> "the scaling hypothesis"

Oh boy, don't get me started.... I first off should say that by no means do I think any of these people (at least those publishing) are dumb. You can also be a genius in one direction and a fucking idiot in another, and that's okay. Certainly describes me haha (well less on the genius side and more on the functioning idiot side. So take everything I say with a grain of salt). Don't get me wrong, scale is incredibly important and is certainly the reason for our recent advancements. But scale taking us to AGI is fairly naive to me. The idea here has a few clear assumptions being made. First is that the data can accurately explain all phenomena if the machine is capable of sufficient imputation. I just don't even know how to tackle this one because it is so well established as false in the statistics literature. Another is that RLHF is enough for alignment. I like to say that RLHF is like Justice Stewart's definition of porn: I know it when I see it. This is certainly a useful tool, but we shouldn't be naive about its limitations. Just go on any reddit discussion on what constitutes NSFW and you'll find tons of disagreement or even the HN discussions of "Is This A Vehicle"[0]. Those comments are just beautiful and crazygringo (top comment) demonstrates this all perfectly. There's a powerful inference and imputation game going hand in hand and this is the issue. There needs to be more time spent thinking about one's brain and questioning assumptions we've made. As you advance, details become more and more important. We get tricked because you can often get away without nuance in the beginning of studying something but with sufficient expertise nuance ends up dominating the discussion and you might often actually see that naivety doesn't take a step in the right direction but rather can take you a step in the wrong direction (but often moving is more important). I'll reference Judea Pearl and Ilya on this one[1]. Pearl is absolutely correct, even if not conveyed well (it is Twitter after all). His book will give a good understanding of this though.

> What math would you use to describe the limitations of deep learning?

This is hard, because there isn't as much research in it as there is in demonstrations. I wouldn't go as far as saying that there's no work, but it is just far less popular and advancements are slower. Some optimal transport people really get into this stuff as well as people that work on Normalizing Flows. Aapo Hyvarinen is a really good person to read and you'll find foundations for many things like diffusion in his works that far predate the boom. I'd also really suggest looking at Max Welling and any/all of his students. If you go down that path you'll find many more people but this is a good place to enter that network.

But honestly, the best math to get started on to learn this stuff isn't "ML math". It's statistics, probability, metric theory, topology, linear algebra, and many specialized domains within these. I'd even go as far to say that category theory and set theory are very useful. It's all that math that you learn for a lot of other things, but you just need to have the correct lens. There is a problem in math education that we're often either far too application focused or too abstract focused that we forget to be generalist and have that deeper understanding[2]. But this is a lot and I'm not sure of a good single resource that pulls it all together in a way good for introductions (this paper certainly has many of the things I'd mention but it is not introductory). After all, things are simpler after they are understood.

I've written a lot and feel like I may have not given a sufficient answer. There's a lot to say and it is hard to convey in general language to general audiences. But I think I have given enough to find the path you're asking about but just wouldn't suggest you're going to get a complete answer in a comment, unfortunately (maybe someone is a better communicator than me)

[0] https://news.ycombinator.com/item?id=36453856

[1] https://twitter.com/yudapearl/status/1735211875191910550

[2] I think the theory focused people do often understand this more, but that's usually after going through the gauntlet and likely isn't even seen by them along that journey and especially prior to the point where many people stop. Certainly Terry Tao understands how math is just models and something like "the wave equation" isn't specifically about waves and far more general. You'll also find a lot of breaktroughs where the key ingredient is taking something from one domain and shoving it into another. Patchwork is often needed but sometimes it gets more generalized (or they derive a generalization, then show that the two are specific instances of that general form).