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Memristor friendly reservoir computing #440

Description

@MartinuzziFrancesco

Paper

https://arxiv.org/pdf/2604.19343

Equations

$$\begin{align} K_p(\mathbf{x}) &= K_{p0}\exp(\eta_p \mathbf{x}), \\\ K_d(\mathbf{x}) &= K_{d0}\exp(-\eta_d \mathbf{x}), \end{align}$$ $$\begin{align} \mathbf{z}(t+1) &= \text{RESCALE}\!\left( \mathbf{W}^{h}\mathbf{h}(t) + \mathbf{W}^{x}\mathbf{x}(t+1) + \mathbf{b} \right), \\[2mm] \mathbf{q}(t+1) &= \left( K_p\!\left(\mathbf{z}(t+1)\right) + K_d\!\left(\mathbf{z}(t+1)\right) \right) \odot \mathbf{h}(t), \\[2mm] \mathbf{r}(t+1) &= K_p\!\left(\mathbf{z}(t+1)\right) - \mathbf{q}(t+1), \\[2mm] \mathbf{h}(t+1) &= \mathbf{r}(t+1)\Delta + \gamma \mathbf{h}(t), \end{align}$$

where

$$\text{RESCALE}(\mathbf{z}) = \frac{b-a}{1+\exp(-s\mathbf{z})} +a .$$

Official implementation

none

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