# Reservoir Computing on the Hypersphere

## TL;DR

This paper introduces a novel reservoir computing approach using orthogonal reservoirs on the hypersphere, removing nonlinear activation functions, and demonstrates enhanced memory capacity and cryptography applications.

## Contribution

It proposes a new RC framework with orthogonal reservoirs on the hypersphere, surpassing traditional memory bounds and enabling cryptography applications.

## Key findings

- Memory capacity exceeds reservoir dimensionality
- System effectively applied to symmetric cryptography
- Orthogonal reservoir approach outperforms traditional RC methods

## Abstract

Reservoir Computing (RC) refers to a Recurrent Neural Networks (RNNs) framework, frequently used for sequence learning and time series prediction. The RC system consists of a random fixed-weight RNN (the input-hidden reservoir layer) and a classifier (the hidden-output readout layer). Here we focus on the sequence learning problem, and we explore a different approach to RC. More specifically, we remove the non-linear neural activation function, and we consider an orthogonal reservoir acting on normalized states on the unit hypersphere. Surprisingly, our numerical results show that the system's memory capacity exceeds the dimensionality of the reservoir, which is the upper bound for the typical RC approach based on Echo State Networks (ESNs). We also show how the proposed system can be applied to symmetric cryptography problems, and we include a numerical implementation.