Compression and entropy
are super interesting! I'm not explaining them away; I'm pointing out that effective compression is likely to end up emulating some of the training data's generative process itself -- the patterns of thought that created text like this -- because it becomes harder and harder to "memorize" as the problem space grows.
If you try to fit samples from the function 5.2*sin(17.3 x + 0.25) using a bunch of piecewise-linear lookup tables as your basis, you'll need a very large table to get good accuracy over any range! A much more effective compression of that data is the function itself. And so if your basis includes sine and cosine functions, you'll get a very accurate fit with those, very quickly and compactly.
Claude Shannon built an early language model which was doing "just" statistics, which he describes in his famous paper A Mathematical Theory of Communication. Compression was exactly his goal. He builds up a Markov model to draws letters from English, including ever-longer correlations. A first order approximation draws random letters according to their frequency of occurrence in English:
OCRO HLI RGWR NMIELWIS...
A second order approximation is based on the probability of transition from one character to the next, for example Q will always be followed by U:
ON IE ANTSOUTINYS ARE T INCTORE...
The next more refined model includes trigram probabilities, for example TH will usually be followed by O or E:
IN NO IST LAT WHEY CRATICT...
It gradually gets more English-like, yes, but you are never going to get GPT-like performance from extending this method to character n-grams of n = 1,000,000. At this point in the paper Shannon starts over, using words and word transition probabilities, to get:
THE HEAD AND IN FRONTAL ATTACK ON AN ENGLISH WRITER THAT...
But even then, just extending this Markov model to account for the transition probabilities of n-grams of words won't get you to GPT. And obviously there's no interesting thought happening inside there.
That's the point I'm trying to make here; when some people say it's "just statistics", they seem to be imagining a Markov model extended to be very large, which knows which words follow other words which follow other words, with various transition probabilities...
But that wouldn't work well enough to correctly play spontaneously-invented logic puzzles. The problem space grows too fast for that to work.
Try to create a chess program that uses a Markov model. You can do it in theory, but you'll effectively need to fit the (10^120)-gram of transition probabilities (Shannon's number). Now compare that to a chess program that does an alpha-beta search. Even monkeys on typewriters are more likely recreate Deep Blue's programming than a decent Markov-based chess program.