Ryan Greenblatt: belief

Transcript context

…So one concern I have is that I think even in mathematics, as far as I’m aware, we have not seen very impressive new theory. We’ve seen a lot of impressive, verifiable, specific results — for example, find a counterexample to this conjecture — but we have not seen “come up with the idea of topology“ kinds of levels of things, or “come up with things like group theory“. It seems like ML research has elements of both of these things. But the less verifiable thing of coming up with new ways of thinking about the problem would be harder to induce. Take, for example, the idea of scaling laws. Obviously, there is some end verification loop such that you can train GPT-4 better if you have the idea of scaling laws from 2020. But there is a longer and potentially more compute-laden road to inducing AIs to be like, “Okay, I got to think carefully about how I should be scaling my parameters and data. What are different kinds of investigations I could run to understand this? Maybe I can come up with a visualization and an isoFLOP analysis or something.” But that does seem like a longer verification loop than just, “Hey, let’s get nanoGPT loss to go down.” Let’s talk about this. First of all, I think in the context of math, the thing I would say is that the AIs can do the equivalent of ‘baby’s first new theory,’ where, for example, they can just prove interesting conjectures via making connections and producing new understanding. It’s like, “Oh, there’s this construction the AI found which is pretty interesting”, or it found this way of thinking about the problem that’s a bit different. We do see that. It’s just that the examples we see are not as impressive as founding the field of group theory. Founding the field of group theory is probably among the best, biggest mathematical accomplishments of all time, and the AIs just aren’t that good at math yet. From my perspective, there’s a continuum between that and the things we’re seeing now, that the AIs are continuing to march up. Second, I think ML is a very shallow domain relative to math. In math, there was much more of a thing where you find some true deep abstraction, and if you really understand that thing, which is hard to understand, then you get somewhere. Whereas I feel like the things that are the equivalent of that in ML are really dumb bullshit. Like with scaling laws, come on guys, we can explain scaling laws really quickly. I think the deepest and most important concepts in math, for example, don’t have the property that you can really understand the underlying thing and why it matters in a very short period of time. But I feel like one effect will be that we will have gotten rid of all the low-hanging fruits by 2030. I feel like scaling laws will have been, in math history, like Descartes finding the Cartesian grid and doing very basic mathematics. Eventually, if we want to keep making progress in the 2030s, it’s going to be like doing whatever bullshit is happening at the frontiers of mathematics right now.…

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