Textbook Group meeting for Parr, Pezzulo, Friston 2022 .

hello cohort one it's meeting 18 we're in our second discussion on chapter seven let's go to the questions and see what we can explore today or see where else to go and or look towards chapter eight but there's any number of ways we can do it so first just on chapter seven does anyone want to uh turn to any of these questions add another question add another reflection or a thought that arose in the last week one question that I um had was are there any ways or sweets for for example taking in an analytical expression and then providing equivalent phrasings that might have other advantages Ali you mean by translating it into natural language or like like what we saw in equation 2.5 and 2.6 like to take in an expression and then output [Music] um isomorphic or I guess not isomorphic but equivalent expressions Expressions that have the exact same value as calculated because some some of the and when we look through the derivation sometimes it's possible to trace the trail but to know which representations of perhaps even the same functional or same term it seems quite relevant actually there's a an AI assistant for deriving formal proofs for mathematical theorems but uh I haven't used it myself but I'm not sure if that's what you mean I'll look at the book the name of that and what just one second I'll post hmm maybe there's a way to um reformulate these um specific terms from like a Bayesian mechanics uh formalism like posterior predictive predicted entropy that looks like something that Dalton probably described as well the question is whether you can just interchange it yeah does working with the particular partition enable equations to be operated with more composably because we can know that there are certain operations that are um like always sometimes never going to be valid I'm just kind of asking I don't even know if that's the threat with a habit um so last time we talked primarily about the um Mouse in the maze and we're going through uh the way that the this the chapter is layering on features of the model so first we saw the mouse just go for it and now we're going to be uh it gets where it gets the queue and this comes to our earlier points about the resolution of the explore exploit trade-off foreign anyone can give a thought while I'm adding it what are posterior predictive entropy and expected ambiguity the part of the decomposition of epistemic value foreign let me just make sure to say the posterior predictive entropy is the expected surprise or the entropy of the distribution of observations conditioned on a policy so we're in expected free energy world we're talking about um evaluating policies with respect to now putting aside pragmatic value we're talking about decompositions of how the informational or the epistemic value of a policy is evaluated so there's two terms here first how dispersed is your distribution of outcomes for that policy one can imagine that all things being equal you would want to select policies that have a tighter distribution of outcomes here we have an expectation interestingly um this is italics e but it's not a fancy e do people think there's a difference that matters or do they think that's a slight error I think there should be a typo yeah I'm going to add it to erata e is italics should be fancy e okay it's the expectation over our hidden State estimates condition on a policy and it's the expectation of the expected ambiguity so entropy of the a matrix functionally how outcomes depend on States so this is saying I want to be I want to be more um is it the case that it says I want to be more certain about observations and how they uh map to policy and I want to have a tighter a matrix Eric so um knife question why is there an expectation on the right and now on the left I was also going to ask this isn't entropy already the expectation of surprise foreign just just so another another point of um clarification for myself that I want to make sure this is right is um the um the O…