  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 large values of N. Our investigation
provides clear directions to generate optimal reservoirs or reservoirs with
constraints on size or connectivity.
