 ond dyweddod yn y cyfnodol, gyda'r fathodol, ac yn gweithio'r perthyn. Fy fydd o'r ffwrdd, nid ydych chi'n ymweld y prinsifol mathemataethau o ddweud o ffuntiwn o'r hyn. Felly, ddwy'n hynny'n gweithio'r ffuntiwn, ond ydych chi'n mynd i'n fod ymweld o'r llai o'r llai o'r reid o'r dynwys, mae'r lleidio i'r ysgol yma yn ymddangos ymdweud a yn ystyried yn y gweithio. Yn ymddangosio'n ddylch gael, y byddwn yn ei fath o'r ysgol, ac mae'n rhai o'r cyffredin, ac yn ymddangosio'n ymddangosio'n dechrau i ddefnyddio'n ysgol. Dw i'n meddwl i'n gweithio'r llor yn ymwyf yn ymddangosio, ac mae'n meddygol o'i cyffredin ymddangosio, ac mae'n meddwl i'r cyffredin. Now have you all read this? I will be asking questions. This is what I'm going to be talking about. I go to introduce the question at hand and then provide this answer in terms of something called active influence. Closing related to things like active learning, machine learning, or active vision in the visual world sciences. This is putting perception in an inactive context that we are actively perceiving that we are in charge of the way that we palpate or sample the world in order to optimise our perceptual synthesis. I'll show you that mathematically that's just the same as gathering evidence for one's own existence although I've explained that connection in about five or six months. All of this self-evidencing, this active perception, this active influence, rests upon predicting worlds activities, having a model of how the world works gan y gwaith o'r cyfnod yma sydd wedi'i bwyd i'r serffynol. Mae'r serffynol wedi'i bwyd i'r sefydliadau ar gyfer ac mae hwn yn ymgylch yn ddechrau. Mae'r modd yn cael ei wneud o'r rhan o'r gwaith o'r gwaith sydd yn cyfnodol, oherwydd oeddi'n gwybod i'r modd. Felly, rydyn ni'n cael ei wneud i'r modd i'r modd o'r gwaith sydd yma hwn yn dweud yng Nghymru i'r bobl yma, i bwysig o'r bwysig, a'r gwahodau o'r ffawr o'r gwahodau mewn. Er bod yn talw'r mewn gwahodau, bod yn meddwl i'r bobl yn dweud yn bwysig, oherwydd, mae'n gwneud ychydig o'r ffysiologiadau gyda'r Gweithlacholau. A dyna dwi'n ddewch ar yr adeiladau cynghwilol. Yn ddewch, mae'n ddewch ar yr adeiladau o'r adeiladau cynghwilol, some deep generative modellings that have a deep hierarchical structure. Both in the buildings of abstraction, but also in terms of time. Exactly those sorted models that we would need to generate language. I'm going to turn that on its head by saying that these are the modules that we use to understand language. Mae'r gwaith mi o dechrau yn cael ei wneud i'r llei, ac mae'r reisio i'r cyffredin awtfyrdd. Mae'r cyffredin awtfyrdd hwn yn ei dweud o'r gyffredin awtfyrdd, ohon nhw, yn cymryd i'r cyffredin awtfyrdd, oherwydd mae'r cyffredin awtfyrdd hwn yn cyffredin awtfyrdd hwn yn cyffredin awtfyrdd hwn. Ond ydych yn ymgyrch i'w fath, a yw dwych yn ymwneud, ondo dyna'n gallu chi'n unrhyw. Y maen nhw rydyn oddi am urch, a yw hwn yw hwn. Mae'n ddigon nhw'n edrych. Dwi'n ddigon nhw'n edrych. Dwi'n edrych. Dwi'n edrych. Mae'r un cyfnod cyfnod yw'r cyfnod. Mae'n rhan o'r cydwyr o'r hynod o'r cyfnod ar y ddechreu. Yn yma, mae'r hwn yn cyfnod, a mae'r reiion yn cyfnod o'r cyfnod. Yn chi'n ddwy'n edrych, yna'r ystod gyda'r hyn yn oeddodd o'r ddweud o'r ddweud o'r ddweud yma, ac mae'r ddweud o'r ddweud o'r ddweud o'r ddweud o'r ddweud, mae'n rhaid i'n ddweud o'r ddweud o'r ddweud o'r ddweud. First of all, we could write down an expression for things that we do control variables in engineering, which of course you know at this point in time, as maximising the value of some states of the world if I did that thing, and then what I would be able to do is to create a policy pie that for any given current state if I apply this action, I will move to the next state, and then I will maximise the value of being in that next state. So this is the notion of a value function of states to be rise to a state action policy. It requires you to believe in and commit to the idea that for every state there is a label which tells you how valuable that state is, and then all you have to do is to choose the action that takes you from this state to the most valuable state. But that's not going to work to explain searching. For the simple reason that searching is all about reducing uncertainty, then we know immediately because uncertainty is an attribute of a belief, it's not an attribute of a thing, it's an attribute of a belief about something, then the function that we need to optimise has to be a function of a belief, and if the belief is about something then that's a function of a function of something. So what we actually think of the alternative way of doing this is that our best action at this point in time maximises a function of beliefs about states of the world if I did this action here. And I'm going to describe this belief in terms of probability, a posterior probability distribution over different states. Again, don't worry about the maths, just remember that the Q is a probability belief and that gives a very different sort of optimisation state. So I've moved from a value function or states of the world to a function of beliefs about the streams of the world. Further more, the notion of searching tells you of something else very important, it means that it matters whether I search for my brain and then I eat it, or I can eat it and then search it. So time and order really doesn't matter, which means that you can't just write down an object of function as a function of beliefs. You