What would it be like to learn Chess like a text-only GPT?
Two thought experiments
Chess. I hear it was once thought to be the pinnacle of human intelligence. If you played it better than another person, you were a Generally Smarter Person. Our understanding of general smartness has since become more refined, but that’s not my question today.
The first question I have is, what would it be like to learn chess like a bat text-only GPT during pre-training? If you’ve never seen a chess board, have no idea what the game was, how it was played, and was only ever learning about the game though reading thousands of records like this and was given nothing else (no “rule books”) (source):
1.e4 d5 2.exd5 Nf6 3.d4 Nxd5 4.c4 Nb6 5.Nc3 g6 6.Be3 Bg7 7.h3 O-O 8.Qd2 Nc6 9.Nf3 e5 10.d5 Ne7 11.g4 f5 12.O-O-O e4 13.Ng5 h6 14.Ne6 Bxe6 15.dxe6 Qxd2+ 16.Rxd2 Rad8 17.Bc5 Rxd2 18.Kxd2 Rd8+ 19.Kc2 Nc6 20.gxf5 Nd4+ 21.Bxd4 Rxd4 22.Rg1 g5 23.c5 Nc4 24.Bxc4 Rxc4 25.Rd1 Bf6 26.Kb3 Rxc5 27.Nxe4 Rxf5 28.Nxf6+ Kf8 29.Ng4 h5 30.Ne3 Rf3 31.Rd5 g4 32.hxg4 1-0
What does your conception of chess look like?
The concept of a “diagonal” would maybe look like developing a sense for noticing that sometimes, a “B” moves by “subtracting/adding n letters and subtracting/adding the same n or -n numbers”.
But what would it be like to learn the entire game like that? Would it be easier? Harder? Would your chess “style” look more like Leela Chess Zero, Maia Chess, or more like GPT-4? Would you come up with wildly new ways of playing chess? Would you think of it as a “word game” that way people think the game “Contact” is a word game? What about the game of Go?
It’s sort of too late for me, I know what chess is already.
This is a thought experiment, but it’s not an impossible thought experiment (just a bit bizarre). Are there volunteers out there who might be willing to (ask someone else to) try this and report back?
(Foreseeable risks: attempters might literally see chess in a drastically different way to other fellow humans. Is this risk greater than that experienced in regular life? Depends on what you think is or isn't happening in "regular life".)
How do you teach chess to a human as you would to a GPT (after pre-training)?
Thought experiment 1 above describes a human learning chess through text associatively — the way a baby learns to figure out what sounds correspond to words in their native languages (i.e., language acquisition through “statistical learning”. Yes, humans do it too!). Here’s a second thought experiment.
Let’s say we want to teach chess to a person or GPT so they/it learns chess “as a second language”. For GPTs, maybe this means adding reinforcement learning after the basic pre-training step, showing it examples of good and bad chess moves/games and rewarding it for outputting good chess moves? Or it might be more akin to the Tree of Thoughts process. I’m not too sure yet.
How would you do it for a human in a way that’s as similar as possible to the GPT experience (i.e., without any reference to visuospatial imagery)?
This one would have to be at least a 2-person effort. One person, the Teacher, would have to somehow convey the rules of the game to the Student without ever referencing anything that could create spatial or visual imagery, because saying “diagonal” to a text-only pre-trained GPT doesn’t mean the same thing it would to a human.
(It won’t stop the GPT from learning to use the word of course, the same way a child or adult will sometimes write or say words like “lateral inhibition”, but you still need to figure out whether they know what it “means” in the external world. Usually through exams, oral interviews, counterfactual questions, or some other way.)
The Teacher could say things like “the piece that starts the game at g1 is called a ‘knight’.” But the Teacher can’t say things like “imagine an 8x8 square board” or “a knight must move in ‘L-shaped’ patterns, for example, by going two spaces forward and one space to the left or right”. No mentions of “forward”, “diagonal”, or one “space”. Nothing that relies on visual images to get across, and nothing that would contain content which would allow a human to create visuospatial images of the board or its pieces.
The Teacher would also have to be careful and make sure that the student only ever sees the text notation version of any chess game. And the Student would obviously need to be prevented from ever seeing a chess board laid out visually. Ideally the Student has no idea it’s a game that’s even played on a board! It would help if the Teacher told the student that Chess was a word game.
I’d be really interested in what would happen if this student plays internet chess with other people through the internet (and the teacher mediating between the visual board). Would the internet visual chess player on the other side notice their opponent (the word game Student) has no idea chess is a board game? Would the word game Student notice?
