Textbook Group meeting for Parr, Pezzulo, Friston 2022 .

All right, welcome everyone. It's 7-11-23. We're in cohort three in our first discussion of chapter eight. So we'll head over to chapter eight and look at some questions and comments. But first, does anyone want to bring up any just general thoughts or reflections on chapter eight? Ali? Well, yes. Actually, chapter eight, as obviously the title suggests, is kind of complementary to chapter seven in terms of being the continuous time counterpart to the active inference formulation of discrete time. So as we saw previously in chapter four, we have both a continuous time version and discrete time version of active inference employing different mathematical technologies and techniques. But of course, they can be regarded as kind of formulating the same or at least similar formulation just using different mathematical techniques. So namely, in discrete time case, we use matrices to represent states, transitions and so on. But in continuous time, we use generalized coordinates in order to describe the states and not just, I mean, discrete matrices for states. And also, the starting point of formalizing active inference in continuous time also differs a bit. Because in continuous time version, we begin with a version or a variant of Eido's stochastic equation. So we're going to be able to do a version by representing a flow plus random variable and then trying to somehow formulate the flows in terms of increasingly granular way. And yeah, tracing the trajectory through the state space, continuous time state space, employing that, I mean, Taylor expansions and other mathematical technologies and so on. Great. Olivier? Yeah. What do you mean by granular here? So, I mean, Eido's stochastic equation is a very general equation describing any kind of, sorry, differential stochastic phenomenon. But in this case, we focus on a particular kinds of state space with particular kinds of behaviors. So, especially in active inference, we focus on active agents as opposed to a more general sense of the term, such as, I mean, describing the whole behavior behavior of self-organizing system or even a simple system that can be basically described with a simple statistical physics. So, the focus of active inference, as I said, is the agents that don't have empty set of active states, right? But of course, it can also be generalized to other kinds of agents with empty active states. But the active inference framework or FEP don't have anything particularly interesting to say about those other kinds of agents. That's what I meant of granular. We focus on a subset of the systems that can be described through Eido's stochastic equation. Okay. Cool. Thank you. We can come back to some of these. And also, Ali, we will be keeping in mind that we need to make the videos for 7, 8, 9, 4, 5. Sure. Yeah. Whatever you want. Okay. Anyone else want to just have any general thought or question, raising their hand or in the chat on 8 and continuous time? I really like that chapters 2 and 3 give us the kind of two ways to get there, to act imph, the low road and the high road, the how and the why. And now it's like we're in the city and now there's two restaurants or there's like two doors to the restaurant with the discrete and the continuous time. So it's another dyad of chapters with 7 and 8 and another juxtaposition that gives us parallax and helps us understand more about each of these two methods by highlighting, on one hand, situations where they seem to apply more naturally. For example, the discrete time formulation seems to be a natural fit for discrete decision-making tasks, like which slot machine are you going to pull? Whereas the continuous time model seems to be a more natural fit for analog perception control systems, like proprioception and sensory motor behavior. And chapter 8 is also going to get us to hybrid nested models. For example, a model with two layers where the lower level is continuous time and the higher level is discrete time. So that…