Fundamentals of Active Inference (Chapter 8, Session 35) August 11, 2026

Welcome back everyone. It is August 11th and we are in the first of the discussions on chapter 8. So if we pull back to the introduction and look at the overall context of the chapters, we are now in the last of the three chapters on the continuous time generalized filtering style active inference implementation. Before we head into the discrete time algorithms in chapter 9 and 10, we're going to be continuing this leveling up of 678. Six, we had the generalized coordinates and all that that entails in the context of just perceptual filtering. Chapter 7 introduced active filtering where there was the possibility or agency over the choice of which autonomous states or external states were under which exogenous forces and how that was one way to conceptualize and model action. And now we're moving into several other cognitive and psychological phenomena and exploring how they fit into this unified approach extending in that trajectory from def filtering. Um I will uh pause there if anybody wants to make any remark on chapter 8 overall as we kick this off. Okay, I'll insert a brief commercial message [gasps] for uh work that I published yesterday, which is a uh 600 or something part skill oriented learning mesh that's built on the skill tree framework. It's available at the active inference institute GitHub active skillfronts. I'll put it in the uh chat. There's a publication and then there's the codebase. In the codebase as per usual style, just go into the top level and tell your agent to run it or just do dot /run.sh SH and you'll pop up like a really cool web application with this kind of micro um skill learning environments for people who are curious about structured curriculum and different paths and having quizzes and access to different materials. Just wanted to mention that since we're in the textbook group. Okay. Anyone want to start with a remark or a question or a section of eight or just any remark on where we are in the book so far? Very cool, Andrew. Didn't know that. Very cool. >> Thanks. >> Y >> yeah, we've had continued conversations in this group where people have been interested. Kobus and Frasier and others. So, yeah, we just put this out. It'll be presented at IY and um full open source repo. Um no requirements to use like LLMs or anything like that. It's just kind of notebook style tutorials. Um different drone and Atari style like game demos that are there. So yeah, for anyone who wants to check it out. >> Nice. Nice work. Okay. So, let us go into chapter 8. So, head over to page 179 and we'll start there. Okay. So, as mentioned, we're continuing in this sub series of chapter 678. Chapter 6 introduced us to generalized coordinates and the concept of filtering as perception. Chapter 7 introduced action as a way to build on that generalized filtering model and introduce the possibility for action selection. And now we're going to take it in several extension directions. Also, when we look at this topic map, we notice that there's a lot more other chapters mentioned, which is not the case for all the topic maps, but it reflects how this is building on a lot of prior work. Um so we we can enter in at different places into this image but let's start with a generative model which we know is like the statistical probabilistic representation of the agent or system of interest to the exclusion of the generative process. So this is the agent side that's being modeled the perceptual internal cognitive and active autonomous states. Um, we learned in chapter 7 that those active states are the outwardfacing emission surface essentially of the markoff blanket of the generative model. So that's kind of just a little review appendage. If we walk back upstream, we can see and remember that in chapter 4 when we were first introduced to variational free energy, it was described as a way to minimize this tractable bounding heristic in the process of recognition dynamics which is to say the observation of observables and then the reduction of uncertainty regarding unobservables. observation of thermometer measurements, reduction of uncertainty about the temperature in the room and those updates to beliefs about latent states are can be described as changes of unobserved variables of the generative model. So it's explicitly modeled in that sense. It's observable to the software but it's not a direct observable to the agent like the temperature in the room is not something that's observed. thermometer readings are are observed. And then this um notion of free action which as the side note will disclose to us is hilariously confusingly named with the same word as active states. But free action is not active states and that's going to be differentiated with the notation call out as well. But it's like a integration through time of variational free energy which is also a very important doorway to go from a sort of snapshot statebased variational free energy minimization into more of like this gauge trajectory fiber path formulization of basian mechanics. So it's just like a little bit of a placeholder for a wormhole that will take you from state-based in instantaneous energy minimization techniques into path and trajectory and gaugebased techniques to come probably more in the next book. So that's this upstairs part. Now chapters chapter 8 is going to develop two important directions of extension to the active generalized