Self modulated reservoir computing

[MartinuzziFrancesco]

Paper

https://doi.org/10.1038/s42005-023-01500-w

Model

$$\begin{align} \mathbf{x}(t) &= (1 - \alpha)\mathbf{x}(t - 1) + \alpha \tanh\!\Big( \mathbf{g}^{\mathrm{res}}(t - 1)\, \mathbf{W}^{\mathrm{res}} \mathbf{x}(t - 1) + \mathbf{g}^{\mathrm{in}}(t - 1)\, \mathbf{W}^{\mathrm{in}} \mathbf{u}(t) + \boldsymbol{\xi} \Big), \\\ \\\ \mathbf{g}^{\mathrm{res}}(t) &= f\!\left( \mathbf{W}^{\mathrm{res}}_{fb} \mathbf{x}(t) + \mathbf{b}^{\mathrm{res}}_{fb} \right), \\\ \\\ \mathbf{g}^{\mathrm{in}}(t) &= f\!\left( \mathbf{W}^{\mathrm{in}}_{fb} \mathbf{x}(t) + \mathbf{b}^{\mathrm{in}}_{fb} \right), \\\ \\\ \mathbf{y}(t) &= \mathbf{W}^{\mathrm{out}} \mathbf{x}(t) + \mathbf{b}^{\mathrm{out}}. \end{align}$$

Official implementation

none

Notes

It would be better if the name of the model is SMESN/SMESNCell instead of the proposed SMRC in the paper.

[MartinuzziFrancesco]

the feedback matrices here are trained with bptt, I didn't notice that on a first read. I will remove the good first issue label