On the approximate realization of continuous mappings by neural networks

By Ken-ichi Funahashi. 1989

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Citations in the corpus

Meta-Learning and Universality: Deep Representations and Gradient Descent can Approximate any Learning Algorithm (2017, background): “The universal function approximation theorem states that a neural network with one hidden layer of ﬁnite width can approximate any continuous function on compact subsets of R n up to arbitrary precision (Hornik et al., 1989; Cybenko, 1989; Funahashi, 1989).”
The Power of Depth for Feedforward Neural Networks (2015, background): “The boundedness assumption is important here: It is well-known that sufﬁciently large depth-2 neural networks, using reasonable activation functions, can approximate any continuous function on a bounded domain (Cy-benko [1989], Hornik et al. [1989], Funahashi [1989], Barron [1994]).”
Learning to Relate Images (2011, methodology): “Of course, squares could be approximated using a feed-forward network with sigmoid hidden unit activations [65].”
Neural Network with Unbounded Activation Functions is Universal Approximator (2015, unknown): “Irie and Miyake [18], Funahashi [19], Jones [20], and Barron [21] used Fourier analysis to show the approximation property in a constructive way.”
Direct-fit to nature: an evolutionary perspective on biological (and artificial) neural networks (2019, background): “The same direct-ﬁt procedures can be expanded to ﬁt arbitrarily complex data structures (Cybenko, 1989; Funahashi, 1989; Hornik et al., 1989; Raghu et al., 2017).”
Deep Autoencoder based Energy Method for the Bending, Vibration, and Buckling Analysis of Kirchhoff Plates (2020, background): “According to the universal approximation theorem [35, 36], any continuous function can be approximated by a feedforward neural network with one single hidden layer.”
Real-Time Profiling of Fine-Grained Air Quality Index Distribution Using UAV Sensing (2017, background): “As it has been proved that a three-layer neural network can compute any arbitrary function [32]–[34], NN is able to present the complicated changes in fine-grained scenario.”
Adaptive output feedback control of uncertain nonlinear systems using single-hidden-layer neural networks (2002, background): “Such an architecture is known to be a universal approximator of continuous nonlinearities with “squashing” activation functions [10], [13].”
A comprehensive survey on machine learning for networking: evolution, applications and research opportunities (2018, methodology): “This was supported by rigorous independent mathematical proofs published in the late eighties and the early nineties by Cybenko [106], Hornik [196], and Funahashi [158].”
Cocaine and Chest Pain (1992, unknown): “It has been shown that they constitute universal approximators [130], both with 1 hidden layer [128] and with 2 hidden layers [129].”