Textbook Group meeting for Parr, Pezzulo, Friston 2022 .

of these questions i think we talked about the oh this is chapter two uh let's go to chapter four okay so we talked about belief policy state i'm not sure if we talked about this question [Music] in the discussion of active inference in pomdp belief updating about policies we find that the posterior that minimizes the free energy does it posterior at time t oh we did discuss this yeah we did discuss this last time so uh this question i think um we did not discuss pi being a policy or a model last time or did we i think we didn't get to this yeah i don't think we discussed that all right so we can open it up and um we'll start here i guess with the the most upvoted so the question reads what is pi on page 69 the authors write at each time step the current state is conditionally dependent on the state at the previous time and on the policy pie currently being perceived pursued then on page 71 they write thus we can interpret the priors of equation 4.6 combined with the likelihood of equation 4.5 as expressing a model pi of a behavioral sequence so which is it policy or model and then they suggest a rewrite of the sentence they say that thus we can interpret the priors of equation 4.6 combined with the likelihood of equation 4.5 and the transition probabilities b sub tau pi as expressing a model for a behavioral sequence where the model is a function of policy pi and then there's some discourse here so in this reframing can we say that the model simulates the agent in the environment as as if it had taken the actions in the policy um and i don't know does anyone have any i don't know who asked that question um oh eric that was you that was your question uh and then does anyone want to maybe take a stab at answering that question or we can continue reading what was written here uh so what's written here says that on page 69 the authors also say policies here may be thought of as indexing alternative trajectories or sequences of actions that could be followed on page 71 they defined the likelihood in equation 4.5 as a matrix a that expresses the probability of an outcome they describe the priors of equation 4.6 as the prior over the initial state vector d and beliefs about how the state at one time transitions to the state at the next time matrix b and they also say that the transitions are conditionally dependent on the policy chosen because of this conditional dependence we can see how the policy influences the model and why the authors use may use these the terms interchangeably so does anyone have any comments there um i guess i would say that that um answer in discourse kind of um agrees with my that i proposed which is that strictly speaking um we should treat the pie as policy but it behaves as a model but once it's executed it's implemented then um the model become the model has become a function of the policy that's been we've seen so far so i i'd say that's a you know that's compatible um interpretation so i think strictly speaking um the um it would be better if the text was consistent and called pi a policy and then um say yeah the model is a function of path that'd be my interpretation yeah i definitely agree with that i think that the model is policy specific so so yeah but they could do a better job of i mean the variables as we've seen are so ambiguous anyway so it could definitely be a lot better uh and by the way uh about the topic of consistency um actually i gave some thoughts about the issue we were discussing in yesterday's math learning session and i also consulted some other papers and active inference and in all of them the notation for matrices and vectors is used consistently as in almost every linear algebra textbook so i'm seriously beginning to suspect that every instance of a matrix or a vector not written in boldface is a typo either in chapters or appendices because otherwise i really cannot find any justification behind using two different types of notation so i'm going to use this assumption as…