Universal approximation bounds for superpositions of a sigmoidal function
From MaRDI portal
Publication:4277151
DOI10.1109/18.256500zbMath0818.68126OpenAlexW2166116275MaRDI QIDQ4277151
Publication date: 7 February 1994
Published in: IEEE Transactions on Information Theory (Search for Journal in Brave)
Full work available at URL: https://semanticscholar.org/paper/04113e8974341f97258800126d05fd8df2751b7e
Related Items
Learning and Convergence of the Normalized Radial Basis Functions Networks, On Approximation by Neural Networks with Optimized Activation Functions and Fixed Weights, Stationary Density Estimation of Itô Diffusions Using Deep Learning, A Regularity Theory for Static Schrödinger Equations on \(\boldsymbol{\mathbb{R}}\)d in Spectral Barron Spaces, Neural network approximation, Convergence of Physics-Informed Neural Networks Applied to Linear Second-Order Elliptic Interface Problems, A Proof that Artificial Neural Networks Overcome the Curse of Dimensionality in the Numerical Approximation of Black–Scholes Partial Differential Equations, Approximation bounds for norm constrained neural networks with applications to regression and GANs, Construction and approximation for a class of feedforward neural networks with sigmoidal function, Adaptive neural network control for nonholonomic systems with partial/full or without state constraints, Deep Neural Networks for Solving Large Linear Systems Arising from High-Dimensional Problems, Computationally efficient integrated design and predictive control of flexible energy systems using multi‐fidelity simulation‐based Bayesian optimization, Neural network approximation: three hidden layers are enough, A deep network construction that adapts to intrinsic dimensionality beyond the domain, On the approximation of functions by tanh neural networks, Theory of deep convolutional neural networks. III: Approximating radial functions, Approximation capabilities of neural networks on unbounded domains, On the capacity of deep generative networks for approximating distributions, On sharpness of error bounds for multivariate neural network approximation, Probabilistic performance validation of deep learning‐based robust NMPC controllers, Rates of approximation by ReLU shallow neural networks, Universality of gradient descent neural network training, A class of dimension-free metrics for the convergence of empirical measures, A priori generalization error analysis of two-layer neural networks for solving high dimensional Schrödinger eigenvalue problems, Neural network interpolation operators optimized by Lagrange polynomial, Neural Networks for Clustered and Longitudinal Data Using Mixed Effects Models, Approximation Analysis of Convolutional Neural Networks, Towards Lower Bounds on the Depth of ReLU Neural Networks, Characterization of the variation spaces corresponding to shallow neural networks, Universal regular conditional distributions via probabilistic transformers, Accuracy and architecture studies of residual neural network method for ordinary differential equations, Approximation bounds for random neural networks and reservoir systems, Unnamed Item, Overall error analysis for the training of deep neural networks via stochastic gradient descent with random initialisation, Friedrichs Learning: Weak Solutions of Partial Differential Equations via Deep Learning, Efficient estimation of average derivatives in NPIV models: simulation comparisons of neural network estimators, A mathematical perspective of machine learning, An extreme learning machine-based method for computational PDEs in higher dimensions, Noncompact uniform universal approximation, Stein variational gradient descent with learned direction, Universal Features for High-Dimensional Learning and Inference, SignReLU neural network and its approximation ability, Deep Neural Networks with ReLU-Sine-Exponential Activations Break Curse of Dimensionality in Approximation on Hölder Class, Convergence rates for shallow neural networks learned by gradient descent, Neural network interpolation operators of multivariate functions, Improved Analysis of PINNs: Alleviate the CoD for Compositional Solutions, Connections between Operator-Splitting Methods and Deep Neural Networks with Applications in Image Segmentation, Optimal learning, Error bounds for approximations using multichannel deep convolutional neural networks with downsampling, Lower bounds for artificial neural network approximations: a proof that shallow neural networks fail to overcome the curse of dimensionality, Approximation of compositional functions with ReLU neural networks, Optimal deep neural networks by maximization of the approximation power, Neural network approximation and estimation of classifiers with classification boundary in a Barron class, Deep learning theory of distribution regression with CNNs, Approximation of nonlinear functionals using deep ReLU networks, Pricing options on flow forwards by neural networks in a Hilbert space, A priori error estimate of deep mixed residual method for elliptic PDEs, Fractional type multivariate neural network operators, On Learning and Convergence of RBF Networks in Regression Estimation and Classification, A neural network-based enrichment of reproducing kernel approximation for modeling brittle fracture, Two-layer networks with the \(\text{ReLU}^k\) activation function: Barron spaces and derivative approximation, Causal inference of general treatment effects using neural networks with a diverging number of confounders, Quadratic Neural Networks for Solving Inverse Problems, Approximation error of single hidden layer neural networks with fixed weights, A Reduced Order Schwarz Method for Nonlinear Multiscale Elliptic Equations Based on Two-Layer Neural Networks, Gradient descent on infinitely wide neural networks: global convergence and generalization, Analysis of the rate of convergence of two regression estimates defined by neural features which are easy to implement, Integral representations of shallow neural network with Rectified Power Unit activation function, Intelligent optimal control of robotic manipulators using neural networks, Approximate models for nonlinear dynamical systems and their generalization properties, Approximating and simulating the stochastic growth model: Parameterized expectations, neural networks, and the genetic algorithm, Estimation of the binary response model using a mixture of distributions estimator (MOD), Stable adaptive neuro-control design via Lyapunov function derivative estimation, Adaptive-critic based optimal neuro control synthesis for distributed parameter systems, Stable hybrid control based on discrete-event automata and receding-horizon neural regulators, Ridge functions and orthonormal ridgelets, An approximation result for nets in functional estimation, Error bounds for approximation with neural networks, Approximation by superpositions of a sigmoidal function, Approximating networks and extended Ritz method for the solution of functional optimization problems, Deep ReLU neural networks overcome the curse of dimensionality for partial integrodifferential equations, Approximating functions with multi-features by deep convolutional neural networks, A New Function Space from Barron Class and Application to Neural Network Approximation, Greedy algorithms for prediction, On the curse of dimensionality in the Ritz method, Non intrusive reduced order modeling of parametrized PDEs by kernel POD and neural networks, Another look at statistical learning theory and regularization, Machine learning from a continuous viewpoint. I, Approximation by max-product neural network operators of Kantorovich type, Adaptive importance sampling for control and inference, Linear and nonlinear approximation of spherical radial basis function networks, Analog quantum computing (AQC) and the need for time-symmetric physics, Approximation by network operators with logistic activation functions, Adaptive control of nonlinear multivariable systems using neural networks, Accuracy of suboptimal solutions to kernel principal component analysis, Neural networks and nonlinear statistical methods: An application to the modelling of price-quality relationships, Neural networks and logistic regression. II., Lower estimation of approximation rate for neural networks, Neural network and regression spline value function approximations for stochastic dynamic programming, An exponential inequality under weak dependence, Rescaled pure greedy algorithm for Hilbert and Banach spaces, Nonlinear dynamical system identification with dynamic noise and observational noise, Persistence of excitation conditions in passive learning control, Convergence and rate of convergence of some greedy algorithms in convex optimization, Neural networks and seasonality: Some technical considerations, Nonlinear function approximation: computing smooth solutions with an adaptive greedy algorithm, Convergence of orthogonal greedy algorithm with errors in projectors, Approximation and learning of convex superpositions, A dynamic recurrent neural-network-based adaptive observer for a class of nonlinear systems, Trigonometric RBF neural robust controller design for a class of nonlinear system with linear input unmodeled dynamics, On the tractability of multivariate integration and approximation by neural networks, Solving Volterra integral equations of the second kind by sigmoidal functions approximation, Nonlinear approximation in finite-dimensional spaces, Approximation by neural networks with sigmoidal functions, Adaptive control of nonlinear dynamic systems using \(\theta\)-adaptive neural networks, Minimizing sequences for a family of functional optimal estimation problems, Designing neural networks for modeling biological data: a statistical perspective, Restricted polynomial regression, Estimates on compressed neural networks regression, Approximation of fuzzy-valued functions by regular fuzzy neural networks and the accuracy analysis, Complete stability analysis of a heuristic approximate dynamic programming control design, A comparison between fixed-basis and variable-basis schemes for function approximation and functional optimization, Predictive neuro-control of uncertain systems: Design and use of a neuro-optimizer, A survey on universal approximation and its limits in soft computing techniques., On Kolmogorov's representation of functions of several variables by functions of one variable, The construction and approximation of feedforward neural network with hyperbolic tangent function, Accuracy of approximations of solutions to Fredholm equations by kernel methods, The errors of