I could totally imagine "free" inference for researchers under the condition that the reasoning traces get to be used as future training data.

Further, some solutions are like running a maze. If you know all the wrong turns/next words to say and can just brute force the right ones you might find a solution like a mouse running through the maze not seeing the whole picture.

Whether this is thinking is more philosophical. To me this demonstrates more that we are closer to bio computers than an LLM is to having some sort of divine soul.

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

(†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.)

Great! It will now correctly structure chess games, but we've created no incentive for it to create a game where white wins or to make the next move be "good"

Ok, so now you change the objective. Now let's say "we don't just want valid games, we want you to predict the next move that will help that color win"

And we train towards that objective and it starts picking better moves (note: the moves are still valid)

You might imagine more sophisticated ways to optimize picking good moves. You continue adjusting the objective function, you might train a pool of models all based off of the initial model and each of them gets a slightly different curriculum and then you have a tournament and pick the winningest model. Great!

Now you might have a skilled chess-playing-model.

It is no longer correct to say it just finds a valid chess program, because the objective function changed several times throughout this process.

This is exactly how you should think about LLMs except the ways the objective function has changed are significantly significantly more complicated than for our chess bot.

So to answer your first question: no, that is not what they do. That is a deep over simplification that was accurate for the first two generations of the models and sort of accurate for the "pretraining" step of modern llms (except not even that accurate, because pretraining does instill other objectives. Almost like swapping our first step "predict valid chess moves" with "predict stockfish outputs")

But that does not mean that the results cannot be dramatic. Just like stacking pixels can result in a beautiful image.

Well, if in all situations you can predict which word Einstein would probably say next, then I think you're in a good spot.

This "most probable" stuff is just absurd handwaving. Every prompt of even a few words is unique, there simply is no trivially "most probable" continuation. Probable given what? What these machines learn to do is predicting what intelligence would do, which is the same as being intelligent.

> Shock! Shock! I learned yesterday that an open problem I’d been working on for several weeks had just been solved by Claude Opus 4.6— Anthropic’s hybrid reasoning model that had been released three weeks earlier! It seems that I’ll have to revise my opinions about “generative AI” one of these days. What a joy it is to learn not only that my conjecture has a nice solution but also to celebrate this dramatic advance in automatic deduction and creative problem solving.

We need enough experimental results to explain to solve these theoretical mismatches and we don't and at present can't explore that frontier.

Once we have more results at that frontier we'd build a theory out from there that has two nearly independent limits for QFT and GR.

What we'd be asking if the AI is something that we can't expect a human to solve even with a lifetime of effort today.

It'll take something in par with Newton realising that the heavens and apples are under the same rules to do it. But at least Newton got to hold the apple and only had to imagine he could a star.