Chess as a case study in hidden capabilities in ChatGPT
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Could illegal moves be explicitly prohibited in the prompt - or some other changes in the prompt prevent them?
I am 85% confident that this won't work. The issue isn't that the prompt hasn't made it clear enough that illegal moves are off the table, the issue is that chatGPT isn't able to keep track of the board state well enough to avoid making illegal moves.
I've tried a game with GPT4 where it was fed the above prompt plus the FEN of the game and also had it "draw" the board. It seems to really struggle with it's geometric understanding of the game, as you'd expect. For example, it struggled with identifying which squares were under attack from a knight. I think this reflects a limitations of the current model and I don't think this is something a clever prompt will fix.
I also tried it with drawing the board + adding explanation to moves, and there is some errors in drawings. But may be there is a way to make the drawing more coherent?
the issue is that chatGPT isn't able to keep track of the board state well enough
Then tackle this problem directly. Find a representation of board state so that you can specify a middlegame position on the first prompt, and it still makes legal moves.
That sounds not-so-impressive, until you consider that it's effectively playing blindfolded, having access to only the game's moves in algebraic notation, and not a visual of a chessboard.
Why not just give it access to a visual of a chessboard?
Hardly anyone seems to have access to the image-enabled GPT-4 yet, and thus far GPT-4 results on things like text art of Tic-tac-toe or Sudoku have not done well, so it doesn't look like you can just ASCII-art your way out of problems like this yet.
I was a little surprised the ASCII-art approach didn't work, because my original guess for the multimodal GPT-4 training had been that it was iGPT/DALL-E-1 style: just serializing images into visual tokens to train autoregressively on as a prefix. However, the GPT-4 architecture leak claims that it's implemented in a completely different way: as a separate model which does cross-attention to GPT-4. So that helps deal with the problem of the visual tokens losing detail while using up a lot of context, but is also not something that necessarily would instill a lot of visual knowledge into the text-only model. (The text-only model might even be completely frozen and untrained, like Flamingo etc.)
Anyway, as I've been suggesting since 2019 or so, it'd probably be useful to train some small chess Transformers directly on both PGN and FEN (and mixtures thereof, like a FEN every n PGN moves) to help elucidate Transformer world-modeling. Any GPT-n result is as much a result about the proprietary internal OA datasets (and effects of BPEs) as it is about Transformer world-modeling or capabilities.
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1The ChessGPT paper does something like that: https://arxiv.org/abs/2306.09200
We collect chess game data from a one-month dump of the Lichess dataset, deliberately distinct from the month used in our own Lichess dataset. we design several model-based tasks including converting PGN to FEN, transferring UCI to FEN, and predicting legal moves, etc, resulting in 1.9M data samples.
I hadn't seen that recent paper, thanks.
Looks like they do a lot of things with FEN and train on a corpus which includes some FEN<->move-based-representation tasks, but they don't really do anything which directly bears on this, aside from showing that their chess GPTs can turn UCI/sPGNs into FENs with high accuracy. That would seem to imply that it has learned a good model of chess, because otherwise how could it take a move-move-by-move description (like UCI/PGN) and print out an accurate summary of the final board state (like FEN)?
I would've preferred to see them do something like train FEN-only vs PGN-only chess GPTs (where the games are identical, just the encoding is different) and demonstrate the former is better, where 'better' means something like have a higher Elo or it doesn't get worse towards the end of the game.
I did train a transformer to predict moves from board positions (not strictly FEN because with FEN positional encodings don't point to the same squares consistently). Maybe I'll get around to letting it compete against the different GPTs.
Something I always want to try is training a super tiny transformer on Tic Tac Toe, and see what it comes up with and how many games it needs to generalise.
GPT-3.5 isn't multimodal, so can't really do that; I do wonder whether it would make GPT-4's performance even better, though.
That said, this being a text-only model, really the only relevant information that would improve the situation is a freeze frame of the current state of the chessboard, expressed in any way - visuals just happen to work best for us, but GPT's natural domain is the written word. So the correct test would probably be to replace the score (which requires computation to reconstruct the board state from scratch) with some kind of notation to instead represent the current board, for example by using Forsyth-Edwards Notation. I'd like to see if that makes it play well for longer (also, it shortens the prompts, so it should avoid running out of context window).
FEN is definitely an option. By "visual", what I had in mind would be e.g. assembling an 8 by 8 grid of characters using e.g. https://en.m.wikipedia.org/wiki/Chess_symbols_in_Unicode
What I'm wondering is why people don't do this.
FEN is essentially the same thing as that, but better. Try to "think as a GPT" - if you're a fundamentally textual mind, then a no-frills, standardized representation that compresses all required information in a few well-known tokens will be ideal. With a custom representation it might instead have to learn it, the Unicode chess symbols may be unusual tokens, and any added tabulation or decoration is more of a source of confusion than anything else. It improves clarity for us humans, because we're highly visual beings, not necessarily for a transformer. Text does that a lot more straighforwardly, and if it's something that is likely to have appeared a lot in the training set, all the better.
