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But… he’s saying something here that is academically true: that neural networks can approximate any possible function, to any arbitrary degree of precision you require (given infinite capacity / depth).

https://en.m.wikipedia.org/wiki/Universal_approximation_theo...

I will highlight one thing, which is that the theorem does not say anything about it being practical to learn this function, given available data or any specific optimization technique.

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'the underlying “rules” that produce any distribution of data...' is clearly meant to convince the reader that it can produce something we would describe as a "rule", that is, a coherent and comprehensible regulating principle. This isn't just because he isn't being precise enough; he quite clearly wants the reader to understand this as neural networks being able to create a mental model of anything, in a manner similar to how a biological neural network would.

It doesn't, it can't, and it won't in our lifetimes.

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