filtering model that we saw in chapter 7 and those are going to be relating to broadly hierarchies and time scales. So first on the hierarchy direction, uh sections 8, 2, 3, and 4 are going to go into these hierarchical forms of the model, which is just stacking more layers on top of each other. And at a sort of intuition level, this is what it looks like to have these multiple layers. If people are familiar with like um thousand brains and Jeff Hawkins or just any number of other works that look at hierarchical compositionality for example in the mammal cortex it's very related to this hierarchical predictive processing hierarchical nested bay where the descending predictions of one layer become like descending for another layer and the ascending get pushed up. We'll look at that. It's a way to encompass multiple scales within a modality. So for example, if we were going to model years and we wanted to make a model that had a scope of 100,000 years, we could have 100,000 clicks of a model that went one year at a time. Or we could have 100 clicks of a model that went a thousand years at a time and then each thousand-year bucket broke down into 10 of a 100 and so on. And so there's this structure learning question. How do you break down even just a string of years into a hierarchical model? Is it better to have a wider model that's shallower? Is it better to have a taller model that's more narrow? That's kind of analogous to the question of neural network architecture in this state space model setting. Also, hierarchical models can be of different modalities. So there can be a lower level modality that could be something more like motor processing like propriceptive sensory input and descending motor control and then a second order of that model which is more like a cognitive decision-making layer. That's kind of a common strategy is have like a lower level continuous time model that relates to motor control and propriception and then have that sending messages up and receiving messages down from more of like a cognitive decision-making goal setting discrete time model. So hierarchical forms are going to turn out to be super interesting from a neurobiology perspective and ability to improve the computational characteristics even working within a modality by reducing state spaces that are otherwise going to be very computationally punishing and provide this really cool compositional way to integrate models across different modalities. In 81, we're going to explore this second branch, although I guess it's first in terms of the chapter of multiple time scales of learning and adaptation. And there are three here, perception, attention, and learning. And so it's important to note how these terms are used here because otherwise like learning might be used in a more broader like statistical learning machine learning setting just to mean all parameter updates are learning. So it's like yes there's a sense in which learning is going to be used to refer to all parameter updates period. Especially for this section though, it's important to note how are perception, attention, and learning different and how does that relate to these sort of zeroth order, first order, and second order parameters of a generative model. And the sort of short version is that perception is the short-term updating of beliefs. For example, about food particle size given the light intensity or about temperature in the room given the thermometer. So it has to do with instantaneous single observation at a time updates of belief about hidden states with respect to new observations coming in. So that's like flow forward just regular runtime of a neural network. Then I'm skipping to attention even though it's a second order parameter because it's slow relative to perception but it's faster relative to learning. And attention, as we'll explore, has a lot to do with shifts in salience or even relevance that happen slower than the level of updating beliefs on a first order level, but slower than what is called learning, which are like fundamental constraints about the setting. So, we're going to go into more detail on what those three layers are and what happens when you fix one or two and let the third one go, which is commonly the case where it's like you'll have learning and attention fixed and then you let perception rip. Or you'll have learning fixed and then you'll let attention and perception rip. Or you can do this sort of like less constrained simultaneous inference on all of these as part of a unified objective function. But that's studying something very different. Like it's one thing to study an animal that already knows how to walk and then it does inference on movements versus like motor babbling with the animal learning how its joints relate to propriceptive feedback which is what happens when you open up learning. Any thoughts or like other pieces at the kind of chapter a overview level anyone wants to add? Yeah, just uh yeah, the the way the textbook describes it, this generally holds in a lot of other uh literature on active inference and where these things are sort of conceived or conceptualized is um so hidden states t and hidden state estimation is part of this like triple estimation of of hidden states and and parameters and precisions. um tends to align like it it's [clears throat] it's neurohysiological like correlate would be at the rate at which we frequently might uh record or do ne neuro imaging with