why we use np.ones(future) to predict future value ?

[JingliangGao]

Hi, I just don't understand why we use the date produced by np.ones(future) to predict future ? Intuitively, there is no connection between np.ones(future) data and future data .

[sungjae-cho]

@JingliangGao You seem to talk about the implementation in mackey.ipynb. pyESN should always take np.ones for bias.

[verzep]

It is an artificial way of introducing a bias term in the update equation. The practical effect it that you end up with an equation of the form:

X(t+1) = tanh( W_res @X(t) + W_fb@teacher(t) + B)

Where B is constant as it is given by W_in@input(t), which is identically 1 for all t.

It is useful for various reasons, but if you play around a bit with the parameters you can obtain good predictions even by setting it to 0.