simultaneous approximation of multivariate functions by neural networks, Estimation of approximating rate for neural network in \(L^p_w\) spaces, The plane wave method for inverse problems associated with Helmholtz-type equations, The ridge function representation of polynomials and an application to neural networks, Complexity of gene circuits, Pfaffian functions and the morphogenesis problem., Can dictionary-based computational models outperform the best linear ones?, Approximation results for neural network operators activated by sigmoidal functions, Multivariate neural network operators with sigmoidal activation functions, Universal approximation by radial basis function networks of Delsarte translates, Generalization ability of fractional polynomial models, Vector greedy algorithms, Markov chain network training and conservation law approximations: Linking microscopic and macroscopic models for evolution, Global adaptive smoothing regression, Radial basis function networks: Generalization in over-realizable and unrealizable scenarios, Density estimation through convex combinations of densities: Approximation and estimation bounds, Convergence properties of cascade correlation in function approximation., A class \(+1\) sigmoidal activation functions for FFANNs, Variable selection in neural network regression models with dependent data: a subsampling approach, Moving-horizon state estimation for nonlinear discrete-time systems: new stability results and approximation schemes, Direct design from data of optimal filters for LPV systems, Schwarz iterative methods: infinite space splittings, Deviation optimal learning using greedy \(Q\)-aggregation, New insights into Witsenhausen's counterexample, Parametric identification of structured nonlinear systems, Some extensions of radial basis functions and their applications in artificial intelligence, Error bounds for suboptimal solutions to kernel principal component analysis, Regularized vector field learning with sparse approximation for mismatch removal, Estimates of variation with respect to a set and applications to optimization problems, Exponential screening and optimal rates of sparse estimation, Some comparisons of complexity in dictionary-based and linear computational models, Analysis of the rate of convergence of least squares neural network regression estimates in case of measurement errors, Multivariate sigmoidal neural network approximation, Simultaneous greedy approximation in Banach spaces, Approximation on anisotropic Besov classes with mixed norms by standard information, Learning with generalization capability by kernel methods of bounded complexity, The approximation operators with sigmoidal functions, Management of water resource systems in the presence of uncertainties by nonlinear approximation techniques and deterministic sampling, Convex polynomial and ridge approximation of Lipschitz functions in \(\mathbb R^d\), Complexity of Gaussian-radial-basis networks approximating smooth functions, Estimates of the approximation error using Rademacher complexity: Learning vector-valued functions, Nonparametric estimation of composite functions, Approximation schemes for functional optimization problems, A note on error bounds for function approximation using nonlinear networks, Uniform approximation by neural networks, The complexity of model classes, and smoothing noisy data, Convergence analysis of convex incremental neural networks, Harmonic analysis of neural networks, Geometrical aspects of discrimination by multilayer perceptrons, Instability, complexity, and evolution, Greedy algorithms and \(M\)-term approximation with regard to redundant dictionaries, On sharpness of error bounds for univariate approximation by single hidden layer feedforward neural networks, Deep learning observables in computational fluid dynamics, Variational training of neural network approximations of solution maps for physical models, Universal approximation by hierarchical fuzzy systems, On simultaneous approximations by radial basis function neural networks, Learning a function from noisy samples at a finite sparse set of points, Global Mittag-Leffler stability of complex valued fractional-order neural network with discrete and distributed delays, Max-product neural network and quasi-interpolation operators activated by sigmoidal functions, Solving Fredholm integral equations using deep learning, Estimates of covering numbers of convex sets with slowly decaying orthogonal subsets, Stein's identity, Fisher information, and projection pursuit: A triangulation, Deep learning for the partially linear Cox model, Error estimates for deep learning methods in fluid dynamics, Numerical bifurcation analysis of PDEs from lattice Boltzmann model simulations: a parsimonious machine learning approach, Density estimation with stagewise optimization of the empirical risk, Annealing stochastic approximation Monte Carlo algorithm for neural network training, Multivariate neural network interpolation operators, Approximating the sheep milk production curve through the use of artificial neural networks and genetic algorithms, A Sobolev-type upper bound for rates of approximation by linear combinations of Heaviside plane waves, Approximation of level continuous fuzzy-valued functions by multilayer regular fuzzy neural