Textbook Group meeting for Parr, Pezzulo, Friston 2022 .

okay we're back in cohort 6 for chapter 8 first meeting so enter however you wna do it nice sound was good um yes so welcome today we're talking about chapter eight in the 2022 active inference textbook by friston par and kulo and uh chapter8 is following chapter 7 where we discuss discreet State space models um as we know the second half of the textbook is largely centered around actually designing your own active inference models as opposed to uh primarily verbal descriptions of the theory in the first half so in chapter eight which complements chapter seven we turn to continuous State space models which the authors state are well suited for modeling physical uations and pinging on sensory receptors and for the continuous motion of the affectors EG muscles we used to change the world around us uh we're presented with model examples for the dynamical systems involved in motor control as well as the concept of generalized synchrony and finally constructing Hybrid models for combining discrete and continuous variables at differing levels uh section 8.2 moves on to movement control uh we're introduces some notation for the stochastic equations involved in continuous time models which we'll notice are a little bit different from those in chapter 7 um and then we also differentiate the the symbols between those of the generative model and those of the those of the generative process which is also a reminder that oftentimes we produce models whose um construction is actually rather similar equation wise to those the generative process an example for motor control and reflex arcs uh viewed as descending proprioceptive signals is given which describes how State predictions can be pulled towards these signals like point detractors we also see how action is involved in uh true State changes in uh the generative process to bring outcomes closer to what the model expects and further how more complex forms of these equations are used in more typical use cases uh as with discreete time models continuous time ative models are used to draw inferences about the causes of Sensations B basing and brain and then uh some simple nomenclatures so in continuous uh State space models usually it's X is the new standin to refer to States Y is now for observations or incoming sensory data and U there there are different ways of of doing it but we also have like for example you can use an Omega to to represent um another aspect like different kinds of fluctuations it actually starts so one of the equations starts to look like a like a linear uh equation model so like a yal g ofx plus Omega um so kind of like a yals MX plus b or or an error term for Omega and there there's quite a bit in this chapter so I'll just give a bit of a summation of the rest 8.3 were introduced to different kinds of dynamical system which better rep kind of illustrate the idea of how attractors come to play in continuous models or or or shown the uh lka voltera Dynamics which follow from uh Predator prey Dynamics researched in say ecology or zoology with an example of three different populations plants herbivores and carnivores uh showing a kind of oscillatory pattern between their populations the idea being that carnivores eat the herbivores uh who eat the plants and so they're all kind of dependent upon one another and they start to show these kind of kind of uh non equilibrium like steady state kind of dynamics that that arise over time and it's as if there's a these kind of attracting points that they they arrive around but never actually land and settle there um we also have luren systems talking about things like criticality um then we'll we'll skip ahead a little bit Section 8 4 a very significant Concept in active inference is generalized synchrony they use a bird song example for modeling uh to to illustrate generalized synchrony so the bird song example for modeling communication and multi-agent inference problems uh they're uh the song birds uh take turns singing so…