[0] https://www.sciencedirect.com/science/article/pii/S002200008...
I think a good example are calculations or counting letters: it's trivial to write turing machines doing that correctly, so you could create neural networks, that do just that. From LLM we know that they are bad at those tasks.
It also doesn't say anything about finding the desired function, rather than a different function which approximates it closely on some compact set but diverges from it outside that set. That's the trouble with extrapolation: you don't know how to compute the function you're looking for because you don't know anything about its behaviour outside of your sample.
https://stackoverflow.com/questions/2497146/is-css-turing-co...
Our brains use quantum computation within each neuron [1].
[1] https://arxiv.org/abs/2303.14959
[2] https://en.wikipedia.org/wiki/Turing_machineAnd given we have no evidence that quantum oracles exceeds the Turing computable, all the evidence we have suggests that they are Turing machines.
> This is meaningless.
[1] https://en.wikipedia.org/wiki/Constructivism_(philosophy_of_mathematics)#Constructive_mathematics
And there's also the other side of the GP's point--Turing completeness not necessary for creativity--not by a long shot. (In fact, humans are not Turing complete.)
> Turing completeness not necessary for creativity--not by a long shot.
This is by far a more extreme claim than the others in this thread. A system that is not even Turing complete is extremely limited. It's near impossible to construct a system with the ability to loop and branch that isn't Turing complete, for example.
>(In fact, humans are not Turing complete.)
Humans are at least trivially Turing complete - to be Turing complete, all we need to be able to do is to read and write a tape or simulation of one, and use a lookup table with 6 entries (for the proven minimal (2,3) Turing machine) to choose which steps to follow.
Maybe you mean to suggest we exceed it. There is no evidence we can.
> A system that is not even Turing complete is extremely limited.
> all we need to be able to do is to read and write a tape or simulation of one
An infinite tape. And to be Turing complete we must "simulate" that tape--the tape head is not Turing complete, the whole UTM is.
> A system that is not even Turing complete is extremely limited.
PDAs are not "extremely limited", and we are more limited than PDAs because of our very finite nature.
I know very well what it means to be Turing complete. All the evidence so far, on the other hand suggests you don't.
> An infinite tape. And to be Turing complete we must "simulate" that tape--the tape head is not Turing complete, the whole UTM is.
An IO port is logically equivalent to infinite tape.
> PDAs are not "extremely limited", and we are more limited than PDAs because of our very finite nature.
You can trivially execute every step in a Turing machine, hence you are Turing equivalent. It is clear you do not understand the subject at even a basic level.
LOL. Such projection. Humans are provably not Turing Complete because they are guaranteed to halt.
As an example, I would like to ask how to parse balanced brackets grammar (S ::= B <EOS>; B ::= | BB | (B) | [B] | {B};) with that Turing complete recurrent network and how it will deal with precision loss for relatively short inputs.
Paper also does not address training (i.e., automatic search of the processors' equations given inputs and outputs).
Mathematically possible != actually possible.