networks, The errors of approximation for feedforward neural networks in thelpmetric, Approximation capabilities of multilayer fuzzy neural networks on the set of fuzzy-valued functions, Approximation properties of deep ReLU CNNs, Uniform approximation rates and metric entropy of shallow neural networks, ReLU deep neural networks from the hierarchical basis perspective, Retracted: Model order reduction method based on machine learning for parameterized time-dependent partial differential equations, High-dimensional change-point estimation: combining filtering with convex optimization, Neural network with unbounded activation functions is universal approximator, Nonconvex regularization for sparse neural networks, Machine learning based data retrieval for inverse scattering problems with incomplete data, Learning nonlinear state-space models using autoencoders, Approximation of discontinuous signals by sampling Kantorovich series, Voronovskaja type theorems and high-order convergence neural network operators with sigmoidal functions, Learning the mapping \(\mathbf{x}\mapsto \sum\limits_{i=1}^d x_i^2\): the cost of finding the needle in a haystack, Approximation-based fixed-time adaptive tracking control for a class of uncertain nonlinear pure-feedback systems, Standard representation and unified stability analysis for dynamic artificial neural network models, Optimal approximation of piecewise smooth functions using deep ReLU neural networks, Cornell potential: a neural network approach, Nonlinear approximation via compositions, Theory of deep convolutional neural networks: downsampling, Universal approximation with quadratic deep networks, Robust min-max optimal control design for systems with uncertain models: a neural dynamic programming approach, Pointwise and uniform approximation by multivariate neural network operators of the max-product type, Estimation of a regression function on a manifold by fully connected deep neural networks, A deep first-order system least squares method for solving elliptic PDEs, Active learning based sampling for high-dimensional nonlinear partial differential equations, A deep Fourier residual method for solving PDEs using neural networks, Deep neural network structures solving variational inequalities, Side effects of learning from low-dimensional data embedded in a Euclidean space, A comparative analysis of optimization and generalization properties of two-layer neural network and random feature models under gradient descent dynamics, Convergence for a family of neural network operators in Orlicz spaces, Correction of AI systems by linear discriminants: probabilistic foundations, Mini-workshop: Analysis of data-driven optimal control. Abstracts from the mini-workshop held May 9--15, 2021 (hybrid meeting), Computation and learning in high dimensions. Abstracts from the workshop held August 1--7, 2021 (hybrid meeting), Low-rank kernel approximation of Lyapunov functions using neural networks, Greedy training algorithms for neural networks and applications to PDEs, Neural network-based variational methods for solving quadratic porous medium equations in high dimensions, Estimating composite functions by model selection, Sobolev-type embeddings for neural network approximation spaces, Nonparametric neural network estimation of Lyapunov exponents and a direct test for chaos, EO-MTRNN: evolutionary optimization of hyperparameters for a neuro-inspired computational model of spatiotemporal learning, Fast construction of correcting ensembles for legacy artificial intelligence systems: algorithms and a case study, Nonparametric regression using deep neural networks with ReLU activation function, A review on deep learning in medical image reconstruction, Analysis of the rate of convergence of fully connected deep neural network regression estimates with smooth activation function, A collocation method for solving nonlinear Volterra integro-differential equations of neutral type by sigmoidal functions, Data driven governing equations approximation using deep neural networks, Convergence of the deep BSDE method for coupled FBSDEs, Negative results for approximation using single layer and multilayer feedforward neural networks, Kolmogorov width decay and poor approximators in machine learning: shallow neural networks, random feature models and neural tangent kernels, Aggregation for Gaussian regression, Deep ReLU network expression rates for option prices in high-dimensional, exponential Lévy models, Parameter redundancy in neural networks: an application of Chebyshev polynomials, Estimation of agent-based models using Bayesian deep learning approach of BayesFlow, A deletion/substitution/addition algorithm for classification neural networks, with applications to biomedical data, Efficient sampling in approximate dynamic programming algorithms, Approximation and learning by greedy algorithms, Almost optimal estimates for approximation and learning by radial basis function networks, Interpolation by neural network operators activated by ramp functions, Approximation by series of sigmoidal functions with applications to neural networks, Specification of Training Sets and the Number of Hidden Neurons for Multilayer Perceptrons, Neural network modeling of vector multivariable functions in ill-posed approximation