We completely characterize those activation functions σ for which the associated complex networks have the universal approximation property, meaning that they can uniformly approximate any continuous function on any compact sub- set of Cd arbitrarily well.
Dec 6, 2020 · Abstract:We generalize the classical universal approximation theorem for neural networks to the case of complex-valued neural networks.
Abstract. We generalize the classical universal approximation theorem for neural networks to the case of complex-valued neural networks.
In the mathematical theory of artificial neural networks, universal approximation theorems are theorems of the following form: Given a family of neural ...
Missing: complex- | Show results with:complex-
Mar 26, 2023 · This theorem suggest that a neural network is capable of learning complex patterns and relationships in data as long as certain conditions are ...
People also ask
What is the universal approximation theorem in neural networks?
What is universal approximation theorem for dummies?
Does ReLU satisfy the universal approximation theorem?
What is the Barron's theorem?
Jul 26, 2024 · The Universal Approximation Theorem is a fundamental result in the field of neural networks and machine learning.
Missing: complex- | Show results with:complex-
Jun 6, 2023 · Shallow networks, on the other hand, are universal if and only if the real part or the imaginary part of σ is not a polyharmonic function.
Universal approximation theorem for vector- and hypercomplex-valued ...
pubmed.ncbi.nlm.nih.gov › ...
The universal approximation theorem states that a neural network with one hidden layer can approximate continuous functions on compact sets with any desired ...
In particular, it has been shown that shallow CVNNs are universal if and only if the activation function ϕ is not polyharmonic.
Sep 24, 2024 · The idea behind the Universal Approximation Theorem is that hidden layers can capture increasingly complex patterns in the data. When enough ...