The Equation That Explains (Nearly) Everything!

Yup. That said it seems like a quick blog post from 2016. There's been more comprehensive breakdowns since ▶ this video

> It means that there is no guarantee that, given a non-continuous function function f(x), there exists an NN that approximates it over its entire domain withing some precision p. And why is this important? > Do you know of a universal algorithm that can take a continuous function and a target precision, and return an NN architecture (number of layers, number of neurons per layer) and a starting set of weights for an NN, and a training set, such that training the NN will reach the final state? > All I'm claiming is that there is no known algorithm of this kind, and also that the existence of such an algorithm is not guaranteed by any known theorem. I think so: the construction proof of the claim that they are universal function approximators seems to meet those requirements. Even better: it just goes direct to giving you the weights and biases. > My point was relevant because we are discussing whether an NN might be equivalent to the human brain, and using the Universal Approximation Theorem to try to decide this. So what I'm saying is that even if "knowning English" were a continuous function and "knowing French" were a continuous function, so by the theorem we know there are NNs that can approximate either one, there is no guarantee that there exists a single NN which can approximate both. There might or might not be one, but the theorem doesn't promise one must exist. I still don't understand your point. It still doesn't seem to matter? If any organic brain can't do $thing

PBS Spacetime has a very good video[0] that helps visualize what's going on in the equation, recent too! ▶ this video