problems, Weighted quadrature formulas and approximation by zonal function networks on the sphere, Nonparametric nonlinear regression using polynomial and neural approximators: a numerical comparison, Simultaneous approximation by greedy algorithms, Algorithms and complexity in biological pattern formation problems, Relevance of functional flexibility for heterogeneous sales response models: a comparison of parametric and semi-nonparametric models, Approximation with random bases: pro et contra, Semi-nonparametric approximation and index options, Piecewise convexity of artificial neural networks, Insights into randomized algorithms for neural networks: practical issues and common pitfalls, Reduction Methods and Chaos for Quadratic Systems of Differential Equations, Universality of deep convolutional neural networks, A machine learning framework for data driven acceleration of computations of differential equations, On deep learning as a remedy for the curse of dimensionality in nonparametric regression, Quantitative approximation by perturbed Kantorovich-Choquet neural network operators, MgNet: a unified framework of multigrid and convolutional neural network, A nonparametric ensemble binary classifier and its statistical properties, Diffusion nets, Machine learning approximation algorithms for high-dimensional fully nonlinear partial differential equations and second-order backward stochastic differential equations, Path relinking and GRG for artificial neural networks, Model selection in neural networks: some difficulties, On universal estimators in learning theory, Greedy approximation in convex optimization, Boosting with early stopping: convergence and consistency, Rates of minimization of error functionals over Boolean variable-basis functions, An empirical comparison of the validity of a neural net based multinomial logit choice model to alternative model specifications, A neural network based shock detection and localization approach for discontinuous Galerkin methods, Structure probing neural network deflation, Int-Deep: a deep learning initialized iterative method for nonlinear problems, Machine learning for prediction with missing dynamics, Approximation theorems for a family of multivariate neural network operators in Orlicz-type spaces, SelectNet: self-paced learning for high-dimensional partial differential equations, Approximation by ridge function fields over compact sets, Set membership identification of nonlinear systems, Multivariate Jackson-type inequality for a new type neural network approximation, Fusion methods for multiple sensor systems with unknown error densities, A receding-horizon regulator for nonlinear systems and a neural approximation, Solving numerically nonlinear systems of balance laws by multivariate sigmoidal functions approximation, Nonlinear black-box modeling in system identification: A unified overview, Nonlinear black-box models in system identification: Mathematical foundations, Neural network prediction of load from the morphology of trabecular bone, Neural network operators: constructive interpolation of multivariate functions, A note on error bounds for approximation in inner product spaces, Networks and closed balls, Some remarks on greedy algorithms, Solvable models of layered neural networks based on their differential structure, Limitations of the approximation capabilities of neural networks with one hidden layer, The convex geometry of linear inverse problems, Comparison of the convergence rate of pure greedy and orthogonal greedy algorithms, Saturation classes for MAX-product neural network operators activated by sigmoidal functions, Complexity estimates based on integral transforms induced by computational units, Analysis of convergence performance of neural networks ranking algorithm, Dynamic programming and value-function approximation in sequential decision problems: error analysis and numerical results, Essential rate for approximation by spherical neural networks, Using radial basis function networks for function approximation and classification, Approximation with neural networks activated by ramp sigmoids, Squared and absolute errors in optimal approximation of nonlinear systems., Towards long-term prediction, Applied harmonic analysis and data processing. Abstracts from the workshop held March 25--31, 2018, On estimation of surrogate models for multivariate computer experiments, Function approximation with zonal function networks with activation functions analogous to the rectified linear unit functions, Learning semidefinite regularizers, Approximation rates for neural networks with general activation functions, Provable approximation properties for deep neural networks, Exponential convergence of the deep neural network approximation for analytic functions, Analysis of a two-layer neural network via displacement convexity, Selection dynamics for deep neural networks, Metamodeling of aircraft infrared signature dispersion, Approximation of functions of finite variation by superpositions of a sigmoidal function., An approximation by neural networks with a fixed weight, How to determine the minimum number of fuzzy rules to achieve given accuracy: a computational geometric approach to SISO case, Regularized greedy algorithms for network training with data noise, A robust solution of a