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

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


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 \(W = [W_r, W_i]\).


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