Topological chaos for elementary cellular automata

Cattaneo, Gianpiero; Finelli, Michele; Margara, Luciano

doi:10.1007/3-540-62592-5_76

Cited by 2 publications

(1 citation statement)

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“…Research on both models has demonstrated that two critical factors influence the dynamics and performance in tasks. These include the topology of the connectivity graph (Cattaneo et al, 1997;Luque and Solé, 2000;Hajnal and Lőrincz, 2006;Snyder et al, 2012;Aljadeff et al, 2015;Cherupally, 2018;Echlin et al, 2018;Galera and Kinouchi, 2020;Steiner et al, 2023) and the synaptic weights that connect the neurons (Bertschinger and Natschläger, 2004;Natschläger et al, 2005;Embrechts et al, 2009;Büsing et al, 2010;Goudarzi et al, 2014;Jalalvand et al, 2018;Krauss et al, 2019a). Such a graph depends on many parameters, in particular its number of nodes N and the degree of vertices K, i.e., the number of synapses per neuron.…”

Section: Introductionmentioning

confidence: 99%

The connectivity degree controls the difficulty in reservoir design of random boolean networks

Calvet,

Reulet,

Rouat

2024

Front. Comput. Neurosci.

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Reservoir Computing (RC) is a paradigm in artificial intelligence where a recurrent neural network (RNN) is used to process temporal data, leveraging the inherent dynamical properties of the reservoir to perform complex computations. In the realm of RC, the excitatory-inhibitory balance b has been shown to be pivotal for driving the dynamics and performance of Echo State Networks (ESN) and, more recently, Random Boolean Network (RBN). However, the relationship between b and other parameters of the network is still poorly understood. This article explores how the interplay of the balance b, the connectivity degree K (i.e., the number of synapses per neuron) and the size of the network (i.e., the number of neurons N) influences the dynamics and performance (memory and prediction) of an RBN reservoir. Our findings reveal that K and b are strongly tied in optimal reservoirs. Reservoirs with high K have two optimal balances, one for globally inhibitory networks (b < 0), and the other one for excitatory networks (b > 0). Both show asymmetric performances about a zero balance. In contrast, for moderate K, the optimal value being K = 4, best reservoirs are obtained when excitation and inhibition almost, but not exactly, balance each other. For almost all K, the influence of the size is such that increasing N leads to better performance, even with very large values of N. Our investigation provides clear directions to generate optimal reservoirs or reservoirs with constraints on size or connectivity.

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