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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.
A recurrent neural network (RNN) possesses the echo state property (ESP) if, for a given input sequence, it ``forgets any internal states of the driven (nonautonomous) system and asymptotically follows a unique, possibly complex trajectory. The lack
Echo state networks (ESNs) have been recently proved to be universal approximants for input/output systems with respect to various $L ^p$-type criteria. When $1leq p< infty$, only $p$-integrability hypotheses need to be imposed, while in the case $p=
In this paper, the echo state network (ESN) memory capacity, which represents the amount of input data an ESN can store, is analyzed for a new type of deep ESNs. In particular, two deep ESN architectures are studied. First, a parallel deep ESN is pro
Echo State Networks (ESNs) are a special type of recurrent neural networks (RNNs), in which the input and recurrent connections are traditionally generated randomly, and only the output weights are trained. Despite the recent success of ESNs in vario
Echo State Networks (ESNs) are recurrent neural networks that only train their output layer, thereby precluding the need to backpropagate gradients through time, which leads to significant computational gains. Nevertheless, a common issue in ESNs is