Textbook Group meeting for Parr, Pezzulo, Friston 2022 .

all right welcome everyone from Co cohort 6 and 2/3 um we're in chapter 7 discussion and then also in cohort 7 were in Chapter 2 so we'll maybe explore a little bit of both of them and also I'll just note that the octopus math sessions are in Full Effect they're Tuesdays one hour earlier than this um the zoom link is here and they're they're doing really fun the recordings are available and they're doing fun math education in octopus is super knowledgeable so if anyone has questions on from from very basic background math to more speculative maths I recommend they look at the recordings or go to those sessions um all right so on seven or or to if if uh it's relevant what's something that anyone would like to begin with so for the discretization of time I feel like there were a few things that I wanted to be a little bit more defined could you say a little bit about how you actually take this thing that the discretization of time or States seems like it could be broken up into smaller and smaller pieces which kind of leads me to believe that there's some bundling that's going on behind the scenes and it makes me feel like I want this discretization as well as the definition of time to be brought into in a little bit more depth could you say a little bit about your thoughts about that yes great question so there's a few different settings where you might be applying a discrete time model first let's let's just go to figure 4.3 kind of the Rosetta Stone with the disree and the continuous time so this image highlights that with the same structural relationship amongst different variables we can have a discreet time or a continuous time active inference setting so that's kind of handled chapter seven and eight that's what a big part of the second part of the book is so H how is time discretized is this a claim about real time is this like an ontological Claim about time or how does it come into play instrumentally so sometimes you may be interested in making an example where there actually is a discrete time counter like it's a metronome or a clock or you're using minutes or hours so again whether or not you took a ontological position that time underlying the minutes was continuous if you were measuring by the minute you whether you're doing trading or or some other kind of measurement you could still make a discrete time just by having um some kind of click um in the mouse te's example it's even less problematic I think because there's no clock time wall time it's just action time so it's like action State step one and then an action is taken so that's kind of like Chess Time where it's disree and there's not even a reference to a wall clock time so that's kind of the simplest setting is where there's no clock it's just like a chess game then the sort of intermediate setting is real time is happening but your modeling discreet units of time like daily or hourly and then the sort of most open and challenging of the settings relatively is where you have a degree of Freedom around how you discretize the time like what should the time discretization be and so there that is basically getting into a parameter sweep over possible Delta T's and then that gets into okay so now we have multiple possible models some are taking at a finer scale some are taking at a slower scale and then do we get like more accuracy or interpretability or are the benefits in accuracy and interpretability worth the increased cost for a faster ticking model so do you mind if I just try and reiterate this again so the question was what uh how do we make the choice about the uh the sort of time that we're going to be modeling modeling in the discrete sense so we're gonna have either some absolute clock time or some purely ordinal sense of events um you know following one another and the question is like how do we choose between those because I think if that is the question uh it would be very use case dependent so you know in in something where there's a lot of…