Emulating complex networks with a single delay differential equation

TL;DR

This paper demonstrates how a single delay differential equation can emulate complex neural networks, including deep and recurrent architectures, with minimal system complexity.

Contribution

It introduces methods to emulate multilayer and recurrent networks using a single delay system with arbitrary size and low complexity.

Findings

Delay systems can replicate complex network architectures.

Single delay differential equations can emulate large neural networks.

Low-variable systems are sufficient for complex network emulation.

Abstract

A single dynamical system with time-delayed feedback can emulate networks. This property of delay systems made them extremely useful tools for Machine Learning applications. Here we describe several possible setups, which allow emulating multilayer (deep) feed-forward networks as well as recurrent networks of coupled discrete maps with arbitrary adjacency matrix by a single system with delayed feedback. While the network's size can be arbitrary, the generating delay system can have a low number of variables, including a scalar case.