Textbook Group meeting for Parr, Pezzulo, Friston 2022 .

Hello, it's February 22nd, 2023. We're in meeting five for cohort three. We're in our second discussion on chapter two. Today we'll be mostly looking at questions from chapter two, hearing people's thoughts on it, written or whatever they want to bring up today. And then in the last few minutes, we'll look ahead to chapter three. First though, wanted to note underneath live meetings on February 27th in five days, we will have Thomas Parr join for a live stream, hashtag first author. So it's at 17 UTC for likely an hour. If anybody wants to join the live stream itself, then just email active inference at Gmail and let us know. And we'll add you to the calendar event. If you want to watch a long live, here's the, or share it. And this is like the watch and the rewatch link. And then if you have any specific questions, it could be something that we've already raised, or it could be something more general slash personal. So just before we jump to chapter two, what does anyone think would be interesting or meaningful to ask Thomas? Feel free to think about it or type it here. But basically when the day comes, it's going to be whoever has, thank you, Jonathan. It's going to be whoever's there in the moment. So just email if you want to join on that stream and whichever questions are here slash questions that we've just curated. And then if there's time or if anyone is watching live, they can put a question in the live chat too. So we'll continue to explore like what kinds of engagements with Thomas, Giovanni, and Carl are best for the book and everything, but this is going to be a lot of fun. Okay. Well, we have many chapter two questions. Does anyone have a specific one they want to jump into first or just any chapter two reflection or comment that they want to share? There's totally time to do that if you want to. Okay. Okay. Let's just try to pick off some comments and questions. Kind of just drawing, drawing from the question posterior. How does active inference go beyond the recognition that action and perception have the same inferential nature? Page 24. What do people think? So this is probably referring to section 2.4. How do we go beyond recognizing, well, maybe perception and learning have a similar inferential nature? Maybe we can have a unified framework that models perception and action together. And maybe they even have a unified imperative. I think the simplest answer is they're different parameters. That's how we move past that recognition. They're modeled as different parameters in a unified model. So we want to add another thought or question on that. Okay. Okay, anyone else want to pick a specific question to go to? Otherwise, we have many that we can come to. Okay. Why express potential energy and expected free energy in the space of log probabilities on page 33? Consistent with the notion of potential energy in physics, expected free energy is expressed in the space of log probabilities. Nice question. Any first thoughts? Let's look at where it was in the textbook. Okay. So we're talking about taking the expected free energy of each policy. So equation 2.6, expected free energy over policies. That's sharpening our action prior, our habits, into the action posterior that we're actually going to sample our actions from. Does anyone want to give a thought on that question? Yeah. So I'm in one of my math modules. We're currently studying Bayesian maths. So one of the benefits of using log probabilities is it makes it easier to calculate derivatives when you're modeling Gaussians. The second point was computational benefit. You might encounter floating point errors when dealing with, I think, marginal evidence, which can be very small for some values. So calculating the log version of those reduces the likelihood of getting into encountering floating point issues and precision errors. That's what I'm trying to say. Awesome. Thank you. Yeah. The log is something that's like very simple, whether it's like a log base 2…