Textbook Group meeting for Parr, Pezzulo, Friston 2022 .

Hello, it's February 15th, 2023. We're in Cohort 2 of the Active Textbook. We are in our first discussion on Chapter 7. So, let's just first look at how Chapter 7 is anticipated in the text. Then, any of you are welcome to give some thoughts or just raise any thoughts or questions on Chapter 7. And then that will go wherever it goes. We can also look at previously submitted questions as well as walk through the text and get a big picture of what's happening. So, the first mention of Chapter 7 is in Chapter 1 when they're summarizing Chapter 7. And they describe that in Chapter 7, they're going to discuss active inference models addressing problems formulated in discrete times as hidden Markov models and partially observable Markov decision processes. And they mention the examples they're going to use, which is a left or right at a T maze. And they also bring in topics, information seeking, learning, novelty seeking. They talk about how preference represented by the C parameter is going to be unpacked in Chapter 7. In Chapter 4, they talk about how message passing will be unpacked further in Chapter 7. In Chapter 5, they talk about E and policy. So, as they're mentioning a bunch of the parameters E, pi, C, message passing, they're describing that they're going to come back to it in Chapter 7. If we want to change the way the signal is interpreted, we need to rely on learning. We will return to this in detail in Chapter 7. In Chapter 7, we will discuss a biologically plausible example of factorization, specifically the what and the where streams. And in Chapter 6, in the recipe, they talk about the updating and the form of the updating. So, several more mentions of Chapter 7 in Chapter 6, and then we actually get to Chapter 7 itself. All right. So, anyone, just to begin with, what were your thoughts or feelings on reading Chapter 7, or what came to mind as you read or remembered reading Chapter 7, Active Inference in Discrete Time? Okay. Just unmute and go for it. Well, I didn't read it completely, but there's a number of questions that popped up in, for instance, in Figure 7.3. So, the A matrix is conditioned not only on one state, but a couple of states. Is that correct? I mean, it's... So, the sequence of preceding states plays a role. That's different to Hidden Markov Model, right? And then... So, this would be one question, how this could be. And then, another question is whether this pie actually makes this whole automaton more powerful, or is this just a convenient way of representing it? So, could this pie actually be merged into the state as an additional factor or something? So, multiply the number of states and... Or does it really increase the computational power of that whole automaton? Great questions. All right. So, yeah. Yeah. Jakob, go for it first. I think that the... In terms of putting the pie into the states themselves, I don't think I've seen that ever being done in an actual model. And I think this is more of a representation rather than really how the model would be implemented because the pie is just... is just a policy. and it's... I think it's... It, like, branches out to the two... the two Bs from, like, a single node only to represent that each B is also conditioned on the policy. But not necessarily that... it's, like, a... one... that it happens within, like, one time snapshot. Yes. Yeah. In... in some other work, Jakob and I have talked a lot about, like, why is pie shown to intervene twice? And even more generally, why is it shown with three time steps? Yes, it helps us understand that it's, like, past, present, and future. But the action perception loop also could be shown with just the transition between two steps and pie intervening once. Whereas this is a little bit ambiguous whether it's a policy of length two intervening at this time point or whether it's just showing the continual unfolding of policy interleaving between the hidden states in a sort of open-ended way. But... what... what…