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Linear independence of internal representations in multilayer perceptrons
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Simple deterministically constructed cycle reservoirs with regular jumps
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Re-visiting the echo state property
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Adaptive neural oscillator with synaptic plasticity enabling fast resonance tuning
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Reservoir sizes and feedback weights interact non-linearly in echo state networks
ICANN'12 Proceedings of the 22nd international conference on Artificial Neural Networks and Machine Learning - Volume Part I
Echo state networks for multi-dimensional data clustering
ICANN'12 Proceedings of the 22nd international conference on Artificial Neural Networks and Machine Learning - Volume Part I
Design strategies for weight matrices of echo state networks
Neural Computation
ICONIP'12 Proceedings of the 19th international conference on Neural Information Processing - Volume Part II
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The design of echo state network (ESN) parameters relies on the selection of the maximum eigenvalue of the linearized system around zero (spectral radius). However, this procedure does not quantify in a systematic manner the performance of the ESN in terms of approximation error. This article presents a functional space approximation framework to better understand the operation of ESNs and proposes an information-theoretic metric, the average entropy of echo states, to assess the richness of the ESN dynamics. Furthermore, it provides an interpretation of the ESN dynamics rooted in system theory as families of coupled linearized systems whose poles move according to the input signal dynamics. With this interpretation, a design methodology for functional approximation is put forward where ESNs are designed with uniform pole distributions covering the frequency spectrum to abide by the richness metric, irrespective of the spectral radius. A single bias parameter at the ESN input, adapted with the modeling error, configures the ESN spectral radius to the input-output joint space. Function approximation examples compare the proposed design methodology versus the conventional design.