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Recurrent Neural Networks (RNNs) have demonstrated their outstanding ability in sequence tasks and have achieved state-of-the-art in wide range of applications, such as industrial, medical, economic and linguistic. Echo State Network (ESN)…

Machine Learning · Computer Science 2020-12-08 Chenxi Sun , Moxian Song , Shenda Hong , Hongyan Li

Echo State Networks (ESNs) are a particular type of untrained Recurrent Neural Networks (RNNs) within the Reservoir Computing (RC) framework, popular for their fast and efficient learning. However, traditional ESNs often struggle with…

Machine Learning · Computer Science 2026-01-30 Matteo Pinna , Andrea Ceni , Claudio Gallicchio

It is a widely accepted fact that data representations intervene noticeably in machine learning tools. The more they are well defined the better the performance results are. Feature extraction-based methods such as autoencoders are…

Neural and Evolutionary Computing · Computer Science 2018-06-12 Naima Chouikhi , Boudour Ammar , Adel M. Alimi

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

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

Recurrent neural networks (RNNs) have drawn interest from machine learning researchers because of their effectiveness at preserving past inputs for time-varying data processing tasks. To understand the success and limitations of RNNs, it is…

Information Theory · Computer Science 2017-01-30 Adam Charles , Dong Yin , Christopher Rozell

The study of deep recurrent neural networks (RNNs) and, in particular, of deep Reservoir Computing (RC) is gaining an increasing research attention in the neural networks community. The recently introduced Deep Echo State Network (DeepESN)…

Machine Learning · Computer Science 2020-09-28 Claudio Gallicchio , Alessio Micheli

Echo state networks (ESNs) are a powerful form of reservoir computing that only require training of linear output weights whilst the internal reservoir is formed of fixed randomly connected neurons. With a correctly scaled connectivity…

Machine Learning · Computer Science 2021-08-03 Luca Manneschi , Matthew O. A. Ellis , Guido Gigante , Andrew C. Lin , Paolo Del Giudice , Eleni Vasilaki

Temporal data modelling techniques with neural networks are useful in many domain applications, including time-series forecasting and control engineering. This paper aims at developing a recurrent version of stochastic configuration…

Machine Learning · Computer Science 2025-04-03 Dianhui Wang , Gang Dang

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

A particular case of Recurrent Neural Network (RNN) was introduced at the beginning of the 2000s under the name of Echo State Networks (ESNs). The ESN model overcomes the limitations during the training of the RNNs while introducing no…

Machine Learning · Computer Science 2015-01-06 Sebastián Basterrech

Echo State Networks (ESNs) are a special type of recurrent neural networks (RNNs), in which the input and recurrent connections are traditionally generated randomly, and only the output weights are trained. Despite the recent success of…

Machine Learning · Computer Science 2022-05-11 Peter Steiner , Azarakhsh Jalalvand , Peter Birkholz

Recurrent neural networks (RNNs) can be interpreted as discrete-time state-space models, where the state evolution corresponds to an infinite-impulse-response (IIR) filtering operation governed by both feedforward weights and recurrent…

Machine Learning · Computer Science 2026-02-26 Alexander Morgan , Ummay Sumaya Khan , Lingjia Liu , Lizhong Zheng

Echo State Networks (ESNs) are typically presented as efficient, readout-trained recurrent models, yet their dynamics and design are often guided by heuristics rather than first principles. We recast ESNs explicitly as state-space models…

Machine Learning · Computer Science 2025-09-05 Pradeep Singh , Balasubramanian Raman

The goal of this paper is to investigate the theoretical properties, the training algorithm, and the predictive control applications of Echo State Networks (ESNs), a particular kind of Recurrent Neural Networks. First, a condition…

Systems and Control · Computer Science 2019-02-06 Luca Bugliari Armenio , Enrico Terzi , Marcello Farina , Riccardo Scattolini

Several variants of recurrent neural networks (RNNs) with orthogonal or unitary recurrent matrices have recently been developed to mitigate the vanishing/exploding gradient problem and to model long-term dependencies of sequences. However,…

Machine Learning · Computer Science 2019-11-20 Kyle Helfrich , Qiang Ye

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

Echo State Networks (ESN) are a class of Recurrent Neural Networks (RNN) that has gained substantial popularity due to their effectiveness, ease of use and potential for compact hardware implementation. An ESN contains the three network…

Machine Learning · Computer Science 2018-07-26 Luca Carcano , Emanuele Plebani , Danilo Pietro Pau , Marco Piastra

Echo States Networks (ESN) and Long-Short Term Memory networks (LSTM) are two popular architectures of Recurrent Neural Networks (RNN) to solve machine learning task involving sequential data. However, little have been done to compare their…

Neural and Evolutionary Computing · Computer Science 2020-12-15 Alexandre Variengien , Xavier Hinaut

Echo state networks (ESN), a type of reservoir computing (RC) architecture, are efficient and accurate artificial neural systems for time series processing and learning. An ESN consists of a core of recurrent neural networks, called a…

Neural and Evolutionary Computing · Computer Science 2015-04-28 Alireza Goudarzi , Alireza Shabani , Darko Stefanovic
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