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We prove an inverse approximation theorem for the approximation of nonlinear sequence-to-sequence relationships using recurrent neural networks (RNNs).
Sur la meilleure approximation de —x— par des polynomes de degrés donnés
Serge Bernstein · 1914
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Learning long-term dependencies with gradient descent is difficult
Y. Bengio, P. Simard, and P. Frasconi · 1941
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Analytical Foundations of Volterra Series
Stephen Boyd, L. O. Chua, and C. A. Desoer · 1984
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Learning representations by back-propagating errors
David E. Rumelhart, Geoffrey E. Hinton, and Ronald J. Williams · 1986
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Approximation by superpositions of a sigmoidal function
G. Cybenko · 1989
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Recurrent neural networks and robust time series prediction
Jerome T. Connor, R. Douglas Martin, and Les E. Atlas · 1994
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Nonlinear approximation
Ronald A DeVore · 1998
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A learning result for continuous-time recurrent neural networks
Eduardo D. Sontag · 1998
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Nonlinear systems third edition (2002), 2002
Hassan K. Khalil · 2002
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Impossibility of Fast Stable Approximation of Analytic Functions from Equispaced Samples
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On the Curse of Memory in Recurrent Neural Networks: Approximation and Optimization Analysis
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Fading memory echo state networks are universal
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Efficiently Modeling Long Sequences with Structured State Spaces
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Learning Recurrent Neural Net Models of Nonlinear Systems
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Approximation and Optimization Theory for Linear Continuous-Time Recurrent Neural Networks
Zhong Li, Jiequn Han, Weinan E, and Qianxiao Li · 2022
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