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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

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 widely-used Recurrent Neural Networks. They are dynamical systems including, in state-space form, a nonlinear state equation and a linear output transformation. The common procedure to train ESNs is to…

Systems and Control · Electrical Eng. & Systems 2019-12-05 Luca Bugliari Armenio , Lorenzo Fagiano , Enrico Terzi , Marcello Farina , Riccardo Scattolini

The prefrontal cortex is known to be involved in many high-level cognitive functions, in particular, working memory. Here, we study to what extent a group of randomly connected units (namely an Echo State Network, ESN) can store and…

Neurons and Cognition · Quantitative Biology 2018-06-19 Anthony Strock , Nicolas Rougier , Xavier Hinaut

Machine learning (ML) is widely used to model chaotic systems. Among ML approaches, echo state networks (ESNs) have received considerable attention due to their simple construction and fast training. However, ESN performance is highly…

Chaotic Dynamics · Physics 2025-07-09 Francesco Martinuzzi

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 (ESNs) are recurrent neural networks usually employed for modeling nonlinear dynamic systems with relatively ease of training. By incorporating physical laws into the training of ESNs, Physics-Informed ESNs (PI-ESNs)…

Machine Learning · Computer Science 2025-02-05 Eric Mochiutti , Eric Aislan Antonelo , Eduardo Camponogara

Memory-augmented neural networks equip a recurrent neural network with an explicit memory to support tasks that require information storage without interference over long times. A key motivation for such research is to perform classic…

Neural and Evolutionary Computing · Computer Science 2021-07-27 Benjamin Paaßen , Alexander Schulz , Barbara Hammer

Echo state networks are powerful recurrent neural networks. However, they are often unstable and shaky, making the process of finding an good ESN for a specific dataset quite hard. Obtaining a superb accuracy by using the Echo State Network…

Machine Learning · Statistics 2018-02-22 Qiuyi Wu , Ernest Fokoue , Dhireesha Kudithipudi

Recurrent neural networks are used to forecast time series in finance, climate, language, and from many other domains. Reservoir computers are a particularly easily trainable form of recurrent neural network. Recently, a "next-generation"…

Machine Learning · Computer Science 2023-03-28 Sarah E. Marzen , Paul M. Riechers , James P. Crutchfield

In real-world applications such as emotion recognition from recorded brain activity, data are captured from electrodes over time. These signals constitute a multidimensional time series. In this paper, Echo State Network (ESN), a recurrent…

Computer Vision and Pattern Recognition · Computer Science 2018-11-26 Rahma Fourati , Boudour Ammar , Javier Sanchez-Medina , Adel M. Alimi

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 (RC) provides an efficient way for designing dynamical recurrent neural models. While training is restricted to a simple output component, the recurrent connections are left untrained after initialization, subject to…

Neural and Evolutionary Computing · Computer Science 2019-09-25 Claudio Gallicchio

Differentiable neural computers extend artificial neural networks with an explicit memory without interference, thus enabling the model to perform classic computation tasks such as graph traversal. However, such models are difficult to…

Machine Learning · Computer Science 2022-06-06 Benjamin Paaßen , Alexander Schulz , Terrence C. Stewart , Barbara Hammer

Memristive devices present a promising foundation for next-generation information processing by combining memory and computation within a single physical substrate. This unique characteristic enables efficient, fast, and adaptive computing,…

Neural and Evolutionary Computing · Computer Science 2026-04-22 Coşku Can Horuz , Andrea Ceni , Claudio Gallicchio , Sebastian Otte

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

Artificial neural networks (ANNs) are known to be powerful methods for many hard problems (e.g. image classification, speech recognition or time series prediction). However, these models tend to produce black-box results and are often…

Machine Learning · Computer Science 2022-11-17 Marco Landt-Hayen , Peer Kröger , Martin Claus , Willi Rath

Neural networks have found extensive application in data-driven control of nonlinear dynamical systems, yet fast online identification and control of unknown dynamics remain central challenges. To meet these challenges, this paper…

Systems and Control · Electrical Eng. & Systems 2026-02-09 Daisuke Inoue , Tadayoshi Matsumori , Gouhei Tanaka , Yuji Ito

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 network (ESN) is viewed as a temporal non-orthogonal expansion with pseudo-random parameters. Such expansions naturally give rise to regressors of various relevance to a teacher output. We illustrate that often only a certain…

Machine Learning · Statistics 2012-07-03 Ján Dolinský , Kei Hirose , Sadanori Konishi