Textbook Group meeting for Parr, Pezzulo, Friston 2022 .

all right hey everyone it's October 24th 23 and we're in our second discussion of chapter 8 in cohort 4 so we can do any number of things but does anyone want to begin with any thoughts on chapter 8 we can look over past notes we can look at the extent questions we can hear any new questions we can look at the text yeah we'll have a very simple question uh in in the continuous case is there some kind of standard code to use to try modeling I mean to test some very simple models uh as there is for the discret case with you know the SPM framework a very good question um I'll give my thought just it may not be fully accurate in the mat lab SPM based and python pmdp based code there's been an emphasis on the discret modeling in the RX and fur Julia package I believe that there's a lot more continuous time models okay so I'm not offand familiar with [Music] um any continuous time uh implementations we can like look at the implementations table that we have eventually I'd love to see um the these repositories of course expand and grow but also annotated with different features of the model so then we could filter and say I'm looking for this language continuous time hierarchical model but almost all of the Python that I've seen was discreet okay any other random thoughts or or question questions otherwise we can look at some some popular questions and look at the notes does anyone have any just even for outside of active inference thoughts on continuous and discreet time anything with digital and analog do do we see one of them as being the general case of the other or do they both derive from a point one oh yes yes Daniel um I'm just wondering what is fundamental difference between um continuous time model and discret time model is that is that the fundamental difference is in terms of the um the state transition uh like in in the discret in the continuous model is represented as a differential equation and in the dynamic model in in the discrete model is expressed as a as a kind of a difference uh question does anyone have a thought on this yeah here what does continuous mean continuous in time or continuous in the in the uh State space uh or refer to both I suppose it you know most means it means the continuous in time right not um does anyone want to give a thought on this yes it is referring to the treatment of time so here in figure 43 We have basically chapter seven and chapter eight laid out in the discret time setting then let's talk about what's the same first broadly their architecture is the same that's why they're being laid out this way what else is the same priors are set the same way similarly enough D and also the upstairs the policy selection apparatus is broadly the same we're still dealing with free energy based policy selection mechanics um also what's the same is the hidden state to observable mapping the partially observable setting with two so really what's different is kind of like the core of the Horizon here in the discrete time setting we have explicit hidden State um or external State um calculations at given time points T minus one t t+ one right those themselves as you pointed out could be continuous so that could be like a number between zero and one um but we're estimating that at 1 p.m 2 p.m 3 P.M 4 P.M right so and then um in the continuous time setting we only are keeping an explicit prediction of the Hidden State at the current moments X and then we're dealing with um the past and the future with a tailor series expansion also known as the generalized coordinates so here whereas B plays the role of a marov transition Matrix in the discrete time model and has a kind of straightforward interpretation where like you have the hidden State at a given time you multiply it by the B and then like you basically transition into the next state right the analogous role in The Continuous time setting is a temporal derivative right and so we're extending out a tailor series which technically goes forever uh…