Fetching the paper…
Reading the bibliography…
This work studies approximation based on single-hidden-layer feedforward and recurrent neural networks with randomly generated internal weights.
Springer (1976)
Bergh, J., Löfström, J.: Interpolation Spaces · 1976
Earlier work this paper cites.
McGraw-Hill (1987)
Rudin, W.: Real and Complex Analysis, third edn · 1987
Earlier work this paper cites.
Neural Networks 4
Hornik, K.: Approximation capabilities of muitilayer feedforward networks · 1991
Earlier work this paper cites.
Proceedings of the 7th Yale Workshop on Adaptive and Learning Systems, 69–72 (1992)
Barron, A.R.: Neural Net Approximation · 1992
Earlier work this paper cites.
Springer-Verlag, Berlin (1992)
Kloeden, P.E., Platen, E.: Numerical solution of stochastic differential equations · 1992
Earlier work this paper cites.
Ph.D. thesis, ETH Zürich (1992)
Matthews, M.B.: On the Uniform Approximation of Nonlinear Discrete-Time Fading-Memory Systems Using Neural Network Models · 1992
Earlier work this paper cites.
IEEE Transactions on Information Theory 39
Barron, A.R.: Universal approximation bounds for superpositions of a sigmoidal function · 1993
Earlier work this paper cites.
Circuits, Systems, and Signal Processing 12
Matthews, M.B.: Approximating nonlinear fading-memory operators using neural network models · 1993
Earlier work this paper cites.
IEEE Transactions on Circuits and Systems II: Analog and Digital Signal Processing 41
Matthews, M., Moschytz, G.: The identification of nonlinear discrete-time fading-memory systems using neural network models · 1994
Earlier work this paper cites.
Princeton University Press (1995)
Folland, G.B.: Introduction to Partial Differential Equations, second edn · 1995
Earlier work this paper cites.
Neural computation 8
Mhaskar, N.H.: Neural networks for optimal approximation of smooth and analytic functions · 1996
Earlier work this paper cites.
Advances in Computational Mathematics 13
Maiorov, V., Meir, R.: On the near optimality of the stochastic approximation of smooth functions by neural networks · 2000
Earlier work this paper cites.
Probability and Its Applications. Springer New York (2002)
Kallenberg, O.: Foundations of Modern Probability, second edn · 2002
Cited alongside, same era.
Science 304
Jaeger, H., Haas, H.: Harnessing Nonlinearity: Predicting Chaotic Systems and Saving Energy in Wireless Communication · 2004
Cited alongside, same era.
Aliprantis, C.D., Border, K.C.: Infinite dimensional analysis: A hitchhiker’s guide (2006)
2006
Cited alongside, same era.
Neurocomputing 70
Huang, G.B., Zhu, Q.Y., Siew, C.K.: Extreme learning machine: Theory and applications · 2006
Cited alongside, same era.
Advances in Neural Information Processing Systems (2007)
Rahimi, A., Recht, B.: Random features for large-scale kernel machines · 2007
Cited alongside, same era.
In: 2008 46th Annual Allerton Conference on Communication, Control, and Computing, pp. 555–561 (2008)
Rahimi, A., Recht, B.: Uniform approximation of functions with random bases · 2008
Journal of Machine Learning Research 19
Grigoryeva, L., Ortega, J.P.: Universal discrete-time reservoir computers with stochastic inputs and linear readouts using non-homogeneous state-affine systems · 2018
Later among the works it cites.
IEEE Transactions on Information Theory 64
Klusowski, J.M., Barron, A.R.: Approximation by combinations of ReLU and squared ReLU ridge functions with l1 and l0 controls · 2018
Later among the works it cites.
Chaos 28
Lu, Z., Hunt, B.R., Ott, E.: Attractor reconstruction by machine learning · 2018
Later among the works it cites.
Physical Review Letters 120
Pathak, J., Hunt, B., Girvan, M., Lu, Z., Ott, E.: Model-Free Prediction of Large Spatiotemporally Chaotic Systems from Data: A Reservoir Computing Approach · 2018
Later among the works it cites.
Journal of Machine Learning Research, 20
Grigoryeva, L., Ortega, J.P.: Differentiable reservoir computing · 2019
Later among the works it cites.
alphaXiv searches the wider corpus for related work and actual follow-ups.
alphaXiv is searching for related work…
Cited alongside, same era.
Advances in Neural Information Processing Systems (2009)
Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning · 2009
Cited alongside, same era.
Cambridge University Press, Cambridge (2010)
Friz, P.K., Victoir, N.B.: Multidimensional stochastic processes as rough paths · 2010
Cited alongside, same era.
Springer Berlin Heidelberg (2013)
Ledoux, M., Talagrand, M.: Probability in Banach Spaces · 2013
Cited alongside, same era.
Chaos 27
Pathak, J., Lu, Z., Hunt, B.R., Girvan, M., Ott, E.: Using machine learning to replicate chaotic attractors and calculate Lyapunov exponents from data · 2017
Cited alongside, same era.
International Journal of Automation and Computing 14
Poggio, T., Mhaskar, H., Rosasco, L., Miranda, B., Liao, Q.: Why and when can deep-but not shallow-networks avoid the curse of dimensionality: A review · 2017
Cited alongside, same era.
Neural Networks 108
Grigoryeva, L., Ortega, J.P.: Echo state networks are universal · 2018
Cited alongside, same era.
Hart, A.G., Hook, J.L., Dawes, J.H.P.: Embedding and approximation theorems for echo state networks · 2019
Later among the works it cites.
Cuchiero, C., Gonon, L., Grigoryeva, L., Ortega, J.P., Teichmann, J.: Approximation of dynamics by randomized signature. In preparation (2020)
2020
Closest in time.
Preprint arXiv:2010.14615 (2020)
Cuchiero, C., Gonon, L., Grigoryeva, L., Ortega, J.P., Teichmann, J.: Discrete-time signatures and randomness in reservoir computing · 2020
Closest in time.
Journal of Machine Learning Research, 21
Gonon, L., Grigoryeva, L., Ortega, J.P.: Risk Bounds for Reservoir Computing · 2020
Closest in time.
IEEE Transactions on Neural Networks and Learning Systems 31
Gonon, L., Ortega, J.P.: Reservoir computing universality with stochastic inputs · 2020
Closest in time.
To appear in Neural Networks (2021)
Gonon, L., Ortega, J.P.: Fading memory echo state networks are universal · 2021
Closest in time.