like EEG or EMG and so it's just like a very rapid fast-paced sort of inference um allowing for you know recognition of different kinds of potential changes in the hidden state of the environment uh and then after that perhaps at the level of seconds and and largely in line with the notion of like neurom modulation uh and and neurotransmission. So a lot of different pre uh pre precision updates get aligned with with uh this idea of attention in a sense of um you know being able to sort of amplify or or dampen the impact of prediction errors at different places within the model. And so it's as if uh as Daniel used the word salience earlier um one is sort of like attending more or less to particular streams from which from whence one is kind of pulling information when eventually leading up to this sort of integration where we're we're computing variational free energy. Um and so precision uh there there are these different precision terms. They've been uh viewed differently for those who are interested in sort of the neuroscientific literature on this. Um there's a precision on on policy inference which is something we'll get into more later in the textbook but it frequently gets related to the notion of like dopamine or dop do dopamineergic pathways. Um and then uh precisions on likelihood get related to serotonin. Um there's definitely more in the literature to to kind of ponder about all of that but it's it's very interesting. And then finally learning is expected to sort of happen over a much slower period of time usually in the span of like days or years is how Sanjief says it. Although of course whenever you actually implement all of these in your own algorithm um you obviously do not have to uh explicitly set them to uh you know the same time scale in in reality. It depends on where you're employing this. If you were trying to do this for for empirical work with like human beings for example then then maybe you would try to actually strive for that sort of empirical uh uh replication but um you know of course you don't have to have a model that only learns after several days or years um you know its parameters. So it's um but in any case it just seemed relevant to to yeah bring up and and sort of how now we've brought a lot of things from preceding chapters. We've already known about perception since chapter 2. Attention and precision uh came in chapter I believe five and then learning was chapter 3. So really chapter 8 is just a big culmination of a lot of things we've seen thus far just before we switch entirely over into discrete state space models which will be quite different but that's for two weeks from now. So >> great comments. Yeah. Perception in the neurobiology setting corresponds to like action potential mediated standard forward communication of neurons. Attention corresponds to neurom modulators like dopamine or otherwise at the syninnapse. Learning corresponds to changes in synaptic strength or even synaptic topology. So it's just kind of interesting that we have this very nice analytical separation, time scale separation, biological mechanism separation. Yeah, Ahmed. Norepinephrine too definitely. And in invertebrates there's tyramine and all these other more important biogenic amines. So totally um and that's like one way that people do precision psychiatry and related systems biology modeling is like look for some algorithmic correspondence to biomarkers. Okay. So in um section 1 8.1 we can just look at that first sentence preceding chapters have underscored the versatility of the VF loss functional. So that hits a big theme which is like all of these diverse cognitive phenomena across different time scales of course different systems of interest the game is going to be bringing them into a variational free energy minimization setting. So variational free energy has this ability to compose across different phenomena which makes the numbers not directly comparable across those settings but within a given model it's extremely informative. And so here we work our way towards this triple estimation problem which is like this stream of information is coming in and you're learning even if we just consider this in a perceptual setting not with action in the loop like a kind of chapter six setting we're learning multiple layers of what um the signal contains or of ways to parse these kind of layers or time scales of inference on that stream. Like if we were trying to parse out what words the radio was saying, we would like of course want to parse those. That's the first order. But then we also have this layer of like the pace and the timing just loosely using the metaphor here of how the words are spoken when to pay attention to what frequency bands and then even at the slower level that's like presupposing our knowledge of the language and of how sounds map to phone and phonemes maps to words and so on which might be interesting if you were studying language acquisition but if you were just studying somebody who was already fluent and just listening to the radio. You might take learning for granted and just focus on their attention and perception. Um, in section 81, which is relatively long, we get to um something that should be pretty familiar in terms of approach with equation 88. where we have a um free energy variational free energy omitting the terms that aren't part of the lelass approximation optimization. And then right below the equation, each of these terms