So can you explain what is a phase transition, and then why is this, like, a helpful signal for something like an RL environment?

Phase transitions are fascinating.

Uh, I mean, I think the, maybe the one that people can most easily relate to in their life is, uh, ice melting probably or water boiling.

Like, you know, you increase the temperature of ice, and it still looks like ice, and it behaves like ice, but there's a certain temperature at which it just stops raising its temperature and then turns into liquid.

So it suddenly goes from this solid phase to liquid phase.

Um, another one that's very relevant to us, of course, is the Ising model.

Uh, and I think computer science and mathematicians also study this maybe under different names, but basically, uh, you can have spins up and down, and they have different interaction terms if they're both up versus one is up, one is down.

Yeah.

And I think that's just sort of like the fundamental belief we have.

Yeah, I mean, so actually Liam and I worked on this a bit when we were looking at the scaling laws for vision models.

And, you know, this also came up a lot in the CLIP paper from OpenAI.

Like the in-domain generalization and the auto-domain generalization are monotonically correlated, but it's not linear necessarily.

And so what that means is you can keep improving your model and it will improve as the power law in-domain.

And for other domain tasks, by which I mean, as Liam said, the things that you're trying to do is a bit different than what's in your training set.

It will also improve the power law, but the slope of the power law may not be good enough.

that, that is the North star for what you guys are doing.