# Performance boost of time-delay reservoir computing by non-resonant clock cycle

## TL;DR

This paper demonstrates that non-resonant ratios of delay and clock cycle in time-delay reservoir computing systems enhance memory capacity and performance, challenging the traditional focus on resonant timing.

## Contribution

It reveals that non-resonant timing between delay and clock cycle improves reservoir computing performance, providing new insights into system design.

## Key findings

- Non-resonant delay and clock cycle ratios maximize memory capacity.
- Resonant timing leads to performance degradation.
- Non-resonant configurations outperform resonant ones in approximation error.

## Abstract

The time-delay-based reservoir computing setup has seen tremendous success in both experiment and simulation. It allows for the construction of large neuromorphic computing systems with only few components. However, until now the interplay of the different timescales has not been investigated thoroughly. In this manuscript, we investigate the effects of a mismatch between the time-delay and the clock cycle for a general model. Typically, these two time scales are considered to be equal. Here we show that the case of equal or resonant time-delay and clock cycle could be actively detrimental and leads to an increase of the approximation error of the reservoir. In particular, we can show that non-resonant ratios of these time scales have maximal memory capacities. We achieve this by translating the periodically driven delay-dynamical system into an equivalent network. Networks that originate from a system with resonant delay-times and clock cycles fail to utilize all of their degrees of freedom, which causes the degradation of their performance.