Kolmogorov's theorem and multilayer neural networks

By Vera Kurková. 1992

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Citations in the corpus

Deep Clustered Convolutional Kernels (2015, background): “…state of the art performance thanks to their theoretically proven modeling and generalization capabilities (Hornik et al., 1989; Hornik, 1991; Kůrková, 1992), and practically driven by improvements in training algorithms for rapid parameter estimation (Martens, 2010; Sutskever et al.,…”
Neural networks for pattern recognition (1995, background): “While Kolmogorov's theorem is remarkable, its relevance to practical neural computing is at best limited (Girosi and Poggio, 1989; Kurkova, 1991; Kurkova, 1992): There are two reasons for this.”
ResNet with one-neuron hidden layers is a Universal Approximator (2018, background): “Results in the late eighties showed that a network with a single hidden layer can approximate any continuous function with compact support to arbitrary accuracy, when the width goes to infinity [7, 15, 10, 18].”
TP model transformation as a way to LMI-based controller design (2004, methodology): “The reason for this is that, although the TP model has the universal approximation property in theory [10]–[13], it suffers from the problem of exponential complexity with regard to approximation accuracy; see the works by Kóczy and Hirota [14].”
How many hidden layers and nodes? (2009, background): “It has been suggested (Kurkova 1992 ) that two hidden layers should be used to compensate for lost efficiency when using regular activation functions.”
The Kolmogorov-Arnold representation theorem revisited (2020, methodology): “The eﬃciency of the approximating neural network is also the main diﬀerence to the related work [17, 22].”