, demonstrating universality and potential for diverse physical implementations in machine learning.

Findings

Wave transmission matrix rank influences learning capacity.

Threshold nonlinearity enables universal interpolation.

Nonlinear wave regimes like solitons are effective for training and computation.

Abstract

We study artificial neural networks with nonlinear waves as a computing reservoir. We discuss universality and the conditions to learn a dataset in terms of output channels and nonlinearity. A feed-forward three-layer model, with an encoding input layer, a wave layer, and a decoding readout, behaves as a conventional neural network in approximating mathematical functions, real-world datasets, and universal Boolean gates. The rank of the transmission matrix has a fundamental role in assessing the learning abilities of the wave. For a given set of training points, a threshold nonlinearity for universal interpolation exists. When considering the nonlinear Schroedinger equation, the use of highly nonlinear regimes implies that solitons, rogue, and shock waves do have a leading role in training and computing. Our results may enable the realization of novel machine learning devices by using diverse physical systems, as nonlinear optics, hydrodynamics, polaritonics, and Bose-Einstein condensates. The application of these concepts to photonics opens the way to a large class of accelerators and new computational paradigms. In complex wave systems, as multimodal fibers, integrated optical circuits, random, topological devices, and metasurfaces, nonlinear waves can be employed to perform computation and solve complex combinatorial optimization.