# Consistency in Echo-State Networks

## TL;DR

This paper explores the concept of consistency in echo-state networks, providing a method to measure how reliably these networks respond to inputs, which enhances understanding of their dynamic properties.

## Contribution

It introduces a novel application of the consistency concept to echo-state networks and proposes a replica test to quantify their echo-state property.

## Key findings

- Consistency levels vary with network parameters
- The replica test effectively measures the echo-state property
- Insights into the functional dependency of networks on inputs

## Abstract

Consistency is an extension to generalized synchronization which quantifies the degree of functional dependency of a driven nonlinear system to its input. We apply this concept to echo-state networks, which are an artificial-neural network version of reservoir computing. Through a replica test we measure the consistency levels of the high-dimensional response, yielding a comprehensive portrait of the echo-state property.