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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

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

Reservoir computing (RC) offers efficient temporal data processing with a low training cost by separating recurrent neural networks into a fixed network with recurrent connections and a trainable linear network. The quality of the fixed…

Emerging Technologies · Computer Science 2021-05-17 John Moon , Wei D. Lu

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

Reservoir computing (RC), a particular form of recurrent neural network, is under explosive development due to its exceptional efficacy and high performance in reconstruction or/and prediction of complex physical systems. However, the…

Machine Learning · Computer Science 2023-05-10 Xing-Yue Duan , Xiong Ying , Si-Yang Leng , Jürgen Kurths , Wei Lin , Huan-Fei Ma

Reservoir Computing (RC) is an appealing approach in Machine Learning that combines the high computational capabilities of Recurrent Neural Networks with a fast and easy training method. Likewise, successful implementation of neuro-inspired…

Adaptation and Self-Organizing Systems · Physics 2021-07-13 Guillermo B. Morales , Claudio R. Mirasso , Miguel C. Soriano

Recent advancements in artificial neural networks have enabled impressive tasks on classical computers, but they demand significant computational resources. While quantum computing offers potential beyond classical systems, the advantages…

Quantum Physics · Physics 2024-12-12 Erik Connerty , Ethan Evans , Gerasimos Angelatos , Vignesh Narayanan

Reservoir computers (RCs) provide a computationally efficient alternative to deep learning while also offering a framework for incorporating brain-inspired computational principles. By using an internal neural network with random, fixed…

Neural and Evolutionary Computing · Computer Science 2025-04-18 Keshav Srinivasan , Dietmar Plenz , Michelle Girvan

Forecasting high-dimensional spatiotemporal systems remains computationally challenging for recurrent neural networks (RNNs) and long short-term memory (LSTM) models due to gradient-based training and memory bottlenecks. Reservoir Computing…

Machine Learning · Computer Science 2026-01-05 Ata Akbari Asanjan , Filip Wudarski , Daniel O'Connor , Shaun Geaney , Elena Strbac , P. Aaron Lott , Davide Venturelli

For many years, Evolutionary Algorithms (EAs) have been applied to improve Neural Networks (NNs) architectures. They have been used for solving different problems, such as training the networks (adjusting the weights), designing network…

Neural and Evolutionary Computing · Computer Science 2022-11-14 Sebastián Basterrech , Tarun Kumar Sharma

Echo State Networks (ESNs) are a special type of the temporally deep network model, the Recurrent Neural Network (RNN), where the recurrent matrix is carefully designed and both the recurrent and input matrices are fixed. An ESN uses the…

Machine Learning · Computer Science 2013-11-14 Hamid Palangi , Li Deng , Rabab K Ward

In this paper we present a computational model which decodes the spatio-temporal data from electro-physiological measurements of neuronal networks and reconstructs the network structure on a macroscopic domain, representing the connectivity…

Quantitative Methods · Quantitative Biology 2025-02-14 Ilya Auslender , Lorenzo Pavesi

What is a neural model with minimum architectural complexity that exhibits reasonable language learning capability? To explore such a simple but sufficient neural language model, we revisit a basic reservoir computing (RC) model, Echo State…

Computation and Language · Computer Science 2025-03-04 Ryo Ueda , Tatsuki Kuribayashi , Shunsuke Kando , Kentaro Inui

Reservoir Computing is a machine learning approach that uses the rich repertoire of complex system dynamics for function approximation. Current approaches to reservoir computing use a network of coupled integrating neurons that require a…

Neural and Evolutionary Computing · Computer Science 2025-07-30 Alexander Yeung , Peter DelMastro , Arjun Karuvally , Hava Siegelmann , Edward Rietman , Hananel Hazan

Echo State Networks (ESNs) are a reservoir computing framework widely used for nonlinear time-series prediction. However, despite their effectiveness, randomly initialized reservoirs often contain redundant nodes, leading to unnecessary…

Machine Learning · Computer Science 2026-05-07 Sudip Laudari

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

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

Over the last decade, deep-learning methods have been gradually incorporated into conventional automatic speech recognition (ASR) frameworks to create acoustic, pronunciation, and language models. Although it led to significant improvements…

Sound · Computer Science 2022-05-26 Zohreh Ansari , Farzin Pourhoseini , Fatemeh Hadaeghi

Reservoir computing is a powerful framework for real-time information processing, characterized by its high computational ability and quick learning, with applications ranging from machine learning to biological systems. In this paper, we…

Disordered Systems and Neural Networks · Physics 2025-10-24 Shotaro Takasu , Toshio Aoyagi

Echo-State Networks (ESNs) distil a key neurobiological insight: richly recurrent but fixed circuitry combined with adaptive linear read-outs can transform temporal streams with remarkable efficiency. Yet fundamental questions about…

Neural and Evolutionary Computing · Computer Science 2025-07-25 Pradeep Singh , Lavanya Sankaranarayanan , Balasubramanian Raman