is a precision weighted squared prediction error for the random variable of interest with init additional log precision term. So it's just like how the linear regression was the sum of squares of the residual error and that's how the linear regression fit through a scatter plot in the standard regression setting. Here we're doing something similar to take a unified kind of like L2 norm if it were a linear regression except that it's a free energy loss function and it is precision weighted squared prediction error which we saw in chapter 4. On the next page in section 812, we get these three time scales stated again the fast changing which is the mu subx and that's what we've been talking about in all the previous chapters updating beliefs about the temperature of the room from the thermometer. Then we get mu sub g xi lower case I believe um that quote track slowly changing contextual effects that lead to changes in hidden states. So um there's all kinds of settings you could imagine that's important. But if there's like some sort of oscilly wave and then the inference is like the faster ripple on that slower wave. Then there's the third layer which is the very slowly changing which is corresponds to learning in this specific narrow sense of learning which is mu sub theta and those are brain states in the brain um or just model states that track very slowly changing nearly invariant properties of the environment such as physical loss. They correspond to long-term weakening or strengthening of connections between and among synapses. So those are the ones where if you're studying like how domain knowledge comes to be acquired like how a world model is bootstrapped you would open that door to learnable uh use sub theta or if you just wanted to study like a learned or skilled agent dropped into a situation you would probably pre-learn or give parameters for that and and fix those and focus inference on just the short-term kind of behavioral trial like single trial behaviors. Um in page 184 we get several pretty important um big mathematical topics. Um 811 is going to describe how those three time scales that were just described, right? The um x, c, and theta can be factorized according to what is called the mean field approximation. which means quote the variational density could be factorized into independent distributions for each of these variables of interest. So let's just say that I'm going to roll a 20-sided die, a six-sided die, and flip a coin. So I have this joint distribution over three variables. [snorts] One of them is going to be a number from 1 to 20. One of them is a number from 1 to six. And then one of them is heads or tails. So that is a quite large joint probability space. It's like 20 * 6 * 2. So in a setting where those three things don't influence each other, they're just conditionally independent, we can factoriize that joint distribution from a three variable joint distribution with a state space size of like 6 * 20 * 2 into just three separate distributions with a state space of 26 and two. So this is a heristic that can take a pretty thorny joint distribution and carve it up at the joints to reduce the state space which otherwise if considered in its kind of full joint richness is going to become exponentially large. Now, if there are intersectional or causal effects, like if it is the case that the the the number of on on the on the six-sided die influences the 20sided dy's outcome, the mean field is going to lock that information. So it's um an example of like where you have these two extremes which is you can consider all the variables in a joint distribution or you can take the full mean field approximation and have all the variables considered separately or you can do partial factorization where you can retain informative joint distributions while partitioning off distributions that are non-interactive with those joint distributions. So it's a vague topic. A lot of it happens under the hood. A lot of it matters more when you're talking about like the performance of these algorithms like the computational complexity and how their performance and resource needs scale with respect to state space sizes. But that's the big idea here of mean field factorization is like of course the fast inference, the neurom modulation and the learning are part of the same integrated biological system. But from a map math modeling view, we're going to instantaneously model them as not influencing each other in the sense that whether a given observation or another comes in, we're going to treat that as not important for the attention inference. And whether the attention zigzags this way or that way instantaneously, we're going to treat that as unimportant for the slower learning rate. That's what meanfield factorization does here. So it takes what would otherwise be a sort of exponentially increasing joint distribution state space and breaks it up into these more tractable even parallelizable smaller substate spaces. [gasps] Okay. just a few centimeters lower down we hit another big topic which is the free action. So first read side note 7 on the left side. So, Sanjie writes, "Confusingly, free action is sometimes referred to as simply action in the AIF literature and and more generally, but it is distinct and entirely different from action as a control signal, which is like the everyday sense of action like taking an act. The term free action is chosen to be analogous to Hamilton's