Structured reservoir computing

[MartinuzziFrancesco]

Description

Introduced in Dong2020 this initialization uses structured transforms to speed-up computations of random matrix multiplications. Also based on Yu2016

Following the description in Dong2020: The general idea is to replace the dense matrices $W = [W, W_{\text{in}}]$ by a succession of Hadamard matrices $H$ (structured orthonormal matrices composed of $\pm1/\sqrt{p}$ components) and diagonal random matrices $D_i$ for $i = 1, 2, 3$ sampled from an i.i.d. Rademacher distribution:

$$ W = \frac{\sqrt{p}}{\sigma} H D_1 H D_2 H D_3 \tag{10} $$

Original implementation

Structured init in the test code provided with the paper