statistical inverse problem in multiscale computational mechanics using an artificial neural network, Efficient approximation of solutions of parametric linear transport equations by ReLU DNNs, New study on neural networks: the essential order of approximation, Topological properties of the set of functions generated by neural networks of fixed size, A selective overview of deep learning, Multivariate extensions of isotonic regression and total variation denoising via entire monotonicity and Hardy-Krause variation, Linearized two-layers neural networks in high dimension, Some problems in the theory of ridge functions, The universal approximation property. Characterization, construction, representation, and existence, Nonlinear autoregressive sieve bootstrap based on extreme learning machines, Numerical solution of the parametric diffusion equation by deep neural networks, Boosting the margin: a new explanation for the effectiveness of voting methods, Gabor neural networks with proven approximation properties, Models of knowing and the investigation of dynamical systems, On the rate of convergence of fully connected deep neural network regression estimates, Theory of deep convolutional neural networks. II: Spherical analysis, High-dimensional dynamics of generalization error in neural networks, High-dimensional distribution generation through deep neural networks, Optimal approximation rate of ReLU networks in terms of width and depth, Rates of approximation by neural network interpolation operators, A note on universal approximation by hierarchical fuzzy systems, Mean-field Langevin dynamics and energy landscape of neural networks, Supervised learning from noisy observations: combining machine-learning techniques with data assimilation, A better approximation for balls, Information-theoretic determination of minimax rates of convergence, The construction and approximation of ReLU neural network operators, On selecting models for nonlinear time series, On the approximation of rough functions with deep neural networks, Functional aggregation for nonparametric regression., Local greedy approximation for nonlinear regression and neural network training., Adaptive estimation in autoregression or \(\beta\)-mixing regression via model selection, Excitable media store and transfer complicated information via topological defect motion, Nonlinear stable adaptive control based upon Elman networks, A priori and a posteriori error estimates for the deep Ritz method applied to the Laplace and Stokes problem, Correlations of random classifiers on large data sets, Approximation properties of local bases assembled from neural network transfer functions, A phase transition for finding needles in nonlinear haystacks with LASSO artificial neural networks, Understanding neural networks with reproducing kernel Banach spaces, Generalization bounds for sparse random feature expansions, Do ideas have shape? Idea registration as the continuous limit of artificial neural networks, Representation formulas and pointwise properties for Barron functions, Modelling the dynamics of nonlinear time series using canonical variate analysis, On best approximation of classes by radial functions, Approximation order to a function in \(\overline C({\mathbb R})\) by superposition of a sigmoidal function, Neural networks based subgrid scale modeling in large eddy simulations, Explaining consumer choice through neural networks: the stacked generalization approach, DNN expression rate analysis of high-dimensional PDEs: application to option pricing, A theoretical analysis of deep neural networks and parametric PDEs, Depth separations in neural networks: what is actually being separated?, Approximation spaces of deep neural networks, The Barron space and the flow-induced function spaces for neural network models, High-order approximation rates for shallow neural networks with cosine and \(\mathrm{ReLU}^k\) activation functions, Interpolation by ridge polynomials and its application in neural networks, Unnamed Item, Deep Adaptive Basis Galerkin Method for High-Dimensional Evolution Equations With Oscillatory Solutions, Generalization Error Analysis of Neural Networks with Gradient Based Regularization, On some similarities and differences between deep neural networks and kernel learning machines, DENSITY RESULTS BY DEEP NEURAL NETWORK OPERATORS WITH INTEGER WEIGHTS, The estimate for approximation error of spherical neural networks, Two-Layer Neural Networks with Values in a Banach Space, Book Review: A mathematical introduction to compressive sensing, Discretization of parameter identification in PDEs using neural networks, Feedforward Neural Networks and Compositional Functions with Applications to Dynamical Systems, An Augmented Lagrangian Deep Learning Method for Variational Problems with Essential Boundary Conditions, Approximation Bounds for Some Sparse Kernel Regression Algorithms, A NONPARAMETRIC ESTIMATOR FOR THE COVARIANCE FUNCTION OF FUNCTIONAL DATA, Deep distributed convolutional neural networks: Universality, Online Adaptive Decision Trees, A Deep Learning Method for Elliptic Hemivariational Inequalities, Optimization of approximating networks for optimal fault diagnosis, On approximations via convolution-defined mixture models, Deep ReLU Networks Overcome the Curse of Dimensionality