Textbook Group meeting for Parr, Pezzulo, Friston 2022 .

all right greetings thank you everyone for joining we're in our second discussion on chapter four let's just jump to it um anyone can write a question in the chat or raise their hand or just like unmute and go for it and it could be like anything you remember from the chapter or like a part you liked or we're curious about or just any any question that you want to jump in with like any any section that people prefer just un unmute just any page any section oh Aon go for it so all um I I was really scratching my head trying to compare figure 44 with figure 46 um there's like a very large amount of overlap between the two sets of diagrams but there's like some very uh so I feel like there's like a clear parallel setup um there's some edges that are different between the two and I was like trying to understand like what do those changes mean um and like right these were yeah uh and in both cases I think especially the left hand side diagram is like virtually identical um between 44 and 46 I think I have the numbering that right um but uh yeah I I don't know if that's like too much to fit into a question but I was I I thought the difference there must be meaningful but I I didn't fully I couldn't make sense of it it's a great question like for sure on first pass it's like two cities like maybe there's some differences and which roads and what's connected to what but at a first pass like they are both very very similar um so a few things are being shown here um to to kind of give context on this qu question let's pull back to figure 43 so here we see this kind of like Rosetta Stone figure with a basian graph for the discrete time model and a basian graph for the continuous time model on the bottom they're kind of being like laid out like this to emphasize their structural similarity even though they're treating time differently which we can return to but the top is treating variables in terms of discrete sequences of events whereas The Continuous time is treating it in terms of higher and higher derivatives of a given um variable X the important thing though that makes these similar other than their structure is that in a base graph you have edges are variables and then the uh I'm sorry nodes are variables and the edges are causal connections okay so now we get to aasian message passing scheme so one of the really cool things about AAS graph is because the edges represent the sparsity of causal Connections in the model you only need to consider edges that are local to a node so it's like the traffic at a node is strictly and entirely defined by the edges leading in um so when constructing a given basian model like you specify the kind of causal architecture of the world and then messages are passed between the variables so this is going to be a slightly different base graph than the figure 4.3 but it's going to emphasize how certain kinds of architectures pass certain messages to each other and then how that enables different kinds of computations to happen like there's a different variable here so like right off the bat even though we see some variables that were in figure 4.3 like pi and S there's also different variables like the um Epsilon and the the ITA um okay so two things are being highlighted in this figure 4.4 on the left is going to be about hierarchy and nesting on the right is going to be about unfolding Dynamics through time so the motif on the left that describes the nesting is going to be like each unit of four is kind of like a level in a nested hierarchical model and basically what's happening is the E is calculating an error like Epsilon for error and then those errors are being passed up to a higher order in the um graphs so that is like the kind of classical predictive processing architecture we have strictly stacked levels and then what's happening within each level is it's doing a differencing and then passing the errors up that's the hierarchical motif The dynamical Motif is going through time so this one…