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Reservoir computing, using nonlinear dynamical systems, offers a cost-effective alternative to neural networks for complex tasks involving processing of sequential data, time series modeling, and system identification. Echo state networks…

Machine Learning · Computer Science 2025-01-14 Peter J. Ehlers , Hendra I. Nurdin , Daniel Soh

A method is provided for designing and training noise-driven recurrent neural networks as models of stochastic processes. The method unifies and generalizes two known separate modeling approaches, Echo State Networks (ESN) and Linear…

Adaptation and Self-Organizing Systems · Physics 2014-04-14 Mathieu N. Galtier , Camille Marini , Gilles Wainrib , Herbert Jaeger

Background: In cognitive neuroscience the potential of Deep Neural Networks (DNNs) for solving complex classification tasks is yet to be fully exploited. The most limiting factor is that DNNs as notorious 'black boxes' do not provide…

Neural and Evolutionary Computing · Computer Science 2016-04-28 Irene Sturm , Sebastian Bach , Wojciech Samek , Klaus-Robert Müller

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

This paper proposes a novel and interpretable recurrent neural-network structure using the echo-state network (ESN) paradigm for time-series prediction. While the traditional ESNs perform well for dynamical systems prediction, it needs a…

Machine Learning · Computer Science 2024-04-01 Debdipta Goswami

Machine learning methods are solving very successfully a plethora of tasks, but they have the disadvantage of not providing any information about their decision. Consequently, estimating the reasoning of the system provides additional…

Machine Learning · Computer Science 2025-01-27 Eric Nyiri , Olivier Gibaru

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

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

Trust and credibility in machine learning models is bolstered by the ability of a model to explain itsdecisions. While explainability of deep learning models is a well-known challenge, a further chal-lenge is clarity of the explanation…

Machine Learning · Computer Science 2020-11-30 hsan Ullah , Andre Rios , Vaibhav Gala , Susan Mckeever

In reservoir computing, an input sequence is processed by a recurrent neural network, the reservoir, which transforms it into a spatial pattern that a shallow readout network can then exploit for tasks such as memorization and time-series…

Neural and Evolutionary Computing · Computer Science 2025-12-30 Denis Kleyko , Christopher J. Kymn , E. Paxon Frady , Amy Loutfi , Friedrich T. Sommer

Explainable AI (XAI) methods help identify which image regions influence a model's prediction, but often face a trade-off between detail and interpretability. Layer-wise Relevance Propagation (LRP) offers a model-aware alternative. However,…

Machine Learning · Computer Science 2025-10-02 Emerald Zhang , Julian Weaver , Samantha R Santacruz , Edward Castillo

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

Inspired by recent theoretical arguments, physics-informed echo state network (ESN) is discussed on the attempt to train a reservoir model absolutely in physics-informed manner. As the plainest work on such a purpose, an ODE (ordinary…

Machine Learning · Computer Science 2020-11-16 Dong Keun Oh

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

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

In recent years, artificial intelligence (AI) systems have come to the forefront. These systems, mostly based on Deep learning (DL), achieve excellent results in areas such as image processing, natural language processing, or speech…

Computer Vision and Pattern Recognition · Computer Science 2023-04-18 Frantisek Sefcik , Wanda Benesova

Distance-based classifiers, such as k-nearest neighbors and support vector machines, continue to be a workhorse of machine learning, widely used in science and industry. In practice, to derive insights from these models, it is also…

Machine Learning · Computer Science 2026-05-05 Florian Bley , Jacob Kauffmann , Simon León Krug , Klaus-Robert Müller , Grégoire Montavon

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

Deep learning has seen a rapid adoption in a variety of wireless communications applications, including at the physical layer. While it has delivered impressive performance in tasks such as channel equalization and receive processing/symbol…

Signal Processing · Electrical Eng. & Systems 2024-10-28 Shashank Jere , Karim Said , Lizhong Zheng , Lingjia Liu

Convolutional neural networks (CNNs) underpin many modern computer vision systems. With applications ranging from common to critical areas, a need to explain and understand the model and its decisions (XAI) emerged. Prior works suggest that…

Computer Vision and Pattern Recognition · Computer Science 2025-11-05 Vojtěch Kůr , Adam Bajger , Adam Kukučka , Marek Hradil , Vít Musil , Tomáš Brázdil