then that's just irrelevant. You don't need to evaluate millions of positions to backtrack (unless you think humans don't backtrack) or play chess. 

Humans are not transformers. The "context window" for a human is literally their entire life.

Setting up the architecture that would allow a pretrained LLM to trial and error whatever you want is relatively trivial.

I agree.  Or at least, I don't see any reason why not.

My point was not that "a relatively simple architecture that contains a Transformer as the core" cannot solve problems via trial and error (in fact I think it's likely such an architecture exists).  My point was that transformers alone cannot do so.

You can call it a "gut claim" if that makes you feel better.  But the actual reason is I did some very simple math (about the window size required and given quadratic scaling for transformers) and concluded that practically speaking it was impossible.

Also, importantly, we don't know what that "relatively simple" architecture looks like.  If you look at the various efforts to "extend" transformers to general learning machines, there are a bunch of different approaches: alpha-geometry, diffusion transformers, baby-agi, voyager, dreamer, chain-of-thought, RAG, continuous fine-tuning, V-JEPA.  Practically speaking, we have no idea which of these techniques is the "correct" one (if any of them are).

In my opinion saying "Transformers are AGI" is a bit like saying "Deep learning is AGI".  While it is extremely possible that an architecture that heavily relies on Transformers and is AGI exists, we don't actually know what that architecture is.

Personally, my bet is either on a sort of generalized alpha-geometry approach (where the transformer generates hypothesis and then GOFAI is used to evaluate them) or Diffusion Transformers (where we iteratively de-noise a solution to a problem).  But I wouldn't be at all surprised if a few years from now it is universally agreed that some key insight we're currently missing marks the dividing line between Transformers and AGI.

Ok? That's how you teach anybody anything. 

Have you never figured out something by yourself?  The way I learned to do Sudoku was: I was given a book of Sudoku puzzles and told "have fun".

you said it would be impossible to train a chess playing model this century.

I didn't say it was impossible to train an LLM to play Chess. I said it was impossible for an LLM to teach itself to play a game of similar difficulty to chess if that game is not in it's training data.

These are two wildly different things.

Obviously LLMs can learn things that are in their training data.  That's what they do.  Obviously if you give LLMs detailed step-by-step instructions for a procedure that is small enough to fit in its attention window, LLMs can follow that procedure.  Again, that is what LLMs do.

What they do not do is teach themselves things that aren't in their training data via trial-and-error.  Which is the primary way humans learn things.

sure.  4000 words (~8000 tokens) to do a 9-state 9-turn game with the entire strategy written out by a human.  Now extrapolate that to chess, go, or any serious game.

And this doesn't address at all my actual point, which is that Transformers cannot teach themselves to play a game.

Lots of people think that.  Occasionally because they are in a situation where the assumptions of Kelly don't hold (for example, you are not playing a repeated game), but more often because they confuse single bets (where Kelly maximizes log dollars) with repeated play (where Kelly maximizes total dollars).

In the long run, Kelly is optimal so long as your utility function is monotonic in dollars since it maximizes your total dollars.

From wikipedia

No matter what the reward function, isn't a rational maximizer engaging in repeated play going to "end up" concave due to e.g Kelly Criterion?  I would think convex agents would be sub-optimal/quickly self-destruct if you tried to create one and nature will basically never do so.