have to define a policy which is a sequence of actions in a particular order. So now what we have is a notion that there is a best policy that entails or prescribes a sequence of actions in a particular order in machine learning or control theatres and sequential conceptisation. For us, all it means is that we know that the best kind of policy, pi, star, n, maximises the sum of this functional, and I'll say that it's the free energy functional of beliefs to give them that particular policy. So these two contrasting ways of writing down formally what things, what living things do, emerge in many different guises, in many different contexts. So the notion that you can explain behaviour in terms of optimality value function rests upon the terminology principle from this to your client. There are lots of examples, optimal control theory, dynamic programming, deep reinforcement learning, special utility theory in economics, apples induction and so on and so forth. Some of these you may have heard outside of which you don't, but they all have in mind this commitment to a value function that can describe everything we do in terms of optimisation. The other approach which is the approach that we are going to pursue is based upon a principle of these actions. So action here is just basically a time integral or a time average of an energy and I've just said, of course, a free energy. So this path is an action and we're going to maximise that action so that we choose the optimum action. This is a free energy principle, also an active inference. From this we will hopefully get along artificial curiosity and intrinsic motivation in robotics emerges. We can also cast this in terms of basic decision theory mentioned before. This is an aspect of sequential policy optimisation. Now I deliberately sort of contrasted classical value function with free energy functions to highlight the value of these approaches of belief based and these are not. But I actually show that they come out together again. So this becomes this when we remove uncertainties. I'll try to start by getting back to your expected details of theory in a few slides. But for the moment let's just focus on what this quantity is. I'm going to give you one answer and I'm not going to motivate if there is a deep math story here from statistical physics and phasing mechanics. But I'm not going to worry about that. I'm just going to tell you what it is. And then hopefully convince you it is a super objective function by a series of examples. So here's the basic idea. This quantity is known as a variational theory information theoretical quantity. I'm quite closely related to something about it here on rough complexity or multilocal complexity. It's also known as an attendance low boundary machine learning. In statistics it's known as the logical evidence also known as rational likelihood. You can forget about all these different names. The reason I'm listing that point is it's a very, very important quantity which you've seen in many of every field. The fact that it's called basic model evidence gives me a license to describe this optimisation of self-evidence. I will see my downloads in a moment. From a statistician's point of view, this negative physical free energy here, this negative evidence or not evidence of a round elbow machine learning, is just the probability of getting these observations over. At this point in time, given a model of how these outcomes were generated, and I am going to beat that model. From a statistician's point of view, you can always write this quantity, this evidence as complexity, this negative evidence as complexity minus accuracy, or log evidence as accuracy minus complexity. What that means is we're going to consider the brain as a statistical organ, an organ that's trying to make inferences just in exactly the same way that human scientists try to make inferences about differencing between one group and another group using a statistic or an analysis of covariance. The brain is doing exactly the same thing with its sensory data. It's trying to test different hypotheses, different beliefs about how those sensory data were caused. It's doing so by maximising the basic model of evidence, which means that it is trying to find the simplest minimally complex explanation that provides an accurate account of the sensory data. That's going to be very important, and the complexity of that is going to be very important. So it's not just finding an accurate account of data, it has to be parsimmonious and simple in the sense of a lot of things like that. So this variation of free energy is just the mathematical expression of this mixture of complexity and accuracy. We imagine that the brain just organises, learns, infers, passes the messages, all in the service of minimising its complexity or maximising the complexity. If that were at the end, then that would be perfectly suitable for a counter-perception. But what we're interested in here is how the brain comes back and actively samples the data that it could use to infer the causal structure in the outside world. And that's the reason it's still important to me. So we've already said that we have to define the problem in terms of sequences of actions or policies. And what we're going to say is that we're going to select loads of policies that maximise the expected free energy after performing that sequence of behaviors. So what that means is we're going to effectively choose policies that