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An Echo State Network (ESN) is a type of single-layer recurrent neural network with randomly-chosen internal weights and a trainable output layer. We prove under mild conditions that a sufficiently large Echo State Network can approximate…

Dynamical Systems · Mathematics 2021-06-28 Allen G. Hart , Kevin R. Olding , A. M. G. Cox , Olga Isupova , J. H. P. Dawes

Neuro-inspired recurrent neural network algorithms, such as echo state networks, are computationally lightweight and thereby map well onto untethered devices. The baseline echo state network algorithms are shown to be efficient in solving…

Machine Learning · Computer Science 2019-03-27 Zachariah Carmichael , Humza Syed , Stuart Burtner , Dhireesha Kudithipudi

The Echo State Network (ESN) is a class of Recurrent Neural Network with a large number of hidden-hidden weights (in the so-called reservoir). Canonical ESN and its variations have recently received significant attention due to their…

Neural and Evolutionary Computing · Computer Science 2022-09-30 Sebastian Basterrech , Gerardo Rubino

Reservoir Computing (RC) is a popular methodology for the efficient design of Recurrent Neural Networks (RNNs). Recently, the advantages of the RC approach have been extended to the context of multi-layered RNNs, with the introduction of…

Machine Learning · Computer Science 2019-09-25 Claudio Gallicchio , Alessio Micheli

Recurrent neural networks (RNNs) have become increasingly popular in information processing tasks involving time series and temporal data. A fundamental property of RNNs is their ability to create reliable input/output responses, often…

Machine Learning · Statistics 2026-05-07 Juan-Pablo Ortega , Florian Rossmannek

Echo State Networks (ESNs) are simplified recurrent neural network models composed of a reservoir and a linear, trainable readout layer. The reservoir is tunable by some hyper-parameters that control the network behaviour. ESNs are known to…

Neural and Evolutionary Computing · Computer Science 2018-11-06 Pietro Verzelli , Lorenzo Livi , Cesare Alippi

This paper proposes a novel sufficient condition for the incremental input-to-state stability of a generic class of recurrent neural networks (RNNs). The established condition is compared with others available in the literature, showing to…

Systems and Control · Electrical Eng. & Systems 2023-11-08 William D'Amico , Alessio La Bella , Marcello Farina

Echo State Networks (ESNs) are a class of single layer recurrent neural networks that have enjoyed recent attention. In this paper we prove that a suitable ESN, trained on a series of measurements of an invertible dynamical system, induces…

Chaotic Dynamics · Physics 2020-05-19 Allen G Hart , James L Hook , Jonathan H P Dawes

We propose an approximation of Echo State Networks (ESN) that can be efficiently implemented on digital hardware based on the mathematics of hyperdimensional computing. The reservoir of the proposed integer Echo State Network (intESN) is a…

Neural and Evolutionary Computing · Computer Science 2022-09-02 Denis Kleyko , E. Paxon Frady , Mansour Kheffache , Evgeny Osipov

Echo State Networks (ESN) are versatile recurrent neural network models in which the hidden layer remains unaltered during training. Interactions among nodes of this static backbone produce diverse representations of the given stimuli that…

Machine Learning · Computer Science 2022-05-25 Kayson Fakhar , Fatemeh Hadaeghi , Claus C. Hilgetag

Recently, the field of hardware neural networks has been actively developing, where neurons and their connections are not simulated on a computer but are implemented at the physical level, transforming the neural network into a tangible…

Neural and Evolutionary Computing · Computer Science 2026-01-14 Ivan Kolesnikov , Nadezhda Semenova

We propose automatic speech recognition (ASR) models inspired by echo state network (ESN), in which a subset of recurrent neural networks (RNN) layers in the models are randomly initialized and untrained. Our study focuses on RNN-T and…

Computation and Language · Computer Science 2021-02-19 Harsh Shrivastava , Ankush Garg , Yuan Cao , Yu Zhang , Tara Sainath

Consistency is an extension to generalized synchronization which quantifies the degree of functional dependency of a driven nonlinear system to its input. We apply this concept to echo-state networks, which are an artificial-neural network…

Dynamical Systems · Mathematics 2019-02-20 Thomas Lymburn , Alexander Khor , Thomas Stemler , Débora C. Corrêa , Michael Small , Thomas Jüngling

In this paper, we elaborate over the well-known interpretability issue in echo state networks. The idea is to investigate the dynamics of reservoir neurons with time-series analysis techniques taken from research on complex systems.…

Data Analysis, Statistics and Probability · Physics 2016-11-21 Filippo Maria Bianchi , Lorenzo Livi , Cesare Alippi

Echo state networks (ESNs) are a class of recurrent neural networks in which only the readout layer is trainable, while the recurrent and input layers are fixed. This architectural constraint enables computationally efficient processing of…

Machine Learning · Computer Science 2025-07-31 Taiki Yamada , Yuichi Katori , Kantaro Fujiwara

In recent years, more and more researchers in the field of neural networks are interested in creating hardware implementations where neurons and the connection between them are realized physically. The physical implementation of ANN…

Neural and Evolutionary Computing · Computer Science 2023-07-24 V. M. Moskvitin , N. Semenova

Recurrent Neural networks (RNN) have shown promising potential for learning dynamics of sequential data. However, artificial neural networks are known to exhibit poor robustness in presence of input noise, where the sequential architecture…

Machine Learning · Computer Science 2021-05-05 Arash Amini , Guangyi Liu , Nader Motee

At the heart of time-series forecasting (TSF) lies a fundamental challenge: how can models efficiently and effectively capture long-range temporal dependencies across ever-growing sequences? While deep learning has brought notable progress,…

Machine Learning · Computer Science 2025-11-18 Hongbo Liu , Jia Xu

As one of the most important paradigms of recurrent neural networks, the echo state network (ESN) has been applied to a wide range of fields, from robotics to medicine, finance, and language processing. A key feature of the ESN paradigm is…

Machine Learning · Computer Science 2020-02-26 Pau Vilimelis Aceituno , Yan Gang , Yang-Yu Liu

An echo state network (ESN) is a type of reservoir computer that uses a recurrent neural network with a sparsely connected hidden layer. Compared with other recurrent neural networks, one great advantage of ESN is the simplicity of its…

Statistical Mechanics · Physics 2024-12-17 Clement Dinh , Yunhao Fan , Gia-Wei Chern