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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.is work con rms this statement in a comprehensive set of experiments. Furthermore, the echo state networks are compared to networks evolved via neuroevolution. e evolved networks outperform the echo state networks, however, the evolution consumes signi cant 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.

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Echo State Networks represent a type of recurrent neural network with a large randomly generated reservoir and a small number of readout connections trained via linear regression. The most common topology of the reservoir is a fully connected network of up to thousands of neurons. Over the years, researchers have introduced a variety of alternative reservoir topologies, such as a circular network or a linear path of connections. When comparing the performance of different topologies or other architectural changes, it is necessary to tune the hyperparameters for each of the topologies separately since their properties may significantly differ. The hyperparameter tuning is usually carried out manually by selecting the best performing set of parameters from a sparse grid of predefined combinations. Unfortunately, this approach may lead to underperforming configurations, especially for sensitive topologies. We propose an alternative approach of hyperparameter tuning based on the Covariance Matrix Adaptation Evolution Strategy (CMA-ES). Using this approach, we have improved multiple topology comparison results by orders of magnitude suggesting that topology alone does not play as important role as properly tuned hyperparameters.