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Explore the main themes, entities and connections around Universal approximation theorem. Start with the topic map, then use the sections below for research and deeper semantic analysis.
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History
19 related topics
Arbitrary-depth case
ReLULebesgue-integrable functionL 1 {\displaystyle L^{1}} distanceBochner–Lebesgue p-integrableFully connected
13 related topics
Arbitrary-width case
10 related topics
Setup
2 related topics
Key facts & relationships
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Topics to explore
A structured outline of related entities, concepts and subtopics. Open any item to build a new map centered on it.Browse the full topic structure. Each item opens a new analysis centered on that subject.
Overview
- Machine learning
- Neural networks Artificial neural network
- Continuous function
- Feedforward networks Feedforward neural network
- Activation function
- Polynomial
- Sigmoid function
- ReLU Rectifier (neural networks)
- Existence theorems Existence theorem
- Training Mathematical optimization
- Backpropagation
Setup
- Artificial neural networks
- Vectors Vector (mathematics and physics)
History
- George Cybenko
- Kurt Hornik Kurt Hornik?action=edit&redlink=1
- De Kurt Hornik
- Halbert White
- Approximation property
- Finite set
- Lp Lp space
- Residual neural networks Residual neural network
- Control-theoretic Control theory
- Kolmogorov–Arnold representation theorem
- Robert Hecht-Nielsen
- Reservoir computing
- Recurrent neural network
- Threshold activation function Step function
- Graph isomorphism classes Graph isomorphism
- Graph convolutional neural networks Graph neural network
- Non-Euclidean spaces Non-Euclidean space
- Convolutional neural network
- Radial basis functions
Arbitrary-width case
- Dense set
- Continuous functions
- If and only if
- Compact Compact subspace
- Perceptron
- Ramp function
- Dirac delta function
- Functional analysis
- Hahn-Banach Hahn–Banach theorem
- Riesz–Markov–Kakutani representation Riesz–Markov–Kakutani representation theorem
Arbitrary-depth case
- ReLU
- Lebesgue-integrable function Lebesgue integration
- L 1 {\displaystyle L^{1}} distance L1 distance
- Bochner–Lebesgue p-integrable Bochner integral
- Fully connected Fully connected network
- Affine Affine transformation
- Depth Deep learning
- Compact subset Compact set
- Continuously differentiable Differentiable function
- Derivative
- Identity Identity function
- Uniform convergence
- Riemannian manifold
Bounded depth and bounded width case
Advanced semantic analysis
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Map overview Semantic statistics
Number of nodes, edges, triples, density and central hubs. Use it to gauge the size and connectivity of the map.Universal approximation theorem
Nodes63
Edges62
Triples50
Avg. degree1.97
Density0.031746
Components1
How this topic connects Entity context
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Universal approximation theorem
Top relations
related to Arbitrary-depth case · 13
Universal approximation theorem → Bochner, For, In, It, L1, Lebesgue, Lebesgue-integrable, Moreover, ReLU, The, They, Universal, Zhou Lu
related to Kolmogorov network · 9
Universal approximation theorem → Arnold, In, Indeed, Kolmogorov, Robert Hecht-Nielsen, The Kolmogorov, This, Vugar Ismailov, Ziming Liu
related to Bounded depth and bounded width case · 7
Universal approximation theorem → For, Maiorov, Pinkus, The, Their, There, Universal
related to Arbitrary-width case · 5
Universal approximation theorem → George Cybenko, In, Kurt Hornik, See, The
related to Setup · 4
Universal approximation theorem → Artificial, In, Most, The
Important terminology Word statistics
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Important terminology
function displaystyle networks approximation universal neural activation width network functions depth theorem arbitrary also mathbb approximate continuous relu hidden layer
Entity relationships Subject–Predicate–Object triples
Extracted RDF-like relationships with confidence and source. The table includes structured facts and lower-confidence contextual relations.| Subject | Predicate | Object | Confidence | Src |
|---|---|---|---|---|
| Gustaf Gripenberg in 2003 | instance of | Moshe Leshno et al in 1993 and later Allan Pinkus in 1999 showed that the universal approximation property is equivalent to having a nonpolynomial activation function.Arbitrary… | 0.80 | text |
| Dmitry Yarotsky | instance of | Moshe Leshno et al in 1993 and later Allan Pinkus in 1999 showed that the universal approximation property is equivalent to having a nonpolynomial activation function.Arbitrary… | 0.80 | text |
| Zhou Lu et al in 2017 | instance of | Moshe Leshno et al in 1993 and later Allan Pinkus in 1999 showed that the universal approximation property is equivalent to having a nonpolynomial activation function.Arbitrary… | 0.80 | text |
| Boris Hanin | instance of | Moshe Leshno et al in 1993 and later Allan Pinkus in 1999 showed that the universal approximation property is equivalent to having a nonpolynomial activation function.Arbitrary… | 0.80 | text |
| Mark Sellke in 2018 who focused on neural networks with ReLU activation function | instance of | Moshe Leshno et al in 1993 and later Allan Pinkus in 1999 showed that the universal approximation property is equivalent to having a nonpolynomial activation function.Arbitrary… | 0.80 | text |
| Gustaf Gripenberg in 2003 | instance of | Arbitrary depthThe arbitrary depth case was also studied by a number of authors | 0.80 | text |
| Dmitry Yarotsky | instance of | Arbitrary depthThe arbitrary depth case was also studied by a number of authors | 0.80 | text |
| Zhou Lu et al in 2017 | instance of | Arbitrary depthThe arbitrary depth case was also studied by a number of authors | 0.80 | text |
| Boris Hanin | instance of | Arbitrary depthThe arbitrary depth case was also studied by a number of authors | 0.80 | text |
| Mark Sellke in 2018 who focused on neural networks with ReLU activation function | instance of | Arbitrary depthThe arbitrary depth case was also studied by a number of authors | 0.80 | text |
| the step function can be approximated by continuous activation functions | instance of | certain non-continuous activation functions | 0.80 | text |
| which then allows the approximation result to apply to those functions | instance of | certain non-continuous activation functions | 0.80 | text |
No triples extracted yet.
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