There is a 1-1 correspondence between data compression and generative models. GPT-2 is a highly effective loseless data compression tool: https://bellard.org/textsynth/sms.html
Always wondered why this insight is not taught as much, especially in the context of things like dimensionality reduction...
The Hutter prize for improved compression algorithms is explicitly about the relationship between compression and intelligence. http://prize.hutter1.net/
I think the actual guessing space for these free response problems is much smaller, through simple priors over the question. For example:
“Richard, Jerry, and Robert are going to share 60 cherries. If Robert has 30 cherries, and has 10 more than Richard, how many more cherries does Robert have than Jerry?”
A rudimentary model will likely already know the answer is between 0-60.
Knowing that the answer involves addition and subtraction narrows it down to maybe 8 answers.
While SAT problems have only 4 answers, there’s usually one trick/trap answer, which I think might be be difficult for a model to not accidentally guess. The analogy I can think of is sometimes it’s better to cover up the answers first and work out a solution, to not get biased by any particular answer choice.
I would argue that it "knows" an awful lot, but it can't actually reason with it.
However impressive GPT3 type models are, I am not particularly convinced that they're much more than glorified hashtables.
If the hash table is large enough, it can produce lot of answers to a lot of questions, or approximately imitate a lot of stuff it's seen before.
Whether it can actually combine "knowledge" it has stored in its weights into a pattern it's never seen before ... I'm not convinced.