Universal Approximation Theorem

URI: https://gptkb.org/entity/Universal_Approximation_Theorem
GPTKB entity
Statements (29)
Predicate Object
gptkbp:instanceOf gptkb:mathematical_concept
gptkbp:activatedBy gptkb:ReLU
sigmoid
tanh
gptkbp:activationFunctionRequirement non-constant, bounded, and continuous
gptkbp:appliesTo continuous functions
feedforward neural networks
compact domains
gptkbp:assumes suitable activation function
gptkbp:citation gptkb:Cybenko,_G._(1989)._Approximation_by_superpositions_of_a_sigmoidal_function._Mathematics_of_Control,_Signals_and_Systems.
gptkb:Hornik,_K.,_Stinchcombe,_M.,_&_White,_H._(1989)._Multilayer_feedforward_networks_are_universal_approximators._Neural_Networks.
gptkbp:describes capability of neural networks to approximate functions
gptkbp:doesNotGuarantee generalization
efficient learning
practical trainability
gptkbp:field gptkb:machine_learning
gptkb:mathematics
neural networks
gptkbp:generalizes gptkb:Leshno_et_al._(1993)
https://www.w3.org/2000/01/rdf-schema#label Universal Approximation Theorem
gptkbp:influenced development of neural network theory
gptkbp:provenBy gptkb:George_Cybenko
gptkbp:relatedTo gptkb:artificial_neural_networks
deep learning
function approximation
gptkbp:state a feedforward network with a single hidden layer containing a finite number of neurons can approximate any continuous function on compact subsets of R^n
gptkbp:yearProved 1989
gptkbp:bfsParent gptkb:George_Cybenko
gptkbp:bfsLayer 6