- 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

- Jonathan Dong, Ruben Ohana, Mushegh Rafayelyan, Florent Krzakala. . "Reservoir Computing Meets Recurrent Kernels and Structured Transforms".
*Arxiv:2006.07310 [cs, Eess, Stat]*. http://arxiv.org/abs/2006.07310.