# Neuroevolution on the Edge of Chaos

## TL;DR

This paper investigates the performance of echo state networks at the edge of chaos, compares them with neuroevolved networks, and proposes local connection variants that balance simplicity and performance.

## Contribution

It confirms the edge of chaos hypothesis for echo state networks and introduces local connection methods that outperform standard echo state networks.

## Key findings

- Echos at the edge of chaos maximize computational performance.
- Evolved networks outperform standard echo state networks.
- Local connection echo state networks combine simplicity and high performance.

## Abstract

Echo state networks represent a special type of recurrent neural networks. Recent papers stated that the echo state networks maximize their computational performance on the transition between order and chaos, the so-called edge of chaos. This work confirms this statement in a comprehensive set of experiments. Furthermore, the echo state networks are compared to networks evolved via neuroevolution. The evolved networks outperform the echo state networks, however, the evolution consumes significant computational resources. It is demonstrated that echo state networks with local connections combine the best of both worlds, the simplicity of random echo state networks and the performance of evolved networks. Finally, it is shown that evolution tends to stay close to the ordered side of the edge of chaos.