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Everything about Universal approximation theorem
Property of artificial neural networks
In the field of machine learning, the universal approximation theorems (UATs) state that neural networks with a certain structure can, in principle, approximate any continuous function to any desired degree of accuracy. These theorems provide a mathematical justification for using neural networks, assuring researchers that a sufficiently large or deep network can model the complex, non-linear relationships often found in real-world data. Wikipedia →
🧭 Start here: a 6-step reading path
- Read the overview: Universal approximation theoremA 5-minute orientation
- Skim a recent paper: Universal Approximation Theorem and Deep Learning for the Solution of Frequency-Domain Electromagnetic Scattering ProblemsInfluential work since 2022
- Pick up a classic book: Artificial intelligenceThe most-reprinted book on the subject
- Read the landmark paper: Learning nonlinear operators via DeepONet based on the universal approximation theorem of operatorsCited 3,680 times
- Go sideways: Barron spaceA closely related topic
- Go sideways: Vanishing gradient problemA closely related topic
📖 Definitions
No dictionary entry for this exact phrase.
🗂️ The subject at a glance
🏆 Landmark papers (most cited)
Learning nonlinear operators via DeepONet based on the universal approximation theorem of operators
Universal approximation theorem for uninorm-based fuzzy systems modeling
Performance of Deep and Shallow Neural Networks, the Universal Approximation Theorem, Activity Cliffs, and QSAR
The universal approximation theorem for complex-valued neural networks
Universal Approximation Theorem for Interval Neural Networks
A Universal Approximation Theorem for Mixture-of-Experts Models
Approximate nonlinear output regulation based on the universal approximation theorem
Universal approximation theorem for vector- and hypercomplex-valued neural networks
🆕 Influential since 2022
Universal Approximation Theorem and Deep Learning for the Solution of Frequency-Domain Electromagnetic Scattering Problems
A novel neural network for isotropic polyconvex hyperelasticity satisfying the universal approximation theorem
Universal Approximation Theorem and Error Bounds for Quantum Neural Networks and Quantum Reservoirs
Universal approximation theorem for a radial basis function fuzzy neural network
Universal approximation theorem for nonlinear resistive networks
📚 Books worth reading
Artificial intelligenceStuart J. Russell, Peter Norvig · 1994
Quantum computation and quantum informationMichael A. Nielsen, Isaac L. Chuang · 2000
Cartesian meditationsEdmund Husserl, Dorion Cairns · 1960- 📕Normal approximations with Malliavin calculusIvan Nourdin · 2012
Topology and GeometryGlen E. Bredon · 1993
Probability, random processes, and statistical analysisHisashi Kobayashi · 2011
An Introduction to Probability Theory and Its Applications [2/2]William Feller · 1966- 📕Lectures on diophantine approximationsKurt Mahler · 1961
Ranked by number of editions on Open Library, a rough measure of how lasting a book is.
🔗 Related topics
- Barron space In functional analysis, the Barron space is a function space. It is a Banach space. It originated from the study of universal approximation properties…
- Vanishing gradient problem In machine learning, the vanishing gradient problem is the problem of greatly diverging gradient magnitudes between earlier and later layers encountered…
- Activation function In artificial neural networks, the activation function of a node is a function that calculates the output of the node based on its individual inputs and…
- Rectified linear unit In the context of artificial neural networks, the rectifier or ReLU (rectified linear unit) activation function is an activation function defined as the…
- Multilayer perceptron In deep learning, a multilayer perceptron (MLP) is a kind of modern feedforward neural network consisting of fully connected neurons with nonlinear activation…
- Extreme learning machine Extreme learning machines are feedforward neural networks for classification, regression, clustering, sparse approximation, compression and feature learning…
- Feedforward neural network A feedforward neural network is an artificial neural network in which information flows in a single direction – inputs are multiplied by weights to obtain…
- Modern Hopfield network Modern Hopfield networks (also known as Dense Associative Memories) are generalizations of the classical Hopfield networks that break the linear scaling…