Deterministic reservoirs with self-loops

[MartinuzziFrancesco]

Description

Building on the minimal complexity reservoirs, the five new topologies introduced in Elsarraj2019 use additional self loops to improve performance.

Equations

In the following r is a weight and sl are the self-loops weights

$$\begin{align*} TP1 &= \begin{bmatrix} sl & 0 & 0 & 0 & r \\\ r & sl & 0 & 0 & 0 \\\ 0 & r & sl & 0 & 0 \\\ 0 & 0 & r & sl & 0 \\\ 0 & 0 & 0 & r & sl \end{bmatrix} \\\ TP2 &= \begin{bmatrix} sl & r & 0 & 0 & r \\\ r & 0 & 0 & 0 & 0 \\\ 0 & r & sl & r & 0 \\\ 0 & 0 & r & 0 & 0 \\\ 0 & 0 & 0 & r & sl \end{bmatrix} \\\ TP3 &= \begin{bmatrix} sl & 0 & r & 0 & 0 \\\ r & sl & 0 & r & 0 \\\ 0 & r & sl & 0 & r \\\ 0 & 0 & r & sl & 0 \\\ 0 & 0 & 0 & r & sl \end{bmatrix} \\\ TP4 &= \begin{bmatrix} sl & 0 & 0 & 0 & 0 \\\ 0 & sl & 0 & 0 & 0 \\\ r & 0 & sl & 0 & 0 \\\ 0 & r & 0 & sl & 0 \\\ 0 & 0 & r & 0 & sl \end{bmatrix} \\\ TP5 &= \begin{bmatrix} 0 & 0 & 0 & 0 & 0 \\\ 0 & 0 & 0 & 0 & 0 \\\ r & 0 & 0 & 0 & 0 \\\ 0 & r & 0 & 0 & 0 \\\ 0 & 0 & r & 0 & 0 \end{bmatrix} \end{align*}$$

Official implementations

None