Double cycle initializer

[MartinuzziFrancesco]

Description (with citation)

Proposed in Fu2023, the double cycle initialization builds on the minimal ESN approach of providing deterministic reservoir architectures that are still accurate in forecasting tasks

Equations

There aren't really equations for this one, but this is how the matrix should look like:

$$\begin{equation} W = \begin{bmatrix} 0 & b & 0 & 0 & 0 & \dots & 0 & b \\\ w & 0 & b & 0 & 0 & \dots & 0 & 0 \\\ 0 & w & 0 & b & 0 & \dots & 0 & 0 \\\ 0 & 0 & w & 0 & b & \dots & 0 & 0 \\\ \vdots & \vdots & \vdots & \vdots & \ddots & \ddots & \vdots & \vdots \\\ 0 & 0 & 0 & 0 & \dots & 0 & b & 0 \\\ 0 & 0 & 0 & 0 & \dots & w & 0 & b \\\ w & 0 & 0 & 0 & \dots & 0 & w & 0 \end{bmatrix}, \end{equation}$$

Suggested API

reservoir_matrix = double_cycle([rng], [T], res_size, res_size; cycle_weight, second_cycle_weight)

Official implementations

None