Implementing Echo-State Networks in tensorflow.

ESN-definition.ipynb Describes the mathematics of leaky echo-state networks together with an analytical method to correct the spectral radius of the inner weights accounting for leakiness and a matricial trick to improve the variance of network states during its dynamics.

ESN.py Contains the definition of a customized tensorflow RNNCell. The inizialization of the weights uses numpy and not a tensorflow graph because tf.self_adjoint_eigvals only works on self-adjoint matrices.

ESN-usage.ipynb Contains two examples of tf graphs based on this custom cell. The first is manual graph while the second uses tensorflow APIs.