Approximation properties of a multilayered feedforward artificial neural network
From MaRDI portal
Publication:1895884
DOI10.1007/BF02070821zbMath0824.41011OpenAlexW2006240266MaRDI QIDQ1895884
Publication date: 30 October 1995
Published in: Advances in Computational Mathematics (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1007/bf02070821
Related Items
Techniques for the mathematical analysis of neural networks ⋮ CONSTRUCTIVE ESTIMATION OF APPROXIMATION FOR TRIGONOMETRIC NEURAL NETWORKS ⋮ On sharpness of an error bound for deep ReLU network approximation ⋮ The universal approximation capabilities of cylindrical approximate identity neural networks ⋮ Discretization of parameter identification in PDEs using neural networks ⋮ On local and global sigma-pi neural networks. A common link ⋮ Deep distributed convolutional neural networks: Universality ⋮ Theoretical issues in deep networks ⋮ Approximations with deep neural networks in Sobolev time-space ⋮ Deep ReLU Networks Overcome the Curse of Dimensionality for Generalized Bandlimited Functions ⋮ Limitations of the approximation capabilities of neural networks with one hidden layer ⋮ Sparse approximation of triangular transports. I: The finite-dimensional case ⋮ Theory of deep convolutional neural networks: downsampling ⋮ A deep network construction that adapts to intrinsic dimensionality beyond the domain ⋮ Theory of deep convolutional neural networks. III: Approximating radial functions ⋮ Rates of approximation by ReLU shallow neural networks ⋮ Bayesian neural tree models for nonparametric regression ⋮ Function approximation by deep networks ⋮ SignReLU neural network and its approximation ability ⋮ Deep learning theory of distribution regression with CNNs ⋮ Approximation of nonlinear functionals using deep ReLU networks ⋮ Learning ability of interpolating deep convolutional neural networks ⋮ Quadratic Neural Networks for Solving Inverse Problems ⋮ Nonparametric regression using deep neural networks with ReLU activation function ⋮ Deep ReLU networks and high-order finite element methods ⋮ Applied harmonic analysis and data processing. Abstracts from the workshop held March 25--31, 2018 ⋮ On estimation of surrogate models for multivariate computer experiments ⋮ Unnamed Item ⋮ The estimation of simultaneous approximation order for neural networks ⋮ Better Approximations of High Dimensional Smooth Functions by Deep Neural Networks with Rectified Power Units ⋮ The universal approximation capabilities of double \(2\pi\)-periodic approximate identity neural networks ⋮ Neural Networks for Localized Approximation ⋮ Efficient approximation of solutions of parametric linear transport equations by ReLU DNNs ⋮ The essential order of simultaneous approximation for neural networks ⋮ Topological properties of the set of functions generated by neural networks of fixed size ⋮ Error bounds for approximation with neural networks ⋮ Adaptive regression estimation with multilayer feedforward neural networks ⋮ Limitations of shallow nets approximation ⋮ Error bounds for approximations with deep ReLU networks ⋮ Universality of deep convolutional neural networks ⋮ Equivalence of approximation by convolutional neural networks and fully-connected networks ⋮ Theory of deep convolutional neural networks. II: Spherical analysis ⋮ Constructive deep ReLU neural network approximation ⋮ Deep neural networks for rotation-invariance approximation and learning ⋮ Data driven approximation of parametrized PDEs by reduced basis and neural networks ⋮ Deep learning volatility: a deep neural network perspective on pricing and calibration in (rough) volatility models ⋮ Representation of functions on big data: graphs and trees ⋮ Solving parametric partial differential equations with deep rectified quadratic unit neural networks ⋮ Approximation of functions from korobov spaces by deep convolutional neural networks ⋮ Optimal Approximation with Sparsely Connected Deep Neural Networks ⋮ Approximating functions with multi-features by deep convolutional neural networks ⋮ Extension of localised approximation by neural networks ⋮ A theoretical analysis of deep neural networks and parametric PDEs ⋮ Approximation spaces of deep neural networks ⋮ Exponential ReLU DNN expression of holomorphic maps in high dimension
Cites Work
- Approximation by Ridge functions and neural networks with one hidden layer
- Approximation by superposition of sigmoidal and radial basis functions
- Multilayer feedforward networks are universal approximators
- Optimal nonlinear approximation
- Regularization Algorithms for Learning That Are Equivalent to Multilayer Networks
- On Some Extremal Functions and their Applications in the Theory of Analytic Functions of Several Complex Variables
- Approximation by superpositions of a sigmoidal function
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
