Textbook Group meeting for Parr, Pezzulo, Friston 2022 .

all right welcome thanks for joining um we're in cohort 5 in the first discussion of chapter nine in terms of the book we made our way through the epistemic first half the recipe for making a generative model in chapter 6 then the discr and the continuous time generative models in seven and 8 now we get to chapter nine which is the data driven component so pretty much up to this point everything has been like you think of it conceptually you create the model and then it generates synthetic data that's using a generative model in the direction that's usually called generative it's generating data the other direction of use for an active inference model or statistical model is as a recognition model so that taking in empirical data and then fitting parameters that recognize the patterns in the empirical data so chapter nine highlights that kind of back and forth about designing generative models that take in data that's being emitted by empirical experiments like behavioral experiments in lab so that's what chapter N9 is about um you if you want to ask the question that you had first and then we can like jump in there explore empirical data look at some pmdp and empirical code just see what happens but what what um was your question before we begin oh I I have no uh specific question it's just I I noticed a lot of people have commented on that paper so I suspect it's something completely a completely new Direction in in the field so um yes so could you could you comment on the main point of this uh of of this paper yes yeah great so this was the the paper path integrals particular kinds and strange things it was first uploaded to Archive in 2022 and then it was um submitted to This Journal called physics life reviews so physics of Life reviews has a very interesting um scope if you look at the structure of this journal um they publish like regular research as well as comments on research and so during the process of this paper being like kind of undergoing peer review from the archive version they also once they get to basically the final version they solicit from a pretty Broad and open Community these short comment papers so like Ali and I wrote a paper commenting on this like just like a two-page paper those comment papers are not peer reviewed exactly they're more like editorially overviewed um so I mean we see many many names that we know because it's kind of like an easy and fun way to to be part of a bigger discussion get a citation pump up the citations to the target paper um so that's kind of the the The Meta um on this okay so as for the contents itself um it is not entirely new it builds on especially the 2019 fris and work free energy principle for a particular physics um to connect it to the text book all throughout the 2022 textbook like we're talking about the continuous time and the discrete time models so um let's look at figure 4.3 so in the discreete time setting we have a transition operator that basically jumps you forward a discret Time Step In The Continuous time setting the way that we've been discussing it in the textbook is in in terms of the tailor series approximation so starting with a point evaluating at the point then taking the first derivative around the point and then the second derivative around the point and so on um so that is in a continuous setting that idea of like doing active inference in a continuous setting is is generalized and formalized by Framing the free energy principle not just in terms of the transition probabilities in a discret model not just in terms of the Taylor series approximation or the generalized State space of continuous time model but actually in a path integral formation so that's kind of like there's like a thread that's like the likeliest thing to happen that's the path of least action like the baseball doing a parabola like whether you knew about it right at the beginning with the initial conditions or whether you had tracked the whole baseball it's like it…