I’ve yet to see anything close to the level of evidence needed to support the 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.
Now consider that you can trivially show that you can get an LLM to "execute" on step of a Turing machine where the context is used as an IO channel, and will have shown it to be Turing complete.
> I think this structure makes it quite hard to really say how much reasoning is possible.
Given the above, I think any argument that they can't be made to reason is effectively an argument that humans can compute functions outside the Turing computable set, which we haven't the slightest shred of evidence to suggest.
What evidence do you have for either of these, since I don't recall any proof that "functions computable by Turing machines" is equal to the set of functions that can exist. And I don't recall pretrained llms being proven to be Turing machines.
As it stands, Church, Turing, and Kleene have proven that the set of generally recursive functions, the lambda calculus, and the Turing computable set are equivalent, and no attempt to categorize computable functions outside those sets has succeeded since.
If you want your name in the history books, all you need to do is find a single function that humans can compute that a is outside the Turing computable set.
As for LLMs, you can trivially test that they can act like a Turing machine if you give them a loop and use the context to provide access to IO: Turn the temperature down, and formulate a prompt to ask one to follow the rules of the simplest known Turing machine. A reminder that the simplest known Turing machine is a 2-state, 3-symbol Turing machine. It's quite hard to find a system that can carry out any kind of complex function that can't act like a Turing machine if you allow it to loop and give it access to IO.
The "next token prediction" is just the API, it doesn't tell you anything about the complexity of the thing that actually does the prediction. (In think there is some temptation to view LLMs as glorified Markov chains - they aren't. They are just "implementing the same API" as Markov chains).
There is still a limit how much an LLM could reason during prediction of a single token, as there is no recurrence between layers, so information can only be passed "forward". But this limit doesn't exist if you consider the generation of the entire text: Suddenly, you do have a recurrence, which is the prediction loop itself: The LLM can "store" information in a generated token and receive that information back as input in the next loop iteration.
I think this structure makes it quite hard to really say how much reasoning is possible.