principle of least action, a key quantity used in Lrangeian mechanics. But as you'll learn if you explore mechanics and basian mechanics and all this least action again it doesn't mean lowest possible movement. It doesn't mean do the least. It means minimize this term called free action. And so to really make that clear that action is the integral through time. That's the integral dt. It's kind of like the book ends of the integral. So we're going to integrate through [snorts] time given time interval this expression or functional which is the variational free energy of observations and the three layers of learning or perception, attention and learning. Three layers of perceptual updating and free action is going to be symbolized with S. Um that leads to several very nice mathematical steps which bring us to 8 18 where we have um this numerical integration scheme for the univariate setting. And we'll notice we have those three layers of inference. Perceptual with the latent states, first order parameters of learning, the slowly changing, and then the second order parameters of attention plus these primes on the first and the second order. So this is quite a consilient equation. Um, algorithm 12. Andrew, go ahead. Actually, this is just a a more general thing. Um, given like I've had a lot of familiarity with continuous models, but but here I was a little interested in the choice. Um I'm I'm supposing that the reason why we're including the uh we're doing estimations of not only the means of the parameters and the precisions but also their respective first temporal derivatives. Um I suppose that is what gives the model a sense of making predictions about if there are contextual changes that might be going on. And that is to say like it gives it that extra degree of depth of being able to sort of see if the environment is changing. Are our parameters themselves actively sort of changing um as well as precisions? And that's what potentially allows for the idea of we have multiple time scales sort of operating here whenever we look at how we're playing out the the algorithm overall. But um that that's been my sort of sense of of why we're doing this. Absolutely. Like right below 817b it says mu theta prime and mu g prime can be thought of a prior that the changes in the parameters or precisions will be near zero. So um we don't have that for the standard first order perception. So we can think of that as kind of like unclamped. We're just doing regular basian updating on perception of latent states. And then for theta and for for she we have both the dot which is the rate of change and we have a dot prime and that dot prime which is a move that we've seen before. Let's just focus in on the theta. So that slow learning parameter. This is how does free energy change with respect to those first order learning parameters as dampened by a learning rate coefficient multiplied by those parameters. So this gives a sort of dampening or tuning knob so that the second or the first and the second order parameters the learning and the attention parameters can be also kind of unclamped which is to say like just doing B optimal updating like perception or they can be more slowly clamped so that they have a dampening effect so that the perception is taking up the slack. So those are some pretty big very deep topics and we get to algorithm 12 and example 8.1 which basically go through like what does this procedurally look like and we see a sort of pattern we've seen before [snorts] where we initialize the state spaces and then we have some loop where the generative process is basically just going to transition emit transition emit transition emit. Generative model the agent side is going to calculate the gradient of the variational free energy with respect to these three layers of inference the x theta g. Then we will define the flow over those five different um they they are rates of change I believe kus they're just the flow over them seven hidden state updates perception then do first order updates learning then second order updates attention or you could do other orders but these are just what to it recalculate the prediction errors and then the VF and then the next observation comes in. So this is like a VF that could include action, but here it's actually just pulling back to again a perceptual example. Okay, so that was kind of the beefy um section 8.1. That was this whole downstairs part. This idea that even for a primary inference problem, we can pull back the curtain two layers and look at learning which are first order parameters that are slowly changing super slow and then second order parameters attention which are an intermediate speed updating. Pretty cool. Okay, then continuing now a little bit faster to this 2 3 4 section. But write write a question or raise your hand if anyone wants to ask. Um, now we're going to take a different approach to a complimentary approach to encompassing multiple orders of change within a given generative model. And this one is going to be structural. It's going to be related to developing hierarchical models. So here in figure oh 8 point I might have made a typo with the figure numbers. So we'll check. Okay. This is 8.3 though. It is okay. Oh, wait. Okay, this one's actually 8.3, but the page numbers and stuff, I just made a few typos. We'll fix it. Um here we kind of have a call back to the previous chapter where we have latent state emitting observations