(So reading this post would automatically disqualify you from being the Student, I’m sorry! But if you ever get consent from someone to teach them about something in a very different way to any other human, I’d be extremely interested to hear how you had to go about teaching the game! Here’s my attempt, but I don’t know chess well enough to teach the strategies or concepts in it, and I definitely don’t know chess notation well enough to explain everything without using any visuospatial concepts. I gave up at pawns.)
In the interactive version of this thought experiment where the Student isn’t learning by playing games with themself only (i.e., “self-play”); if the teacher plays practice games with the student, the teacher would have to constantly be very careful about not explaining moves with any physical, visual, or spatial concepts like “edge” or “surround”. Things like “attack” or “defense” or “threat” are probably borderline okay as long as it’s invoked and explained in terms that would make sense in a word game. Something more similar to the way threat is explained in cybersecurity maybe — as an abstracted concept?
Also, I am aware blind and visually impaired people can and do learn to play chess, but being blind or visually impaired does not preclude one from creating visual or spatial images, so I can’t just ask them. Learning through braille chess boards also wouldn’t count as not developing a spatial representation of chess the board game. Previously sighted people who have seen a chess board before they became visually impaired, and can mentally create visual images are also out. Someone who was verbally told that a Knight can be “moved two spaces up and one to the left” or that a Queen “can move diagonally and adjacently as many squares as is legal but cannot jump through pieces” would likely be out too.
It’s actually kind of tricky to remove all reference to visuospatial concepts or anything that could help the person draw mental pictures in their head. We get visuospatial information through at least 3 of our 5 most well-known sensory modalities (i.e., sight, touch, hearing). And in humans, language lets us easily port concepts from one sensory modality to another. Most people do it so intuitively it’s actually really hard to prevent.
This thought experiment is similar in spirit to trying to explain colour to a (congenitally) blind person, without referencing facts about the colour the blind person might already know, as shown in the video below.
Short of the drastic interventions of the sort I described…if you think you have aphantasia (inability to form mental images) and play chess, I’d be super happy to hear you describe your experience of what chess is to you. Does anything I describe here ring true to your understanding of the chess rules?
Why do I even want to know this?
Mainly because I can’t ask ChatGPT or any chess playing GPT what it’s like to learn chess and have it mean anything (yet?), but I sure can ask a human.
Of the (now) many AIs that are capable of playing any chess, Deep Blue, Stockfish, AlphaZero, MuZero, Leela Chess Zero etc. all “learn” to play chess by representing the game as a tree. Actually, Deep Blue and Stockfish don’t learn how to represent the state of the board. The board is just given to them by human programmers, so I’m going to stop talking about those.
AlphaZero and MuZero use roughly the same method to represent the chess board state. They see “encode the current board state” using ResNet layers, the same layers that were invented for computer vision (although AlphaZero never needed to “learn” the rules of chess, whereas MuZero did; see “Comparison to AlphaZero”).
Humans normally represent chess visuospatially. Which means, by default, I would not be too surprised if we find out that MuZero formed some of the same visual concepts that humans would when learning chess. Like a “diagonal”. Or “forwards”. Or “L-shaped”.
What happens if you don’t?
Maybe one day, someone will swap out the ResNet representation system in MuZero with a text-only representation system (e.g., BERT or GPT) and find out? (And it’s not just about the architecture per say. Swapping in a Vision Transformer inside of ResNets for representation doesn’t quite help to answer what I’m curious about, I think).
Though, with MuZero and co., the purely self-play RL reward signal is also different from normal human learning. So the better comparison might be to swap out the representation system from Maia Chess, which is an AlphaGo-but-Chess model where it’s trained with data from chess games played by humans, rather than pure self-play.
(This is assuming someone first does the work of making Maia chess a little more similar to human chess. If I’m interpreting correctly, Fig 4. says Maia is roughly 50% similar to “humans”. Sure it’s better than the competition, but on an absolute scale, 50% is not that similar).
Of course, this leads me to a related question, what would it be like to learn chess (and/or Go) entirely by playing against yourself (as visual board game or otherwise)? Would you develop strategies that look like Alpha Zero strategies and concepts? Would you follow the same growth and concept formation trajectories? Some people play chess against themself after having learned chess and say it might useful as a study method. But that’s a different thought experiment for another day.
If you know of anything that looks like what I’m curious about already being done and published somewhere, I would appreciate any pointers in that direction!