Geodesic
Dynamics of a network of map-based model neurons for supervised learning of a reservoir computing system
Izvestiya VUZ. Applied Nonlinear Dynamics, Tome 28 (2020) no. 1, pp. 77-89.

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The purpose of this work is to develop a reservoir computing system that contains a network of model neurons with discrete time, and to study the characteristics of the system when it is trained to autonomously generate a harmonic target signal. Methods of work include approaches of nonlinear dynamics (phase space analysis depending on parameters), machine learning (reservoir computing, supervised error minimization) and computer modeling (implementation of numerical algorithms, plotting of characteristics and diagrams). Results. A reservoir computing system based on a network of coupled discrete model neurons was constructed, and the possibility of its supervised training in generating the target signal using the controlled error minimization method FORCE was demonstrated. It has been found that with increasing network size, the mean square error of learning decreases. The dynamic regimes arising at the level of individual activity of intra-reservoir neurons at various stages of training are studied. It is shown that in the process of training, the network-reservoir transits from the state of space-time disorder to the state with regular clusters of spiking activity. The optimal values of the coupling coefficients and the parameters of the intrinsic dynamics of neurons corresponding to the minimum learning error were found. Conclusion. A new reservoir computing system is proposed in the work, the basic unit of which is the Courbage-Nekorkin discrete-time model neuron. The advantage of a network based on such a spiking neuron model is that the model is specified in the form of a mapping, therefore, there is no need to perform an integration operation. The proposed system has shown its effectiveness in training autonomous generation of a harmonic function, as well as for a number of other target functions.
Keywords: reservoir computing, machine learning, discrete-time model neuron, target signal, error function. 
@article{IVP_2020_28_1_a5,
     author = {M. M. Pugavko and O. V. Maslennikov and V. I. Nekorkin},
     title = {Dynamics of a network of map-based model neurons for supervised learning of a reservoir computing system},
     journal = {Izvestiya VUZ. Applied Nonlinear Dynamics},
     pages = {77--89},
     publisher = {mathdoc},
     volume = {28},
     number = {1},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVP_2020_28_1_a5/}
}
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M. M. Pugavko; O. V. Maslennikov; V. I. Nekorkin. Dynamics of a network of map-based model neurons for supervised learning of a reservoir computing system. Izvestiya VUZ. Applied Nonlinear Dynamics, Tome 28 (2020) no. 1, pp. 77-89. http://geodesic.mathdoc.fr/item/IVP_2020_28_1_a5/