Active Inference in String Diagrams

Hello and welcome everyone. It is September 1st, 2023. We're here in Active Inference Math Stream number 6.1. Here with Sean Toll. We'll be hearing a presentation, Active Inference in String Diagrams, followed by a discussion. This is super exciting, so if you're watching live, please feel free to write your questions in the live chat. Really looking forward to this, so thank you, Sean, again for joining and to you for the presentation. All right, thanks very much. Thanks everyone who's watching and thanks to the organizers for this chance to speak to you and for Daniel for getting in touch and inviting me to speak. So, yeah, I'm really excited to share this work with this community, basically, and to hear from those people who work with Active Inference and do any formal work, what they think of what I'll present today. So, I'm going to be presenting a formal approach to how you can describe Active Inference in terms of an entirely graphical language called the language of string diagrams, and it's based on this mathematics called category theory, and I won't assume that you're too familiar with this already, and try and introduce it to you in the talk. And ultimately, I'd like to sort of convince you that this diagrammatic language will be really useful for those of you who work formally with Active Inference, and encourage you to pick it up in your own work. I've just introduced myself. I'm Sean Tull. I'm a researcher at Continuum, formerly a postdoc in computer science in Oxford, and at Continuum in this Oxford team, where I'm based, we study what we call compositional intelligence, which includes applying category theory to topics in AI. And as well as this, the project was supported by a grant from FQXI, which is located at the bottom and hosted at Topos Institute, which is the Centre for Applied Category Theory. So let me get started, I think. So yeah, here we go. So for Active Inference, I won't spend too much time introducing it. I'll assume most people here are familiar with it, and many of you probably know more about it than I do in fact. So I just mentioned the parts of it that I'll be addressing in the talk. So thinking of it as a model of cognition that simply we can think of as applying at many levels, say from a whole organism or just to a single neuron. And the key idea is that in this approach, you think of an agent that's coming with this generative model that it uses to explain the observations it receives from the world in terms of some hidden states, which you might call perception, and in terms of its own actions. And in Active Inference, it achieves both of these things through this form of Bayesian inference or an approximate form of Bayesian inference by minimizing this quantity called free energy. And these are the ingredients that we will look at in the talk. And the thing that's really exciting about Active Inference, I think, for those of a formal background as well, is that it aims to offer like a very principled approach to cognition that you can hopefully apply at all these many levels. But I think at the moment, it could also benefit from more formal work. And that's what this talk's about. It's about formal approaches to the theory. In particular, I think, nice clear formalizations of what Active Inference is, would help to clarify sort of what the core of the key ideas of the theory are. So we'd like to be this very distinct principle that ideally we just apply to a generative model and everything else follows from. And once we've got to this, we can actually generalize it, understand it better, and also make it just more acceptable to those who come from formal backgrounds, like in mathematics and so on, and get them working on this topic very quickly, and connect it with approaches in artificial intelligence as well. But the most important thing about a good formalization, I think, should just be to make learning about Active Inference easier, make it very much simpler to understand. So…