ML//neural network//universal approximation theorem

A neural network with even one hidden layer can approximate any continuous function to arbitrary precision, given enough neurons (Cybenko 1989, Hornik 1991).

A neural network with even one hidden layer can approximate any continuous function to arbitrary precision, given enough neurons (Cybenko 1989, Hornik 1991).

An existence proof, not a recipe: it says a good weight setting exists, not how to find it, nor how many neurons "enough" is.

Depth, in practice, is what makes the search tractable, not raw width.

Explains why nets are expressive, but not why training via backpropagation actually finds good solutions.