Degree of approximation by neural and translation networks with a single hidden layer
From MaRDI portal
Publication:1902810
DOI10.1006/aama.1995.1008zbMath0885.42012OpenAlexW2002023932MaRDI QIDQ1902810
Charles A. Micchelli, Hrushikesh N. Mhaskar
Publication date: 20 April 1998
Published in: Advances in Applied Mathematics (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1006/aama.1995.1008
neural networkswavelet analysistranslatesdegree of approximation\(2\pi\)-periodic functionsdilatesapproximation by radial basis functions
General harmonic expansions, frames (42C15) Harmonic analysis in several variables (42B99) Rate of convergence, degree of approximation (41A25) Approximation by other special function classes (41A30)
Related Items
On Approximation by Neural Networks with Optimized Activation Functions and Fixed Weights, A Proof that Artificial Neural Networks Overcome the Curse of Dimensionality in the Numerical Approximation of Black–Scholes Partial Differential Equations, Approximation by network operators with logistic activation functions, Multivariate Jackson-type inequality for a new type neural network approximation, The estimate for approximation error of spherical neural networks, Lower estimation of approximation rate for neural networks, An analog of the Jackson-Nikol'skij theorem on the approximation by superpositions of sigmoidal functions, The errors of approximation for feedforward neural networks in thelpmetric, Full error analysis for the training of deep neural networks, Neural network interpolation operators activated by smooth ramp functions, Networks and closed balls, Limitations of the approximation capabilities of neural networks with one hidden layer, Approximation by neural networks with sigmoidal functions, A note on the applications of one primary function in deep neural networks, Modified neural network operators and their convergence properties with summability methods, The construction and approximation of some neural network operators, An analysis of training and generalization errors in shallow and deep networks, Neural network interpolation operators optimized by Lagrange polynomial, Towards Lower Bounds on the Depth of ReLU Neural Networks, Overall error analysis for the training of deep neural networks via stochastic gradient descent with random initialisation, Neural network interpolation operators of multivariate functions, On approximation by reproducing kernel spaces in weighted \(L^p\) spaces, Approximation error of single hidden layer neural networks with fixed weights, Essential rate for approximation by spherical neural networks, The errors of simultaneous approximation of multivariate functions by neural networks, The ridge function representation of polynomials and an application to neural networks, Computing the Approximation Error for Neural Networks with Weights Varying on Fixed Directions, Approximation results for neural network operators activated by sigmoidal functions, Multivariate neural network operators with sigmoidal activation functions, Simultaneous Approximations of Polynomials and Derivatives and Their Applications to Neural Networks, Applications of classical approximation theory to periodic basis function networks and computational harmonic analysis, Approximation rates for neural networks with general activation functions, Finite Neuron Method and Convergence Analysis, Interpolation by neural network operators activated by ramp functions, The convergence rate for a \(K\)-functional in learning theory, Approximation by series of sigmoidal functions with applications to neural networks, Multivariate sigmoidal neural network approximation, The approximation operators with sigmoidal functions, Complexity of neural network approximation with limited information: A worst case approach, A way of constructing translation network operators by Bernstein operators, New study on neural networks: the essential order of approximation, The essential order of approximation for nearly exponential type neural networks, Error bounds for approximation with neural networks, Optimization based on quasi-Monte Carlo sampling to design state estimators for non-linear systems, Some problems in the theory of ridge functions, DEGREE OF APPROXIMATION BY PERIODIC NEURAL NETWORKS, Quantitative approximation by perturbed Kantorovich-Choquet neural network operators, Rates of approximation by neural network interpolation operators, Convergence Analysis of Machine Learning Algorithms for the Numerical Solution of Mean Field Control and Games I: The Ergodic Case, Simultaneous \(\mathbf L^p\)-approximation order for neural networks, The construction and approximation of ReLU neural network operators, Neural Networks for Functional Approximation and System Identification, On the order of approximation by periodic neural networks based on scattered nodes, Approximation by perturbed neural network operators, Convergence analysis of machine learning algorithms for the numerical solution of mean field control and games. II: The finite horizon case, Approximations by multivariate perturbed neural network operators, Optimal Approximation with Sparsely Connected Deep Neural Networks, Approximation spaces of deep neural networks