Comment by mitthrowaway2

2 years ago

> probability larger than zero

Strictly speaking, it should be a mistake to assign a probability equal to zero to any moves, even for illegal board moves, but especially for an AI that learns by example and self-play. It never gets taught the rules, it only gets shown the games -- there's no reason that it should conclude that the probability of a rook moving diagonally is exactly zero just because it's never seen it happen in the data, and gets penalized in training every time it tries it.

But even for a human, assigning probability of exactly zero is too strong. It would forbid any possibility that you misunderstand any rules, or forgot any special cases. It's a good idea to always maintain at least a small amount of epistemic humility that you might be mistaken about the rules, so that sufficiently overwhelmingly strong evidence could convince you that a move you thought was illegal turns out to be legal.

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mitthrowaway2

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goatlover  2 years ago

The rules of chess are small and well known. For example, rooks can't go diagonal no matter the situation. There's no need for epistemic humility.

  • ben_w  2 years ago

    Every so often, I encounter someone saying that about some topic while also being wrong.

    Also, it took me actually writing a chess game to learn about en passant capturing, the 50 moves without capturing or pawn move forced draw, and the 3 state repetition forced draw.

    • mitthrowaway2  2 years ago

      That's exactly right. A probability of zero is a truly absurd degree of self-confidence. It would be like if someone continued to insist that en passant capturing is illegal, even while being told otherwise by official chess judges, being read multiple rulebooks, being shown records of historic chess games in which it was used, and so on. P=0 means one's mind truly cannot be changed by anything, which leaves one wondering how it got to that state in the first place!

      Probably most of us even know about en passant, so we think we know everything. But if I found myself in that same bewildering situation being talked down by a judge after an an opponent moved their rook diagonally, I'd have to either admit I was wrong about knowing all the rules, or else at least wonder how and why such an epic prank was being coordinated against me!

    • goatlover  2 years ago

      But the topic is chess, which does have a small number of fixed rules. You not knowing about en passant or 3 state repetition just means you never bothered to read all the rules. At some point, an LLM will learn the complete rule set.

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  • bongodongobob  2 years ago

    Just for funsies:

    Say a white rook is on h7 and a white pawn is on g7.

    Rook gets taken, then the pawn moves to g8 and promotes to a rook.

    The rook kind of moved diagonally.

    "Ah, when the two pieces are in this position, if you land on my rook, I have the option to remove my pawn from the board and then move my rook diagonally in front of where my pawn used to be."

    Functionally, kind of the same? Idk.

redcobra762  2 years ago

There's got to be a probability cut-off, though. LLMs don't infinitely connect every token with every other token, some aren't connected at all, even if some association is taught, right?

  • the8472  2 years ago

    The weights have finite precision which means they represent value-ranges / have error bars. So even if the weight is exactly 0 it does not represent complete confidence in it never occurring.