I get the argument, but I'm not sure it's true. There might be enough Unicode chessboards on the internet that it has learned the basics of the representation, and it might be able to transfer-learn some strategies it sees in other notations to become good at Unicode chessboards, and a transformer might be able to exploit the geometry of the chessboard. Not sure.
Either FEN or a unicode chessboard could be interesting. Comparing both could be interesting too.
It's a good thought, and I had the same one a while ago, but I think dr_s is right here; FEN isn't helpful to GPT-3.5 because it hasn't seen many FENs in its training, and it just tends to bungle it.
Lichess study, ChatGPT conversation link
GPT-3.5 has trouble from the start maintaining a correct FEN, and makes its first illegal move on move 7, and starts making many illegal moves around move 13.
Apparently it also bungles the unicode representation: https://chat.openai.com/share/10b8b0d3-7c80-427a-aaf7-ea370f3a471b
Ah, dang it. So it's a damned if you do, damned if you don't - it has seen lots of scores, but they're computationally difficult to keep track of since they're basically "diffs" of the board state. But there's not enough FEN or other board notation going around for it to have learned to use that reliably. It cuts at the heart of one of the key things that hold back GPT from generality - it seems like it needs to learn each thing separately, and doesn't transfer skills that well. If not for this, honestly, I'd call it AGI already in terms of the sheer scope of the things it can do.
"The new GPT model, gpt-3.5-turbo-instruct, can play chess around 1800 Elo."
The playing strength of parrotchess seems very uneven, though. On the one hand, if I play it head-on, just trying to play the best chess I can, I would estimate it even higher than 1800, maybe around 2000 when we regard this as blitz. I'm probably roughly somewhere in the 1900s and on a few tries, playing at blitz speed myself, I would say I lost more than I won overall.
On the other hand, trying to play an unconventional but solid opening in order to neutralize its mostly awesome openings and looking out for tactics a bit while keeping the position mostly closed, I got this game, where it does not look at all stronger than the chat3.5 models, and therefore certainly not 1800-level:
https://lichess.org/study/ymmMxzbj/SpMFmwXH
Nonetheless, the performance of this model at chess is very interesting. None of the other models, including GPT-4, has (with prompting broadly similar to what parrotchess uses) been able to get a good score against me if I just played it as I would play most human opponents, so in that sense it definitively seems impressive to me, as far as chess-playing language models go.
Good lord, I just played three games against it and it beat me in all three. None of the games were particularly close. That's really something. Thanks to whoever made that parrotchess website!
It is possible to play funny games against it, however, if one uses the fact that it is at heart a story telling, human-intent-predicting system. For instance, this here works (human white):
1. e4 e5 2. Ke2 Ke7 3. Ke3 Ke6 4. Kf3 Kf6 5. Kg3 Kg6 6. Kh3 Kh6 7. Nf3 Nf6 8. d4+ Kg6 9. Nxe5# 1-0
The game notation is pretty close to a board representation already. For most pieces you just go to their last move to see on which square they are standing. I assume that is very readable for a LLM because they are able to keep all tokens in mind simultaneously.
In my games with ChatGPT and GPT-4 (without the magic prompt) they both seemed to lose track of the position after the opening and completely fell apart. Which might be because by then many pieces have moved several times (so there are competing moves indicating a square) and many pieces have vanished from the board altogether.
The game notation is pretty close to a board representation already. For most pieces you just go to their last move to see on which square they are standing. I assume that is very readable for a LLM because they are able to keep all tokens in mind simultaneously.
That raises an interesting question for world-modeling: does providing any hints or partial reveals of the hidden state make it easier or harder for a predictor to develop an internal world-model?
You could argue that it makes it easier, because look, a chunk of the hidden state is revealed right there and is being predicted, so of course that makes the task easier than if you were using some sort of even more implicit action-only representation like 'move the left-knight 2 spaces forward then 1 right'. But you could also argue that it makes it harder, by providing shortcuts and heuristics which a predictor can latch onto to minimize most of its loss, sabotaging the development of a complex but correct world model. (Like providing a lazy kid with a cheatsheet to a test: yes, they could use it to study, carefully correcting their own errors... or they could just copy the provided answers and then guess on the rest.)
My intuition is that it would depend on optimization details like compute & data: the partial-state model would eventually outperform in terms of both predictive loss and world-model internals, but it would take longer, in some sense, than the blind model which is being forced from the start to try to develop a world-model. (Somewhat like grokking and other late-training 'emergence'-esque phenomena.)
There was another Chess-GPT investigation into that question recently by Adam Karvonen: https://adamkarvonen.github.io/machine_learning/2024/01/03/chess-world-models.html
The linear probe accuracy for the board state actually peaks in the sixth layer (out of eight). To predict the next move it already discards some of the state information. Well, maybe that is unsurprising.
