Textbook Group meeting for Parr, Pezzulo, Friston 2022 .

all right we're in an open slen session so Adam perhaps begin with the question and then Andrew go for it okay thank you so in chapter seven in the summary it says that um inference using both simple and more complex generative models can always proceed through free energy minimization which illustrates the generality of the approach and my question is about uh whether or not there is a partition function for the model of the minimum free energy State uh and I wanted to note how about in section 7.3 they talk about sorting the states of the world into categories of whether the could treater has control or whether it does not and then it says that the the transition prob ilities for the ones that it doesn't are invariant and then each state that the creature has a control over the world has like a unique transition probability so then it's always going to try to select the transition probability which is most effective at bringing it towards a free energy minimum state right so um that would be the equilibrium I suppose which was making me think about um whether or not there's a partition function yeah so uh it's kind of like to answer that there are a few different pieces going on so yeah with like you can see in that chapter where um let's see page 126 the the just the second page of the chapter you can see like like the breakdown of the the B Matrix as they call it at the bottom of the page and so like yeah you're going to have a unique B Matrix for uh every hidden State Factor um and it's the dimensionality is kind of like um the we're gonna what is the state going to be at the next time step conditioned on uh what you infer the state to be in the current time step as well as um a a policy so it's kind of like the agent will uh you know they'll try to think what can I do now to change what I think is going on now in terms of the Hidden state to um you know a particular hidden state that I I kind of want to see in the next step and I I would say in a kind of all things controlled for kind of way what you said is correct it it will you know go with what the action that is you know most probable uh to get it to a state it wants to be in and that said because free energy is being run across all of these different you know components of the model um it's not necessarily the case that you can just look at the B Matrix and immediately know what the agent is going to do just because one state trans position is more probable than another um when it's Computing expected free energy for example that you know gets broken down into epistemic and pragmatic value um an agent might choose to transition it might choose to do something to make a state transition that it isn't really clear on for example it might compute like oh there's epistemic value there um you know and then if you have your agent like learning and B Matrix those values will get updated over time um so I I hope that that kind of framing is is useful in some way as far as a partition function um so I just want to I want to better understand and maybe it'll be helpful for others too how how would you define a partition function in in the way that you mean it yeah you know what um I don't even really know like honestly I've never actually formally studied um statistical physics so when I like I've asked there's also like a partition function in is it number Theory and I was I asked all over nil about it on on YouTube and he gave me this I'm gonna be rambling on he he sent me a paper that was actually discussing like the relationship between the partition function in number Theory with the partition function in statistical physics in my question to him was was it the same one and he said he didn't really know and I had the paper I was reading it was interesting I forget I don't have it off hand and um in this case I'm kind of wondering like the word partitioning in terms of sorting the two states of the world from the ones we can change the ones that we cannot and then at…