> They can't possibly remember even a few positions.
Sure they could, but that's irrelevant.
A chess position is just a matter of remembering what piece number is on each square - just a list of 64 numbers. A trained model may store a trillion numbers (weights). It could store a TON of chess positions if it needed to.
However, that's not how LLMs work. They don't memorize inputs - they predict them, based on discovering predictive patterns, and those predictive patterns are not input patterns (e.g. board positions). They are deep patterns (maybe 100 layers of abstraction removed from the input), representing partial inputs, generalized across many training samples.
> Don't you know the legend about rice grains on a chess board?
Sure, but this has nothing to do with chess, and nothing to do with how many games were in the LLM's training data.
> The claim here is not about intelligence, it is about generality. There's no doubt for me the LLMs are intelligent.
Intelligent humans created the training data, and the LLM attempts to predict (copy) the training data, so of course it looks intelligent. If I say "E=mc^2", does that make you think I am Einstein?