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An approach to the time-accurate prediction of chaotic solutions is by learning temporal patterns from data. Echo State Networks (ESNs), which are a class of Reservoir Computing, can accurately predict the chaotic dynamics well beyond the…

Machine Learning · Computer Science 2021-03-16 Alberto Racca , Luca Magri

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

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

We report about probabilistic likelihood estimates that are performed on time series using an echo state network with orthogonal recurrent connectivity. The results from tests using synthetic stochastic input time series with temporal…

Neural and Evolutionary Computing · Computer Science 2017-06-14 Norbert Michael Mayer , Ying-Hao Yu

We propose a novel algorithm for performing federated learning with Echo State Networks (ESNs) in a client-server scenario. In particular, our proposal focuses on the adaptation of reservoirs by combining Intrinsic Plasticity with Federated…

Neural and Evolutionary Computing · Computer Science 2022-06-23 Valerio De Caro , Claudio Gallicchio , Davide Bacciu

As an efficient recurrent neural network (RNN) model, reservoir computing (RC) models, such as Echo State Networks, have attracted widespread attention in the last decade. However, while they have had great success with time series data…

Machine Learning · Computer Science 2017-11-16 Qianli Ma , Lifeng Shen , Garrison W. Cottrell

Among the various architectures of Recurrent Neural Networks, Echo State Networks (ESNs) emerged due to their simplified and inexpensive training procedure. These networks are known to be sensitive to the setting of hyper-parameters, which…

Neural and Evolutionary Computing · Computer Science 2019-09-23 Pietro Verzelli , Cesare Alippi , Lorenzo Livi

We propose a physics-informed Echo State Network (ESN) to predict the evolution of chaotic systems. Compared to conventional ESNs, the physics-informed ESNs are trained to solve supervised learning tasks while ensuring that their…

Physics and Society · Physics 2019-06-28 Nguyen Anh Khoa Doan , Wolfgang Polifke , Luca Magri

We propose an innovative design for an optical Echo State Network (ESN), an advanced type of reservoir computer known for its universal computational capabilities. Our design enables an optical implementation of arbitrary ESNs, featuring…

Optics · Physics 2025-11-17 Ishwar S Kaushik , Peter J Ehlers , Daniel Soh

Echo state network (ESN), a kind of recurrent neural networks, consists of a fixed reservoir in which neurons are connected randomly and recursively and obtains the desired output only by training output connection weights. First-order…

Machine Learning · Computer Science 2024-01-22 Yansong Li , Kai Hu , Kohei Nakajima , Yongping Pan

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 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

In the last decade, a new computational paradigm was introduced in the field of Machine Learning, under the name of Reservoir Computing (RC). RC models are neural networks which a recurrent part (the reservoir) that does not participate in…

Neural and Evolutionary Computing · Computer Science 2013-04-08 Sebastián Basterrech , Gerardo Rubino

Machine learning has become a widely popular and successful paradigm, including in data-driven science and engineering. A major application problem is data-driven forecasting of future states from a complex dynamical. Artificial neural…

Data Analysis, Statistics and Probability · Physics 2021-03-19 Erik Bollt

The Echo State Network (ESN) is a specific recurrent network, which has gained popularity during the last years. The model has a recurrent network named reservoir, that is fixed during the learning process. The reservoir is used for…

Neural and Evolutionary Computing · Computer Science 2017-03-21 Sebastián Basterrech

Reservoir Computing (RC) has established itself as an efficient paradigm for temporal processing. However, its scalability remains severely constrained by (i) the necessity of processing temporal data sequentially and (ii) the prohibitive…

Machine Learning · Computer Science 2026-02-02 Matteo Pinna , Giacomo Lagomarsini , Andrea Ceni , Claudio Gallicchio

We introduce a diagonalization-based optimization for Linear Echo State Networks (ESNs) that reduces the per-step computational complexity of reservoir state updates from O(N^2) to O(N). By reformulating reservoir dynamics in the eigenbasis…

Distributed, Parallel, and Cluster Computing · Computer Science 2026-02-24 Romain de Coudenhove , Yannis Bendi-Ouis , Anthony Strock , Xavier Hinaut

Recurrent neural networks are a powerful means to cope with time series. We show how autoregressive linear, i.e., linearly activated recurrent neural networks (LRNNs) can approximate any time-dependent function f(t). The approximation can…

Machine Learning · Computer Science 2025-10-01 Frieder Stolzenburg , Sandra Litz , Olivia Michael , Oliver Obst

We first study the generalization error of models that use a fixed feature representation (frozen intermediate layers) followed by a trainable readout layer. This setting encompasses a range of architectures, from deep random-feature models…

Statistics Theory · Mathematics 2025-11-10 Yessin Moakher , Malik Tiomoko , Cosme Louart , Zhenyu Liao

We present neural machine translation (NMT) models inspired by echo state network (ESN), named Echo State NMT (ESNMT), in which the encoder and decoder layer weights are randomly generated then fixed throughout training. We show that even…

Computation and Language · Computer Science 2020-02-28 Ankush Garg , Yuan Cao , Qi Ge