Textbook Group meeting for Parr, Pezzulo, Friston 2022 .

All right, greetings. It's March 22nd, 2023. We're in Cohort 3 and Meeting 9 in our second discussion on Chapter 4 of the textbook. So last time we went through some sections and we have also a lot of questions that have been addressed. So before we go back to the text or to the questions, does anyone who's here want to just like give any thought or reflection? Yeah, what are you still looking to... reduce your uncertainty on? Yeah, I'm just finding a lot of the mathematics. It's just not explained in a way that disambiguates what a particular expression might be. I've got certain uncertainties about some of the mathematical objects themselves. And then particularly on the section on Taylor series, and I feel that I have a pretty good grasp on Taylor series. That's feeling particularly opaque to me, which feels surprising. Yeah, I'm finding it a slightly frustrating chapter, which sort of dives into the maths, but in some sense without enough detail for me to really deeply understand it. But maybe that's just a matter of time. Thank you. Thank you. Well, definitely when building on a sort of meat and potatoes mathematical concept, someone with your expertise should not be overly confused. It should feel like you have already been on the on-ramp to understanding where this is going. Because it's hard to imagine it would be clearer for someone who is less familiar with the foundational pieces. So let's definitely keep that in mind when we move through. Okay. Anyone else want to just like give any overview thought on a section of four or anything else on how they're thinking about any aspect of it since last week? Okay. Okay. Okay. Then we will look at the questions. And then continue to move through the text. I'm just looking at the previous video to see where we ended. Okay. Okay. Okay. Okay. Okay. Any other comments? Otherwise, we're going to go to 410 and continue or a little bit before. Okay. All right. Let's pull back to 4-4 and just please raise your hand. Or write in the chat with any thoughts or questions. So just looking at the questions that were submitted in this cohort. Many of them involve the equations. 4, 7, 8, 10, and so on. So these are ones where like we can look at what was written for those where things were written or otherwise just like kind of given the constraints on what we can do in 50 minutes. So just recognize these are like important areas for there to be asynchronous development on. But this looks like a great answer. Whomever has written this and it's like an exemplar of how to address it asynchronously. Yes, Jonathan. Yeah. So this was my contribution here. The explanation underneath. I still have some questions about it, despite the fact that I think I now understand the sort of the vector aspect. So I have created an Overleaf document that sort of explains all of this. I'm still slightly confused by something quite simple here in the expected free energy, because there are these tau indices floating around and tau indicates, I think the time, the moment in time. So for instance, s of p subscript pi tau is the probability of being in a given state at a particular time, given that you're undertaking some policy pi. And so there's a tau index floating around, but it's still not quite clear to me in the calculation of the expected free energy what you do with that tau index. Are you summing over all of these terms? Are you integrating over them? It is an expectation value over all of the different time steps. So that was the one thing that was sort of least clear to me here. Yes. Great point. Is it expected free energy as an expectation of snapshot free energies? Is it expected free energy as the sum of the expected futures? Or is it even the expectation at that last time step alone? And the other ones are discarded. Good points. Good points. In figure 4-3, we have the discrete time, partially observable Markov decision process, POMDP, and the continuous time cousin. In the discrete time case,…