Textbook Group meeting for Parr, Pezzulo, Friston 2022 .

Hello, it is March 15th, 2023. We're in our first discussion of Chapter 4 in Cohort 3, and there's a lot of great questions. First, is there any general comments or reflections that anyone wants to share about Chapter 4? Yeah, just previously people were reflecting on this kind of accuracy, complexity, trade-off, and how much and what maths to show. Ali? Yeah, as Jonathan and Francois also mentioned, this chapter is pretty dense, probably one of the most difficult chapters in the whole book. But in my own experience, the step-by-step tutorial paper is extremely helpful when reading this chapter because some of the missing gaps in the explanations and some of the, in my opinion, necessary details that are somehow, for some reason, have been omitted from this chapter can be found in quite helpful detail on that paper. So, yeah, I definitely highly recommend reading that one. Oh, that's great. I will do so. The thing is, I know that the step-by-step paper is only for discrete time, but this Chapter 4 also goes to continuous time. Is there a similar resource that you could recommend for... Raphael Bogach's paper on tutorial on free energy principle somehow does the same kind of, not simplification, but kind of pedagogical walkthrough through the continuous time active inference. So, both of those papers can be seen as complementary to each other, one for discrete and the other one for continuous time situations. Thank you. Added the link here. Any other general comments? We had Chapter 1, Introduction. Then, we walked on the low road and the high road to active inference. And now in Chapter 4, we're at the generative models of active inference. So, if it's an active inference generative model, it's active inference. If it's something else, it's something else. A focus in this whole textbook and field is about how time is represented. And those who have done any kind of dynamical systems modeling will be familiar with a lot of the fundamental differences and challenges. For example, continuous and discrete representations of time, and how to discretize time, and so on. So, Section 4.2. From Bayesian Inference to Free Energy. The preceding two chapters with the high and the low road were outlining important connections with active inference and other paradigms. And especially the low road helped us look at the Bayesian brain. Starting from the bottom, starting from the how. With respect to the high road, this is where we bring in notions of cognitive entities and the kinds of bounded inference or bounded rationality that support self-organization and persistence and adaptive decision-making. This chapter recaps Bayesian inference and specifically the variational approach of Bayesian inference. That is what is going to connect generative models, which are how active inference models are specified, to the concept of free energy, which is going to be shown to be kind of like a criteria or an imperative that's used to fit or describe different generative models in the data. This section is more technical than the previous chapters, appealing to a little linear algebra, differentiation in calculus, and the Taylor series expansion. Some of those topics are in the appendices, and even the points that people like on the structure and what would have been helpful to know when. Those are all helpful comments to write or to surface. There's no one single linear layout that would have been perfect for every single case, but even just like sharing what would have made it helpful for any given person or what detours or cul-de-sacs they went on, that's all really useful. Those who do not want to delve into theoretical underpinnings may skip this chapter. So soon. Bayes equation in 4.1. Does anyone want to just bring up anything or describe it or call it like they see it? Let's see if we have the natural language description. Let's see if we have the natural language description. Let's see if we have the natural language description. Let's see if…