Wikipedia describes "effective theories" as follows.
In science, an effective theory is a scientific theory which proposes to describe a certain set of observations, but explicitly without the claim or implication that the mechanism employed in the theory has a direct counterpart in the actual causes of the observed phenomena to which the theory is fitted. That means, the theory proposes to model a certain effect, without proposing to adequately model any of the causes which contribute to the effect.
While Wikipedia starts with the context 'in science', I have only seen this language used in Physics so I am asking here on Physics.SE.
Theorems such as the Universal Function Approximation Theorem show that certain classes of artificial neural networks can approximate Lebesque measurable functions to arbitrary precision (up to measure zero) with sufficient width and depth of the layers of the network. This has led me to tell a joke to people that "Neural networks will never be a Theory of Everything, but they are already a Theory of 'Anything'".
Tying the notion of effective theories together with neural networks, do neural networks actually count as effective theories? Or is there a nuance here in which they do not qualify?
Presumably one could ask a similar question about polynomials in the context of the Stone-Weierstrass theorem, but I suspect the answer will be similar in character.