Claude's Cycles [pdf]

Was it? It was an open problem to Knuth - who generally knows how to search literature. However there is enough literature to search that it wouldn't be a surprise at all to discover it was already solved but he just used slightly different terms and so didn't find it. Or maybe it was sovled because this is a specialization of something that looks unrelated and so he wouldn't have realized it when he read it. Or...

Overall I'm going with unsolved, because Knuth is a smart person who I'd expect to not miss the above. I'm also sure he falls for the above all the time even though the majority of the time he doesn't.

>Are not LLMs supposed to just find the most probable word that follows next like many people here have touted?

The base models are trained to do this. If a web page contains a problem, and then the word "Answer: ", it is statistically very likely that what follows on that web page is an answer. If the base model wants to be good at predicting text, at some point learning the answer to common question becomes a good strategy, so that it can complete text that contains these.

NN training tries to push models to generalize instead of memorizing the training set, so this creates an incentive for the model to learn a computation pattern that can answer many questions, instead of just memorizing. Whether they actually generalize in practice... it depends. Sometimes you still get copy-pasted input that was clearly pulled verbatim from the training set.

But that's only base models. The actual production LLMs you chat with don't predict the most probable word according to the raw statistical distribution. They output the words that RLHF has rewarded them to output, which includes acting as an assistant that answers questions instead of just predicting text. RLHF is also the reason there are so many AI SIGNS [1] like "you're absolutely right" and way more use of the word "delve" than is common in western English.

[1]: https://en.wikipedia.org/wiki/WP:AISIGNS

I wonder how long we have until we start solving some truly hard problems with AI. How long until we throw AI at "connect general relativity and quantum physics", give the AI 6 months and a few data centers, and have it pop out a solution?

That description is really only fair for base models†. Something like Opus 4.6 has all kinds of other training on top of that which teach it behaviors beyond "predict most probable token," like problem-solving and being a good chatbot.

(†And even then is kind of overly-dismissive and underspecified. The "most probable word" is defined over some training data set. So imagine if you train on e.g. mathematicians solving problems... To do a good job at predicting [w/o overfitting] your model will have to in fact get good at thinking like a mathematician. In general "to be able to predict what is likely to happen next" is probably one pretty good definition of intelligence.)

Agreed with all of that, but with the added point that Knuth has done a lot of work in this exact area in The Art of Computer Programming Volume 4. If he considers this conjecture open given his particular knowledge of the field, it likely is (although agreed, it's not guaranteed).