for Generalized Bandlimited Functions, Consistency of Ridge Function Fields for Varying Nonparametric Regression, Information Geometry of U-Boost and Bregman Divergence, A Classification Paradigm for Distributed Vertically Partitioned Data, Full error analysis for the training of deep neural networks, Neural network interpolation operators activated by smooth ramp functions, Solving polynomial systems using a fast adaptive back propagation-type neural network algorithm, Unnamed Item, Deep Ritz Method for the Spectral Fractional Laplacian Equation Using the Caffarelli--Silvestre Extension, A note on the applications of one primary function in deep neural networks, Wavelet neural networks functional approximation and application, Artificial neural networks: an econometric perspective∗, Unnamed Item, Unnamed Item, Convergence results for a family of Kantorovich max-product neural network operators in a multivariate setting, Unnamed Item, Unnamed Item, Deep learning in high dimension: Neural network expression rates for generalized polynomial chaos expansions in UQ, Computing the Approximation Error for Neural Networks with Weights Varying on Fixed Directions, A Single Hidden Layer Feedforward Network with Only One Neuron in the Hidden Layer Can Approximate Any Univariate Function, Deep ReLU networks and high-order finite element methods, Simultaneous Approximations of Polynomials and Derivatives and Their Applications to Neural Networks, A methodology for the constructive approximation of nonlinear operators defined on noncompact sets, Approximation by finite mixtures of continuous density functions that vanish at infinity, Minimization of Error Functionals over Perceptron Networks, LATTICE OPTION PRICING BY MULTIDIMENSIONAL INTERPOLATION, CONVERGENCE OF A LEAST‐SQUARES MONTE CARLO ALGORITHM FOR AMERICAN OPTION PRICING WITH DEPENDENT SAMPLE DATA, Stochastically ordered multiple regression, Unnamed Item, Applications of Topological Derivatives and Neural Networks for Inverse Problems, A taxonomy for wavelet neural networks applied to nonlinear modelling, Approximation Properties of Ridge Functions and Extreme Learning Machines, Deep Network Approximation for Smooth Functions, On function recovery by neural networks based on orthogonal expansions, Unnamed Item, Plateau Phenomenon in Gradient Descent Training of RELU Networks: Explanation, Quantification, and Avoidance, Learning on dynamic statistical manifolds, Integral combinations of Heavisides, Machine Learning and Computational Mathematics, Finite Neuron Method and Convergence Analysis, Deep Network Approximation Characterized by Number of Neurons, Butterfly-Net: Optimal Function Representation Based on Convolutional Neural Networks, Neural model-based adaptive control for systems with unknown Preisach-type hysteresis, Input Variable Selection in Neural Network Models, An adaptive learning rate backpropagation‐type neural network for solving n × n systems on nonlinear algebraic equations, Robust control of dynamical systems using neural networks with input–output feedback linearization, Unnamed Item, A General Form for Global Dynamical Data Models for Three-Dimensional Systems, Unnamed Item, Sigmoidal FFANN’s and the best approximation property, Neural Networks for Localized Approximation, Geometric Rates of Approximation by Neural Networks, Optimization based on quasi-Monte Carlo sampling to design state estimators for non-linear systems, Optimal control of non-linear systems through hybrid cell-mapping/artificial-neural-networks techniques, Adaptive regression estimation with multilayer feedforward neural networks, INTELLIGENT OPTIMAL CONTROL OF ROBOTIC MANIPULATORS USING WAVELETS, Risk bounds for mixture density estimation, Effect of Depth and Width on Local Minima in Deep Learning, Value and Policy Function Approximations in Infinite-Horizon Optimization Problems, Comparing Methods for Multivariate Nonparametric Regression, The Random Feature Model for Input-Output Maps between Banach Spaces, Equivalence of approximation by convolutional neural networks and fully-connected networks, Parameter Estimation of Sigmoid Superpositions: Dynamical System Approach, An Integral Upper Bound for Neural Network Approximation, Properties of the neural network sieve bootstrap, Construct Deep Neural Networks based on Direct Sampling Methods for Solving Electrical Impedance Tomography, Unnamed Item, Deep Network With Approximation Error Being Reciprocal of Width to Power of Square Root of Depth, On the Achievability of Blind Source Separation for High-Dimensional Nonlinear Source Mixtures, Neural Networks for Functional Approximation and System Identification, A SELF-ORGANIZING QUANTUM NEURAL FUZZY NETWORK AND ITS APPLICATIONS, Unnamed Item, Approximation by perturbed neural network operators, Unnamed Item, Unnamed Item, Solving high-dimensional optimal stopping problems using deep learning, An analytic theory of shallow networks dynamics for hinge loss classification*, Approximations by multivariate perturbed neural network operators, Optimal Approximation with Sparsely Connected Deep Neural Networks, Multilinear Compressive Sensing and an Application to Convolutional Linear Networks, A Theoretical Perspective on Hyperdimensional Computing, Extension of localised approximation by neural networks
