LLMs playing chess are sensitive to how the position came to be

This is speculation but i don't think this information (how it came to be) is actually irrelevant information for the LLM.

Your state, which transformer LLMs notably have no way of transferring is "just" the computation that preceded the prediction. I think LLMs use previous tokens to compute the likely state vector that preceded the tokens and make predictions that continue this computed state.

So the 2 board positions at time x may be identical but the state preceding it or "strategy" was not and so the next move is not identical. This way also, you can make a decision based on the perceived competence of your opponent.

These 2 papers kind of touch on what i've been thinking for a while now. They demonstrate task vectors and function vectors here for explicit in context learning tasks.

In the absence of explicit tasks, perhaps state vectors would be more appropriate.

In-Context Learning Creates Task Vectors - https://arxiv.org/abs/2310.15916

Function Vectors in Large Language Models - https://arxiv.org/abs/2310.15213

Put another way:

"When the autocomplete system ingests the play-by-play of an idiomatic game that arrives at a particular board position, it appends the suffix A"

"When the autocomplete system ingests the play-by-play of a seemingly random game (seriously, look at the PGN generator output), it appends a (questionable) suffix B"

Considering LLMs are just "finishing the string" this seems tautological. An interesting study, but not particularly surprising (at least from my perspective).

Further, I have a strong suspicion that this is sensitive to how "in theory" or "out of theory" the move-list is (not the position) since there is presumably a LOT of PGN training data for known lines.

Isn't this the same for regular language?

If someone is telling something making grammar mistakes, it's likely that the next word will also contain a mistake, so the LLM reproduces it.

And to be fair, I also think that most humans also have this same sensitivity in chess. I've seen even super GMs needing extra effort to realize something like "oh, this opening is just like the Sicilian defense, but with an extra tempo for white", and then instantly "loading" mentally the top strategies for Sicilian defense, that they weren't considering before.

This seems like an artifact due to the original purpose of the LLM. It was trained on human language, where the context of how a sentence arrives to a specific word is extremely important.

All this says is that LLM do not know there is symmetry in chess that can be exploited to lower the search space.

Which is a fair assumption, since there is not the same symmetry in human language.

Perhaps there is actually useful information in there about the skill of the players

lol...It's taking the sequence of moves up to that point... In theory I could see with enough data it could not change the answer for a different sequence (same state), but wow on the surface it seems like "enough" would be a lot.

Apparently human grandmasters remember around 50,000 board positions and play moves that manipulate the current board position to a more favourable one. They don't see moves in the same fashion that a beginner does.

It seems like the LLMs are closer to the approach used by grandmasters.