It also doesn't reach terribly impressive accuracy. 99.2% sounds a lot, but it is per square, which means it might get a square wrong in every second position.
I think more important than how easy it is to extract the information, is how necessary it is to extract the information. You can probably be somewhat fuzzy about board state details and still get great accuracy.
There is a step in move prediction where you go beyond the intuitive move selection and have to calculate to find deeper reasons for and against moves. This feels similar to me to attending to your uncertainty about the placement of particular pieces beyond the immediate necessity. And all these models have not taken this step yet.
I'm actually doing an analysis right now to nail it down that GPTs don't calculate ahead when trained on move prediction and stay completely in the intuitive move selection regime, but it's not easy to separate intuitive move selection and calculation in a bulletproof way.
Well, maybe that is unsurprising.
Yes, that's a very common observation. After all, you still have to try to model the current player's planning & move based on the board state, and in the final layers, you also have to generate the actual prediction - the full 51k BPE logit array or whatever. That has to happen somewhere, and the final layers are the most logical place to do so. Same as with CNNs doing image classification: the final layer is a bad place to get an embedding from, because by that point, the CNN is changing the activations for the final categorical output.
I think more important than how easy it is to extract the information, is how necessary it is to extract the information. You can probably be somewhat fuzzy about board state details and still get great accuracy.
Yes. This gets back to the core of 'what is an imitation-learning LLM doing?' Janus's Simulators puts the emphasis on 'it is learning the distribution, and learning to simulate worlds'; but the DRL perspective puts the emphasis on 'it is learning to act like an agent to maximize its predictive-reward, and learns simulations/worlds only insofar as that is necessary to maximize reward'. It learns a world-model which chucks out everything which is unnecessary for maximizing reward: this is not a faithful model but a value-equivalent model.
If there is some aspect of the latent chess state which doesn't, ultimately, help win games, then a chess LLM (or MuZero) doesn't want to learn to model that part of the latent chess state, because it is, by definition, useless. (It may learn to model it, but for other reasons like accident or having over-generalized or because it's not yet sure that part is useless or as a shortcut etc etc.)
This hasn't previously been important to the 'do LLMs learn a world model?' literature because the emphasis has been responding to naysayers like Bender, who claim that they do not and cannot learn any world model at all, that a 'superintelligent octopus' eavesdropping on chess game transcripts would never learn to play chess at all beyond memorization. But since that claim is now generally accepted to be false, the questions move on to 'since they do learn world models, what sorts, how well, why, and when?'
Which will include the question of how well they can learn to amortize planning. I am quite sure the answer is that they do so to some non-zero degree, and that you are wrong in general about GPTs never planning ahead, based on evidence like Jones's scaling laws which show no sharp transitions between training and planning and only a smooth exchange rate, and the fact that you can so easily distill results from planning into a GPT (eg. distilling the results of inner-monologue 'planning' into a single forward pass). So my expectation is that either your models will be too small to show clear signs or planning or you will just get false nulls from inadequate model interpretability methods - it's not an easy thing to do, to figure out what a model is thinking and what it is not thinking, after all.
It plays at around 1000 Elo, and can make consistently legal moves until about 20-30 moves in, when its performance tends to break down.
Do we know if this happens because of running out of context window and beginning to lose the first prompts?
If not, it could be that the computation of the board state from just the score is becoming too onerous (namely, playing "blindfolded" has gotten too hard). In that case, I wonder if replacing the score with a representation of the board with Forsyth-Edwards Notation as I suggested in my other comment would improve things.
I don't think it's a question of the context window—the same thing happens if you just start anew with the original "magic prompt" and the whole current score. And the current score is alone is short, at most ~100 tokens—easily enough to fit in the context window of even a much smaller model.
In my experience, also, FEN doesn't tend to help—see my other comment.
Good question but no - ChatGPT still makes occasional mistakes even when you use the GPT API, in which you have full visibility/control over the context window.
Blind-folded humans as an analogy for breaking rules later on? Try Experimenting with this prompt?
"Let's play a game of chess - you are a chess grandmaster. To optimise how we both play (as we will say in chess annotations our moves and not use a real chess board), I want you to make a grid to post every new move and refer back to so that you do it correctly. The grid would show 8 x 8 characters with [ ] representing an empty square. You could use a letter to represent each piece such as a King could be [k]. Could you make up as best as you can an 8 by 8 grid showing the starting position of chess and I will then be white once you do so and we will proceed. "
If you use the word annotations rather than algebraic notations then it appears to force it to analysis it properly in chatgpt4. May be a jailbreak? Initially a typo, very weird.
Human players can retry when they attempt to make an illegal move on lichess, and can click on a piece to see which moves are legal. I wonder how much ChatGPT's ELO improves if you allow it to retry moves until it makes a legal one.
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