You can still try and frame it as some overall statistical model of moves -> next move (I think there's discussions on this in the comments that I don't fancy getting into) but I think the paper does a good job of discussing this in terms of surface statistics:
> From various philosophical [1] and mathematical [2] perspectives, some researchers argue that it is fundamentally impossible for models trained with guess-the-next-word to learn the “meanings'' of language and their performance is merely the result of memorizing “surface statistics”, i.e., a long list of correlations that do not reflect a causal model of the process generating the sequence.
On the other side, it's reasonable to think that these models can learn a model of the world but don't necessarily do so. And sufficiently advanced surface statistics will look very much like an agent with a model of the world until it does something catastrophically stupid. To be fair to the models, I do the same thing. I have good models of some things and others I just perform known-good actions and it seems to get me by.
Right, they found the bits in the internal state that seem to correspond to the board state. This means the LLM is building an internal model of the world.
This is different from if the LLM is learning just that [sequence of moves] is usually followed by [move]. It's learning that [sequence of moves] results in [board state] and then that [board state] should be followed by [move]. They're testing this by giving it [sequence of moves], then altering the bits of the internal state that model the board and checking to see what move it makes. If they haven't found the bits of internal state, the resulting move isn't something you'd expect to make sense.