I don't think you've understood what I meant by "flattening". I wanted to imply something like an embedding of search paths into a high dimensional space within

I don't think you've understood what I meant by "flattening". I wanted to imply something like an embedding of search paths into a high dimensional space within which a point in the space represents a whole path, and the proximity of paths implies similar realisations. I'd imagine one could directly realise this by training a network with chess games and the distances between them -- by some useful path related measure -- as inputs. I think that the network would succeed in learning an embedding for chess games. I wouldn't be surprised if such an embedding could be fine tuned to output win probability instead for example. I also wouldn't be surprised if you could train a network on an auto-completion task of one-move-ahead prediction, and then using that to assign win probabilities, much in the same way that LLMs are used for part of speech tagging.