# Reservoir Computing meets Recurrent Kernels and Structured Transforms by Dong, J., Ohana, R., Rafayelyan, M., & Krzakala, F. (2020)

source
(Dong et al. 2020)
tags
Reservoir computing, Kernel Methods

## Summary

This paper presents a connection between large size reservoir computing and kernel methods.

The authors formulate a reservoir computing model as a form of recurrent kernel iteration. If the reservoir update is written $x^{(t+1)} = \dfrac{1}{\sqrt{N}} f \left(W_r x^{(t)} + W_i i^{(t)} \right)$ with $$x^{(t)}$$ the state of the reservoir at time $$t$$ and $$i^{(t)}$$ sequential input at time $$t$$, $$W_r \in \mathbb{R}^{N\times N}$$ and $$W_i \in \mathbb{R}^{N\times d}$$, we may re-frame it as a random feature embedding of the vector $$\left[ x^{(t)} , i^{(t)} \right]$$ with the matrix $$W = [W_r, W_i]$$.

## Bibliography

1. . . "Reservoir Computing Meets Recurrent Kernels and Structured Transforms". Arxiv:2006.07310 [cs, Eess, Stat]. http://arxiv.org/abs/2006.07310.
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