Reservoir Computing Dynamics for Single Nonlinear Node with Delay Line Structure

TL;DR

This paper analyzes the dynamics of a reservoir computer with a single nonlinear node and delay line, demonstrating bounded output differences and translating separation properties from echo state networks to this simpler structure.

Contribution

It introduces a theoretical framework for understanding the separation properties of single nonlinear node reservoirs with delay lines, extending echo state network concepts.

Findings

Output distances are bounded by input distances after finite time

Separation properties from echo state networks are applicable to single nonlinear node structures

The study provides a mathematical basis for reservoir computing with minimal components

Abstract

For a reservoir computer composed of a single nonlinear node and delay line, we show that after a finite period of discrete time, the distance between two reservoir outputs is bounded above by a constant multiple of the distance between their respective inputs. We also translate familiar separation properties from the context of Echo State Networks to that of the single nonlinear node structure.