https://doi.org/10.1140/epjs/s11734-025-01697-7
Regular Article
Impact of white Gaussian internal noise on echo state neural networks
Saratov State University, Institute of Physics, 83 Astrakhanskaya str., 410012, Saratov, Russia
Received:
6
February
2025
Accepted:
19
May
2025
Published online:
27
June
2025
Recent years have seen the emergence of a large number of works devoted to the analog (hardware) implementation of artificial neural networks, where neurons and their connections are based on physical principles rather than conventional computer calculations. These networks can offer improved energy efficiency and scalability in certain applications, but they may also be vulnerable to internal noise. This paper investigates the impact of internal noise on trained echo state neural networks (ESNs). White Gaussian noise is introduced in four different ways: additive and multiplicative (depending on its effect on individual neurons) as well as correlated and uncorrelated (depending on its influence on the entire reservoir). This study considers ESNs with typical reservoir connection matrices, including random uniform and band matrices with varying degrees of connectivity. All ESNs were trained to predict chaotic realizations of the Mackey–Glass system. Our findings indicate that the propagation of noise within the reservoir is primarily governed by the statistical properties of the output connection matrix, specifically its mean and mean square values. These metrics significantly influence the type of noise that accumulates within the network. We also demonstrate that there are conditions under which noise intensity as low as 
can completely obliterate a useful signal. Furthermore, we identify which types of noise are most critical for networks utilizing different activation functions (hyperbolic tangent, sigmoid, and linear) and whether the network is self-closed.
Copyright comment Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
© The Author(s), under exclusive licence to EDP Sciences, Springer-Verlag GmbH Germany, part of Springer Nature 2025
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
