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Ok, so by your reasoning let's have a function as a point of input, and whether it halts or not as a point of output.

So now we have a function, I can't wait till "we have good techniques for constructing such a network" that maps those inputs and outputs in an abstract plane :)

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That is a good example. But you are forgetting that neural networks are approximating the actual functions, so the function you described could be built with some kind of confidence level in the answer. Just like you can have some confidence that certain code will not halt from experience, neural network could also be built to do that. Not all possible functions though, unless you have infinitely large network with infinite computing power.

Yeah but it's still misleading as we are talking about approximating continuous functions here, not any function. Those examples are not clearly computable, or even just continuous..

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