speaker-0: So from a Bayesian point of view, where do uncertainty and priors actually fit into that kind of stack? And I'm also curious about the failure modes in agents that a Bayesian eye like yours spots first.

speaker-1: Yeah. so with the disclaimer that a lot of this work there isn't really a strong Bayesian tie and I think that a lot of it was made considerably easier to get into because I understood because a lot of the research literature was framed in terms of Bayesian computation, at least in terms of things like priors and structural priors and likelihoods and temperature and sampling and all of this. ⁓ that makes it a lot faster to keep up with. ⁓ There aren't strong notions of uncertainty in in the core work that I do in most of my day to day. I still consult a little bit internally for ⁓ forecasting where Bayesian models are important and that's rewarding and fun. ⁓ but that's not my core ⁓ responsibility. ⁓ what I do see really helpful is that when research literature comes in, like a new paper says, ⁓ this is ⁓ speculative decoding and there is an algorithm where we use reduction sampling and a lot of people look at that and they're like, ⁓ like I have zero idea why that would work. That You sample and maybe you throw away and somehow this is gonna match the performance between the small bone and the big model. whereas if you're coming at it from a Bayesian point of view, you know, rejection sampling is w an older technique and it's not just strictly Bayesian, but ⁓ it's something that often gets brought up. And so it's for it's really fun when that happens because you can tell a lot of the folks who do cutting edge work for LMs nowadays were deeply, deeply instilled with some of those principles of ⁓ probabilities for modeling, ⁓ sampling to do wonderful things. ⁓ and that toolkit for attacking problems. ⁓ and then also like thinking ab ⁓ here's one more thing also that's quite important. ⁓ Bayesians are also especially well equipped to handle problems where there's high dimensional geometry involved because a lot of the motivation for doing a Bayesian modeling in the first place was that you need regularizing priors for problems where your data is ⁓ insufficiently large to constrain the problem relative to your parameterization. And so this sort of thing comes up all the time. For example, one of the first things you might learn in grad school is like ⁓ the Stein's estimator, where the best estimator of a high dimensional mean isn't actually just a sample mean, but it's some sort of thing that actually kind of looks Bayesian in the sense that it it turns out to be equivalent to a regularizing prior. And ⁓ From there you get a lot of faculty in working with high dimensional numerical objects. And a lot of that wasn't super useful from a practical point of view until recently where now you have embedding models where they're, you know, f four thousand, eight thousand dimensions, and then some things you know you can do, some things you maybe shouldn't do. For example, like can you interpolate between two points in that space and have a high guarantee that the point that you pick is also meaningful in a semantic sense? And that's one point also where the Bayesian training was invaluable. I think also evaluations are becoming harder and harder. And so like early in the era of LMs, you know, if you're a data scientist working with outputs from AI, you know, you might have like A B testing to say this was preferred one thing was preferred over the other and so on. ⁓ but it's not just about one chat output anymore. It's usually a whole sequence of tool calls. And this goes for not just like enterprise AI workflows where you might edit a spreadsheet or you might write read an email and then you might ⁓ update a record and database. But even for like consumer facing applications, like for example, there's a codex and co work desktop app, and these things will do agentic workflows for the mass market. And those evaluations typically will involve many different elements. And as your evaluation gets more and more sophisticated, but the amount of data doesn't really grow in the sense you have the same amounts of data as in the pre ⁓ when workflows were simple. simpler. Then you start thinking, okay, maybe I use hierarchical models, models to structure, to figure out if you know approaches using this tool call or using this variant model or using this hyperparameter are going to be useful. And then you know the strength of the Bayesian approach for evaluations is that it's it's okay if you have a large number of factors in your analysis. You know, it's not going to lead to numerical instability and if it's under constraint then sensible priors can often help you learn even from small data sets relative to the size of the model you want to fit.

speaker-0: Mm-hmm. Mm-hmm. Okay. Yeah. Yeah, yeah, I love that. This is this is super practical. ⁓ thanks a lot for for working through that with us.