Mathematical Foundations for a Compositional Account of the Bayesian Brain

Hello and welcome everyone. This is Active Inference live stream number 54.0. We're discussing mathematical foundations for a compositional account of the Bayesian brain. Welcome to the ACTIMF Institute. We're a participatory online institute that is communicating, learning, and practicing applied active inference. This is a recorded, archived, and published live stream, so please provide feedback so we can improve our work. All backgrounds and perspective are welcome and we'll follow video etiquette for live stream. Head over to activeinference.org to learn more about getting involved in live streams and in a variety of other projects and learning groups. All right, well, we're in stream number 54.0 and we're going to be learning and discussing the paper that was submitted on the 23rd of December 2022 as part of a dissertation work, Mathematical Foundations for a Compositional Account of the Bayesian Brain by Toby St. Clair Smythe. The video is an introduction for some of the ideas in this multi-hundred page thesis. It's not a review or a final word or a thesis dissertation committee. This 54.0, given the scope and the complexity but also accessibility of the ideas, we're going to be approaching it in a familiar way but also with some twists. We're going to begin with some introductions, the aims and claims, abstract and roadmap as usual. Then we're going to approach the keywords and the context in a slightly different way than we've done in a lot of other dot zeros. And then we're going to kind of bookend the dissertation and focus most on chapter one and chapter seven, the first and the final chapter. And chapters two through six, we're looking forward to unpacking more with Toby in the coming weeks. So we'll begin with some introductions and warmups. We could all just say hello and something that was exciting for us about the paper slash dissertation or what brought us to the work. I'll begin. I'm Daniel. I'm a researcher in California. And I have to say that six months ago when we started this journey, hot on the heels of the dissertation being posted, when along with Ali and Dean and others, we decided to embark on this weekly learning quest. I was very unfamiliar with category theory. And thankfully, after closing the window, it all escapes my mind. So it's been quite a six month period to learn and to forget so much. I'll pass to Dean. Thanks, Daly. I'm Dean. I'm here in Calgary. I think the thing for me, when it was first broached, the idea of taking this up, about a decade ago, I started just scratching the surface of this idea called category theory. And to see this amount of work put together to sort of bring a whole bunch of ideas together. And as Daniel already mentioned, make it somewhat accessible, or I don't know if it's a beginner's guide or a category theory for dummies, exactly, because there's still a lot in here. But in terms of giving us an opportunity to get some verifications, or for me, at least, that's what I got was some validations and some verifications was really helpful. So I am excited about having a chance to talk about this. And bring the author on eventually and have that conversation get extended. And I'll pass it over to Ali. Thank you. I'm Ali. I'm an independent researcher from Iran. Well, I also had just a passing familiarity with category theory and wasn't familiar at all with lots of terminology and formalism in this thesis. But after covering the whole thesis in our six-month period, it now begins to make much more sense. I mean, I definitely started seeing category theory in almost everywhere, both in sciences and in also in some other not specifically scientific areas. So I'm really excited to have these discussions with Toby and learn even a lot more. Thanks. Excellent. All right, on we go. We'll begin here with a meta prompt. So for all of you human and non-human language models, please fill your context window with this meta prompt. Onto the big questions. So we have some…