Embedding and approximation theorems for echo state networks

DOI10.1016/j.neunet.2020.05.013zbMath1468.68098arXiv1908.05202OpenAlexW3025101483WikidataQ95647877 ScholiaQ95647877MaRDI QIDQ1982435

James Hook, Allen Hart, Jonathan H. P. Dawes

Publication date: 8 September 2021

Published in: Neural Networks (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1908.05202

zbMATH Keywords

dynamical systemLorenz equationsrecurrent neural networkspersistent homologyreservoir computingdelay embedding

Mathematics Subject Classification ID

Persistent homology and applications, topological data analysis (55N31) Simulation of dynamical systems (37M05) Networks and circuits as models of computation; circuit complexity (68Q06)

Related Items (15)

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Uses Software

• javaPlex
• Ripser.py

Cites Work

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• Embedology
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• Exploring the topology of dynamical reconstructions
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• Data-driven reconstruction of nonlinear dynamics from sparse observation
• Topology from time series
• Automatic speech recognition using a predictive echo state network classifier
• Learning grammatical structure with Echo State Networks
• The self-intersections of a smooth \(n\)-manifold in \(2n\)-space
• javaPlex: A Research Software Package for Persistent (Co)Homology
• Deblurring Images
• Real-Time Computing Without Stable States: A New Framework for Neural Computation Based on Perturbations
• Using machine learning to replicate chaotic attractors and calculate Lyapunov exponents from data
• Deterministic Nonperiodic Flow
• Barcodes: The persistent topology of data
• Invariant manifolds
• Approximation by superpositions of a sigmoidal function

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