Is ReLU a universal approximator?

Is ReLU a universal approximator?

We show a universal approximation theorem for width-bounded ReLU networks: width-(n + 4) ReLU networks, where n is the input dimension, are universal approximators. Moreover, except for a measure zero set, all functions cannot be approximated by width-n ReLU networks, which exhibits a phase transition.

What do you mean by universal approximation theorem explain it?

The Universal Approximation Theorem tells us that Neural Networks has a kind of universality i.e. no matter what f(x) is, there is a network that can approximately approach the result and do the job! This result holds for any number of inputs and outputs.

What is the definition of the universal approximation theorem?

From Wikipedia, the free encyclopedia In the mathematical theory of artificial neural networks, universal approximation theorems are results that establish the density of an algorithmically generated class of functions within a given function space of interest.

When did Kurt Hornik prove the universal approximation theorem?

One of the first versions of the theorem was proved by George Cybenko in 1989 for sigmoid activation functions. Kurt Hornik showed in 1991 that it is not the specific choice of the activation function, but rather the multilayer feedforward architecture itself which gives neural networks the potential of being universal approximators.

Which is the universal approximation theorem for deep neural networks?

Although feed-forward networks with a single hidden layer are universal approximators, the width of such networks has to be exponentially large. In 2017 Lu et al. proved universal approximation theorem for width-bounded deep neural networks.

Can a neural network be a universal approximator?

Technically, “universal approximator” is misleading. I can construct a function that a neural network cannot approximate to arbitrary precision. It was proven to approximate continuous functions to arbitrary accuracy. In reality, a function that is continuous at almost all points can be approximated arbitrarily closely.