ReLiCADA -- Reservoir Computing using Linear Cellular Automata Design Algorithm

TL;DR

The paper tackles the challenge of designing reservoir computing systems based on linear cellular automata by introducing ReLiCA, a design algorithm that pre-selects a small set of promising CA rules to dramatically cut hyperparameter search. Building on a refined ReCA architecture, the method leverages mathematical analysis of linear CA properties to identify rules that yield robust time-series performance with low computational complexity. Across extensive simulations on diverse benchmarks, ReLiCA-selected models achieve competitive NMSE while requiring far less design effort and search time than exhaustive rule exploration. The work also highlights the edge-of-chaos regime as a favorable operating point and demonstrates substantial potential for hardware-efficient, real-time time-series processing.

Abstract

In this paper, we present a novel algorithm to optimize the design of Reservoir Computing using Cellular Automata models for time series applications. Besides selecting the models' hyperparameters, the proposed algorithm particularly solves the open problem of linear Cellular Automaton rule selection. The selection method pre-selects only a few promising candidate rules out of an exponentially growing rule space. When applied to relevant benchmark datasets, the selected rules achieve low errors, with the best rules being among the top 5% of the overall rule space. The algorithm was developed based on mathematical analysis of linear Cellular Automaton properties and is backed by almost one million experiments, adding up to a computational runtime of nearly one year. Comparisons to other state-of-the-art time series models show that the proposed Reservoir Computing using Cellular Automata models have lower computational complexity, at the same time, achieve lower errors. Hence, our approach reduces the time needed for training and hyperparameter optimization by up to several orders of magnitude.

Figures (14)

• Figure 1: Echo State Network as an example for Reservoir Computing.
• Figure 2: Lattice of a one-dimensional Cellular Automaton with periodic boundary conditions. Using only the orange weights results in ${n = 3}$; using the orange and green weights results in ${n = 5}$. The state of the cell ${s_0}$ in the ${(i)\textsuperscript{th}}$ iteration is the weighted sum of the cell states in its neighborhood in the ${(i-1)\textsuperscript{th}}$ iteration.
• Figure 3: architecture as initially proposed by Yilmaz Yilmaz2014
• Figure 4: Iteration diagram of linear with ${m=4}$, ${\hat{n}=3}$, ${N=12}$, ${\mathbf{w} = (0,2,1)}$ (resulting in ${H=2}$) and (a) a single cell initialized with state 1 (impulse) or (b) random initial configuration for ${I=9}$ iterations. Figures (c) and (d) have the same setup, but with ${\mathbf{w} = (1,2,1)}$ (resulting in ${H=4}$). The colors indicate different cell states in ${\mathbb{Z}_m}$.
• Figure 5: Refined architecture