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 part about backtracking is baseless? Typical Prolog interpreters can be implemented in a few MBs of binary code (the high level specification is even simpler & can be in a few hundred KB)¹ but none of the LLMs (open source or not) are capable of backtracking even though there is plenty of room for a basic Prolog interpreter. This seems like a very obvious shortcoming to me that no amount of smooth approximation can overcome.

If you think there is a threshold at which point some large enough feedforward network develops the capability to backtrack then I'd like to see your argument for it.

¹https://en.wikipedia.org/wiki/Warren_Abstract_Machine

Backtracking makes sense in a search context which is basically what prolog is. Why would you expect a next-token-predictor to do backtracking and what should that even look like?

I don't expect a Markov chain to be capable of backtracking. That's the point I am making. Logical reasoning as it is implemented in Prolog interpreters is not something that can be done w/ LLMs regardless of the size of their weights, biases, & activation functions between the nodes in the graph.

A (2,3) Turing machine can be trivially implemented with a loop around an LLM that treats the context as an IO channel, and a Prolog interpreter runs on a Turing complete computer, and so per Truing equivalence you can run a Prolog interpreter on an LLM.

Of course this would be pointless, but it demonstrates that a system where an LLM provides the logic can backtrack, as there's nothing computationally special about backtracking.

That current UIs to LLMs are set up for conversation-style use that makes this harder isn't an inherent limitation of what we can do with LLMs.

Loop around an LLM is not an LLM.