that observed with this action that's forcing the latent state. So that's just reminding us about single layer generative models. And we get 8.5. Oh man, I'm very off with the numbering. This one's actually 8.5. Um where we have all the edges drawn. Um and we see the um latent state as well as the attention and the first order learning parameters. So this is kind of like building out our sort of simpler version of just latent state emitting values for observations. Now in this middle row we have those zeroth, first and second order inference time scales that we just discussed in section 8.1 and we have action. So we have the chapter 7 maneuver. So this kind of gets us onto the same page for a active generalized filtering model with these three layers for the triple estimation problem again which you might leave fixed or you might leave open to inference. And section 822 is going to take us to figure 8.6. where if uh if you ignore the top Tetris piece, you have literally just what you had in the previous visualization. Here's that same row with the the zeroith first and second order inference. Um, this looks like a typo in the PDF with a bracket that's unclosed. And also, if you look at the caption, it says, note that y is defined as v 0. So, it's kind of weird in one way to say, well, we're going to call v. The the important thing is that the gray means it's an observable and we're just going to call that observable v 0 which gives us notational continuity with stacking these models rather than have like y at the bottom and then have vub1 v2 v3 but this is basically a hierarchical vertical composition of the generative models so that what was that exogenous force Action coming down for the first layer model is itself emitted like an observation from the second order model [snorts] second hierarchical level. Exciting. Very exciting. And then as we start to see Sanjieve up to some of his tricks again, 832, what do we see? Llas approximations of a little bit more sophisticated, but the V is again the observation. And we have essentially a weighted free energy functional of these exact same components but summed over the number of layers. So it's just like we were looking at in here. here in 88 and the difference is now we're summating it over all the levels but we still see an observation on the left which is V but that is equivalent to Y here zero order perceptual first order learning second order attention Um section 83 goes into recognition dynamics and brings up what is um some more neurobiologically grounded um model architectures. Again like thousand brains and other work has explored how the cortical columns within a cortical column you have like a prediction error unit and then laterally across or among columns you have hierarchical relationships. And so that allows for this flexible compositional hierarchical multicolumnar neoortical inference architecture in mammals. Um section 84 goes into the complete active generalized filtering algorithm. So that is figure 88. So okay this is that's this one. So here we have that V observable and then we have the three of the zero order inference, first order inference, second order inference and that descending V at the higher level. So here we have the vertical composed stack and then here it is unfolding through time where um tao and t represent basically the absolute and the relative time step. Um Andrew, >> yeah just in reference to that um 8.8 and eight you were just showing um yeah I just want to provide like a little bit of the intuition of like whenever we've seen the phrases um ascending prediction errors and descending predictions um I think it's visualizations like this that help give a bit of a a better understanding of you know descending meaning to come down just as here we're seeing in these higher layers um you know they they make their predictions and send them down to the lay the layers below. Whereas with the lowest level here, we're using zero indexing. So you can think of L equals 0 as the first or lowest uh layer. And typically it's the lowest layer that we would assign to being the one that sort of interfaces more directly with the environment. Um it's we can think of this as at the lowest layer we are sort of bringing in or sensing observations which then leads to prediction errors which then gets sent upward. And so that's sort of where this terminology of ascending and descending comes from. Of course there are like many many potentially arbitrary ways that one could choose to sort of produce a model reflected in a factor graph like this. So it's not necessarily that you do it exactly like that, but that's been the typical implementation is this lowest what's conceived as the lowest level is what directly receives the raw observations and it's everything at the top that's actually sort of architecturally further removed from receiving those observations. So most of what they can do is just sort of receive the uh the the the prediction errors from below to update themselves as if those as if the higher layer layers aren't observing the environment directly. They're just observing whatever's going on at the lower layer, the layer immediately below. So yeah, again, you could you could do this in many different ways, but this is the general way it's been conceived. And then as Daniel said, it gets aligned with the idea of like these different sort of cortical columns uh in in the brain and and sort of uh superficial and