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There are many evaluation strategies for tensor contractions; naively translating into nested for loops and then doing direct random-access arithmetic is just one approach. If you …

So in this metaphor, the "Extended Church-Turing Hypothesis" is the belief that there is no haybale?

This is, strictly speaking, not true. Talking about an "orthonormal" basis implies that you have in mind some Hilbert space; but in any such instance there will be interesting func…

One of the things about continuous functions is that they aren't necessarily differentiable, cf. https://en.wikipedia.org/wiki/Weierstrass_function

No, neural networks cannot "represent any arbitrary function". Find a theorem that you think states otherwise, and then read what the theorem actually states.