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According to Jaeger, when using tanh ESNs, the spectral radius of the internal weight matrix should be smaller than 1 and the as well as the largest singular value. The spectral radius should be close to 1 since Jaeger proposes that value as a good starting value for later tuning. So the proposal is to modify the ESN generator function so the spectral radius and singular values can be specified and the network is generated to have those values as close as possible to the given parameters.
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