I am trying to define my own RNNCell (Echo State Network) in Tensorflow, according to below definition.

x(t + 1) = tanh(Win*u(t) + W*x(t) + Wfb*y(t))

y(t) = Wout*z(t)

z(t) = [x(t), u(t)]

x is state, u is input, y is output. Win, W, and Wfb are not trainable. All weights are randomly initialized, but W is modified like this: "Set a certain percentage of elements of W to 0, scale W to keep its spectral radius below 1.0

I have this code to generate the equation.

x = tf.Variable(tf.reshape(tf.zeros([N]), [-1, N]), trainable=False, name="state_vector")

W = tf.Variable(tf.random_normal([N, N], 0.0, 0.05), trainable=False)

# TODO: setup W according to the ESN paper

W_x = tf.matmul(x, W)u = tf.placeholder("float", [None, K], name="input_vector")

W_in = tf.Variable(tf.random_normal([K, N], 0.0, 0.05), trainable=False)

W_in_u = tf.matmul(u, W_in)z = tf.concat(1, [x, u])

W_out = tf.Variable(tf.random_normal([K + N, L], 0.0, 0.05))

y = tf.matmul(z, W_out)

W_fb = tf.Variable(tf.random_normal([L, N], 0.0, 0.05), trainable=False)

W_fb_y = tf.matmul(y, W_fb)x_next = tf.tanh(W_in_u + W_x + W_fb_y)

y_ = tf.placeholder("float", [None, L], name="train_output")

My problem is two-fold. First I don't know how to implement this as a superclass of RNNCell. Second I don't know how to generate a W tensor according to the above specification.

Any help about any of these question is greatly appreciated. Maybe I can figure out a way to prepare W, but I sure as hell don't understand how to implement my own RNN as a superclass of RNNCell.