> How do you see CoT as "giving hints"?

CoT prompting has you give examples. The exact sample from the paper is

Q: Roger has 5 tennis balls. He buys 2 more cans of
tennis balls. Each can has 3 tennis balls. How many
tennis balls does he have now?

A (not CoT): The answer is 11

A (replace above with this for CoT): Roger started with 5 balls. 2 cans of 3 tennis balls each is 6 tennis balls. 5 + 6 = 11. The answer is 11.

Both actually have demonstrations, which are hinting. The second A has stronger hinting because it is prompting the model to follow a certain form. There's a good example from this conversation a few weeks back[0]. I link to the parent and see their chat log vs mine. May also want to look at the context as other comments have relevant information. But you can see in mine that I'm being incredibly careful to not tell GPT anything other than it is wrong, then work towards the parent's method. The hinting is very subtle in these examples but they are enough to spoil the test. But to be clear, it depends on what we're testing. If we're testing if a model can get to a solution, then hint all you want as long as you don't explicitly tell it (CoT is often pretty close to this line though, as in the above example). But if you're testing how robust a model is, how "intelligent" it is by human standards, then CoT is cheating. The context matters. Essentially the more robust a model is the less prompt engineering it requires. In this sense humans are rather robust despite the large amount of disagreements we have. Of course you can also make the argument that humans' robustness is due to hinting and cultural priors which is why there's(?) a larger rate of miscommunication across cultures but that's a whole other can of worms discussion.

Obviously the fact that you have to hint doesn't make it a bad tool, but it does tell you that you should be exceptionally cautious of results when you don't hint (maybe you don't know) or are outside its main wheelhouse. Which what this is is rather unknown, especially considering the sequential nature of the design.

> And what are your thoughts on the various papers over the past year looking at transmitting capabilities from larger models to smaller models using synthetic data from the larger models?

I'll address this and the next part here since they're tied together. Distillation is awesome. But it is also directly tied to these loss landscapes that I'm discussing. Your teacher model is essentially telling you "hey, this way" because it already has explored the landscape. A teacher model doesn't even have to be bigger than the student model, just better. Now with generative models it's important to remember that they are also classifiers (and your classifier is secretly a generative model[1]. The arguments shouldn't be surprising if you have a deep understanding, though might result in you feeling 1) dumb because you didn't realize it a priori or 2) overly confident because "of course" and you forgot your a priori predisposition. The tyranny of good ideas). In the current state of the art typically GANs still reign in regards to actual fidelity (tricking humans) and sampling speed but diffusion's big win is diversity. This is due to diffusion models approximating the density function of the target distribution (what we're trying to learn)[2]. One way to think about this is the density of the distribution as a whole. Imagine a solid red circle but some parts are more red than others and some chunks are just not red at all! The better model should be more uniformly red (our target is all red) and so sampling from this we are going to more evenly sample from areas that are underrepresented. Pretty awesome! Of course we have to be careful and there is a lot of nuance too. You're not going to teach the student model something the teacher hasn't learned, although you might see new behavior since the student can better be primed to learn something the teacher didn't (yeah, this gets messy super fucking fast). There's also the danger of tightening the distribution and locking you out of learning things you want to learn. But this should help explain why even given the same training data we're starting to see bigger improvements, because we often don't actually care about fidelity (especially since transformers fucking love augmentations and noise injection is rather an important augmentation). We really care more about distributions. Of course, if you wanted to be really tricky (but this would likely be very expensive) you could monitor the density of the student model and have the teacher intelligently increase sampling density to these regions.

Really the tldr here is thinking about the geometry of our models (we are assuming manifolds so we can leverage this, even if the assumption isn't absolutely correct). I tell students and by lab members that you don't need math to train good models, but you do need math to know why your models are wrong. It's also incredibly important to discuss our limitations because that's like knowing where our low density regions are and where we need to over invest in sampling to create better models. Essentially the nuance is incredibly important and we shouldn't shy away from it. Okay sorry, this got a bit ranty. Being terse is hard.

[0] https://news.ycombinator.com/item?id=36307880

[1] https://openreview.net/forum?id=Hkxzx0NtDB

[2] Note that the real world breaks a lot of our assumptions in ML. Things aren't always distributions, let alone i.i.d. Nor does data always lie on a a manifold and realistically it most certainly does not. Also note that the diffusion model is a reduction or what we'd call an approximate density function. A VAE is a clearer example because we typically do dimensional reduction but this is not necessary. Diffusion is because we don't have bijective maps. For exact density you're going to look at Normalizing Flows or Autoregressive models (don't confuse) or NODEs (I kinda call these all the same thing though NFs though tbh since they're isomorphic transformations). GANs are called implicit density estimators since you don't actually learn the density function but rather just a distribution that has similar sampling features.