The wall confronting large language models

There is a formal extensional equivalence between Markov chains & LLMs but the only person who seems to be saying anything about this is Gary Marcus. He is constantly making the point that symbolic understanding can not be reduced to a probabilistic computation regardless of how large the graph gets it will still be missing basic stuff like backtracking (which is available in programming languages like Prolog). I think that Gary is right on basically all counts. Probabilistic generative models are fun but no amount of probabilistic sequence generation can be a substitute for logical reasoning.

I don't understand what point you're hinting at.

Either way, I can get arbitrarily good approximations of arbitrary nonlinear differential/difference equations using only linear probabilistic evolution at the cost of a (much) larger state space. So if you can implement it in a brain or a computer, there is a sufficiently large probabilistic dynamic that can model it. More really is different.

So I view all deductive ab-initio arguments about what LLMs can/can't do due to their architecture as fairly baseless.

(Note that the "large" here is doing a lot of heavy lifting. You need _really_ large. See https://en.m.wikipedia.org/wiki/Transfer_operator)

What hinting? The comment was very clear. Arbitrarily good approximation is different from symbolic understanding.

"if you can implement it in a brain"

But we didn't. You have no idea how a brain works. Neither does anyone.

We know the healthy brain is unpredictable. We suspect error minimization and prediction are not central tenets. We know the brain creates memory via differences in sharp wave ripples. That it's oscillatory. That it neither uses symbols nor represents. That words are wholly external to what we call thought. The authors deal with molecules which are neither arbitrary nor specific. Yet tumors ARE specific, while words are wholly arbitrary. Knowing these things should offer a deep suspicion of ML/LLMs. They have so little to do with how brains work and the units brains actually use (all oscillation is specific, all stats emerge from arbitrary symbols and worse: metaphors) that mistaking LLMs for reasoning/inference is less lexemic hallucination and more eugenic.

What do you think about the idea that LLMs are not reasoning/inferring, but are rather an approximation of the result? Just like you yourself might have to spend some effort reasoning, on how a plant grows, in order to answer questions about that subject. When asked, you wouldn't replicate that reasoning, instead you would recall the crystallized representation of the knowledge you accumulated while previously reasoning/learning. The "thinking" in the process isn't modelled by the LLM data, but rather by the code/strategies used to iterate over this crystallized knowledge, and present it to the user.