parameal cells and what they generate. So um and the the 2022 textbook is a really nice resource on those kinds of dynamics too in chapter five. So I pop that in the chat for anyone who wants to see that. >> Great question. Does arrow direction suggest dependency? I'll just copy this to the chapter eight. Um, or does it illustrate connections? The answer is like a little bit of both. When we talk about a diagram, first off, there are diagrams that are just informal associative connections like a topic map. And then there are diagrams that actually represent a causal graph. And um those connections are causal. And the simplest way of causality being modeled is basically like depending on X, what does Y how does Y differ? And if changes in X don't change in Y, it's not a causal variable. Whereas if changes in X influence Y, which is to say there is a dependency like Y given X. So that is the relationship between the topology of connection and dependency as causality in this setting of causal inference. Um figure 8.9 we see this um multi- columnar hierarchical inference and it's broken out into the top down predictions and the bottom up errors. That's a common neuroscientific paradigm. Algorithm 13 is all of page 200. That's a big one. That's a big one. Um, we get 810, which is a beautiful expansion of these different update rules and motifs within this pattern. And so you can imagine in something like ngcarn or rx infer where you can control the topology of different units, their semantics and the scheduling of their updates. you can really have a lot of control over. For example, well, we want to update the autonomous state first, then the then the error, then the, you know, you can schedule things in terms of which updates happen on what kind of a clock or what kind of a conditionality. And many of these, but not not exclusively, reflect known neural circuit topologies. So that's like a nice to have because a given computational architecture might be under such different constraints than a biological architecture that they just have different morphologies to do even analogous functions. But when we do see the computational architecture recapitulate the topology of the neural circuit, it's a very interesting finding. Um, the next several images, including the massive 815, go into even more detail about these different variables within a layer and different messages that are passed within and across layers. Then 81 16 gives us this unified view on the objective function and the flow functions for those layers that we've been discussing. And 817 is like almost as full as we've gotten in the book in terms of like all the variables written out in one image where we have a super top level single line per node and then this like very detailed variables. [snorts] And then as uh usual, the closing pages um summarize what the chapter did. And then the last two paragraphs mention some related literature and the last paragraph connects to salience. So it's a dense challenging chapter. There's a lot of notation. However, if we focus on these two branches, 81 introducing these three time scales of inference within a layer, the triple estimation of perception, attention and learning and then different hierarchical compositional methods within and across modalities. it gives a lot of sense to the chapter. So if anyone wants to ask a question or a final thought otherwise I'll stop the recording. >> Yeah. Uh from previous sessions I learned uh you know from this active process. So I wrote like uh execution logic for testing this I mean how to reduce a pred predive error and it just a little slower. >> Wait wait wait just just a little little slower please. And then just first off is this related to the textbook. >> Uh it's related to test I mean textbook but the the things that we learned from the previous sessions and also from the facial >> okay it's a little slower but go ahead ask the question. >> Yeah it's not question. So the thing is that from the things that I learned like uh perception changes, belief and those things from that I wrote a small execution logic for using using that same things as a you know engineering way like uh logical way for uh you know robots and autonomous system. So I published it on Zeno. So could I share it like you know? >> Yeah, put it in the chat. >> Absolutely. Put it in the chat. >> Okay. Okay. >> Awesome. So from this uh from this we can and also there's one more link too. So wait a second. >> Okay. >> Yeah. Wait a second. I will copy that link. >> Okay. If there's a question please ask otherwise anyone who has a question can ask. And yeah I mean and anyone in this session can test that thing actually because I I provided a way there called an appendix lost appendix they can input their own uh you know they can give a to the robot and they can give to like a next robot. So >> great >> and >> great awesome I hope people check it out if they are interested in it but absolutely how to apply this to embodied motion and language is critical >> then and also you can provide your own scenario so you can it's to find like where the robot breaks from not being a human I mean like not being a social human like for instance it's it's supposed to be the robot supposed to be similar very similar to how actual human beings supposed to handle situation. >> Okay. If there's any question or comment on the textbook otherwise I'll end the recording. >> Yeah, of course. >> All right.