Structured Active Inference

Hello and welcome. It is August 12th, 2024, and we are in ActInf Math Stream number 11.11111111 and with repeat friend Toby Smythe. Today we're going to talk about structured active inference. There will be a presentation followed by a discussion. So thank you Toby for joining and everybody for watching and asking questions and looking forward to learning more here. So go for it. Cool. Great. Thanks, Daniel. Thanks for having me on again. So as Daniel says, this is going to be a talk about structured active inference, which is really my account of the structure of active inference systems. And really it kind of extends beyond active inference to any kind of system that you could think of as being kind of agential and that has some kind of compositional structure in particular. But we'll get to that. Okay. The way I like to begin thinking about structure and active inference is at the moment it's kind of like, if you wanted to model in active inference, an agent or a person getting onto a bicycle or getting into a car, then I think as things stand, it might be a bit tricky because that process involves like changing the agent's Markov blanket or how I like to think of it is changing the agent's interface. And to be able to talk about that precisely, you need to have a good notion of what interface is. So, you know, you, as you're, you know, getting into the, getting onto the bike, let's say, you move, you change from, you know, walking by taking steps one after another to, you know, like changing your direction by like leaning and pedaling. So the kind of type of actions you can take and the things that you pay attention to change, yes, because you're now this kind of composite system, you and the bicycle. And it's a similar story when you get into the car. So that, that really, that means that you don't just have like one like set of observations and like one set of actions you can take. This, this kind of composing process means that you have to have a bit more flexibility. And in particular, you need to say precisely what those sets of observations and sets of actions should be. So the basic idea behind structure, structured active inference is really just to put the ideas of active inference into categorical systems theory. And so categorical systems theory is just an account of how dynamical systems of very general kind. are made up of parts and how those parts compose together. And it separates out the notion of the system from the notion of its interface. And so this allows us to be very precise about what is the kind of agent Markov blanket and how does that change? So we inherited a number of features of categorical systems theory in this notion of structured active inference. In particular, we inherit this kind of idea of structured interface. And that means not only do we have to be precise about what the interfaces are, but we also are able to say what the structure in some sense of the interface is and how does it change? And how does it interact with other kinds of interface? I'll say a lot more about that in the next few slides. Because categorical systems theory is all about the composition of systems and their interfaces, so is structured active inference. And that means that we get a nice kind of modular account of active inference. And we can compare active inference with other accounts of agency. And we can compare active inference systems of various different kinds in a nice precise way. And so that means we could sort of translate between continuous time and discrete time systems or various different kinds of continuous time or stochastic systems. Those are all different systems theories of their own. And active inference has lots to say about how to do inference and policy selection on those different kinds of systems. But categorical systems theory means that we're very precise about what those different systems and how that inference process works. And so this kind of comparability comes into, is…