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To say any specific LLM can reason is a somewhat significant claim.

To say LLMs as a class is architecturally able to be trained to reason is - in the complete absence of evidence to suggest humans can compute functions outside the Turing computable - is effectively only an argument that they can implement a minimal Turing machine given the context is used as IO. Given the size of the rules needed to implement the smallest known Turing machines, it'd take a really tiny model for them to be unable to.

Now, you can then argue that it doesn't "count" if it needs to be fed a huge program step by step via IO, but if it can do something that way, I'd need some really convincing evidence for why the static elements those steps could not progressively be embedded into a model.

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wizzwizz4 3 days ago | parent [-]

No such evidence exists: we can construct such a model manually. I'd need some quite convincing evidence that any given training process is approximately equivalent to that, though.

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vidarh 3 days ago | parent [-]

That's fine. I've made no claim about any given training process. I've addressed the annoying repetitive dismissal via the "but they're next token predictors" argument. The point is that being next token predictors does not limit their theoretical limits, so it's a meaningless argument.

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wizzwizz4 3 days ago | parent [-]

The architecture of the model does place limits on how much computation can be performed per token generated, though. Combined with the window size, that's a hard bound on computational complexity that's significantly lower than a Turing machine – unless you do something clever with the program that drives the model.

	▲	vidarh 3 days ago \| parent [-]
		Hence the requirement for using the context for IO. A Turing machine requires two memory "slots" (the position of the read head, and the current state) + IO and a loop. That doesn't require much cleverness at all.