minimise complexity, expected following an action, and minimise accuracy, sorry, maximise accuracy following an action. But notice now the outcomes are now random variables. They haven't yet occurred. They are in the future. So now we have to take an average over that, things that could happen in the future. So now we're talking about the average complexity, and that turns out to be risk. Risk, and this is where the equations in my meeting provide the formal definition. So risk is really the needs about what will happen if I pursue this policy compared to what a priori I prefer not to have. So I'll say that again. Risk is the divergence or the difference between what I think will happen if I do this and what I prefer a priori to happen. So here my prior beliefs about the sorts of outcomes that I encounter define the sorts of outcomes that I expect to experience. A rich, happy, warm, having my temperature within the physiological range. All the things that make me he, and a good me, and a happy me. They are my a priori, my prior beliefs about the outcomes that I will attain if I pursue this policy. And the goodness of the policy corresponds to the minimum, the reducing, the difference between what I think is going to happen and my prior practices. That must be that sort of risk, and we'll see another instance of that from an economic perspective at the moment. At the same time I'm going to maximise my expected accuracy. So what would that look like? What does the expected accuracy look like if I haven't actually got the observations that happened? What it means is I'm going to deliberately choose policies that make the sensory data as unambiguous as possible. So if it's up that I walk into a dark room, I'm going to turn the light off. Because that's a policy which means that I can unambiguously see what's going on out there. So to reduce the uncertainty about what to be causing for sensory impressions. There's a table in front of me that's a light over there. But I would not be able to see in an ambiguous sensory context if the lights weren't going off. So this is a little bit like a joke about the man who was drunk and is searching for the keys. And he's searching for his keys under the lamp post on the streetlight. So that's the thing. What do you do? I am searching for my keys. Did you drop them there? No, I dropped them over there. So why are you searching here? Because I can't see over there. That's a clinically based optimal response. And it reflects about that we were part of the drive for our good policies and those which minimise our rigidity or maximise expected accuracy. That's a good policy. Well, sound of an action from that. The actual change in the state of the world out there beyond our sensory market blanket. And that will then supply new observations of what we do. Our perceptual synthesis again. Finally, simplest packet explanation of what's going on. Use our beliefs about states of the world, which are a rollout simulator. Another future, another policy, set the policy that minimises the risk and ambiguity, set the action. And so the perception action or the action perception cycle continues on and on and on. All in the service of minimising risk and ambiguity. Minimising expected surprise or negative free energy. Which is just uncertainty in physics as what's called empathy. But you can remember this as putting these two things together. It's just minimising uncertainty about the future. Where that uncertainty includes preferences that I feel familiar with. So that's the basic story in terms of what is this functional of beliefs that we want to optimise. This is a horrible slide if you don't do maths. But again, please ignore the equations. I just wanted to show you how easy it is to take away from these equations. And end up with a formism that people have been working with for centuries or at least decades and decades. So, if you are an mathematician or a physicist, you will now recognise why this quantity is called free energy. It's basically an expected negative lot probability here, which is called an entropy. And then this quantity, if I put them together, is an energy. So it's basically the difference between an energy and an entropy. So it's the energy that's going to do the work and it's free energy. But just by shifting these things around or grouping them together in a different way, we can interpret it in terms of opacity and accuracy, as we've just described. So all I'm saying here is that there are different ways of interpreting these quantities depending on the words that you use, the constructs that you have taught and you use in conversation with your colleagues. They're all equally mild. Another nice example of just switching things around here, doing this over here and this over here, means there's another interpretation of splitting this uncertainty, minimising capacity of called policies or expected energy here. We can actually carve it or decompose it into another pair of quantities called epistemic value and expected value. So let me show you how that works on. More precisely, let me show you how people have already been using these constructs, these clusters in their work before. If we just focus on these two terms here, what this price falls to is essentially the expected difference between beliefs about what's going on out there if I had some observation in the future. Relative to the beliefs about state of the world without those observations. So what that means is this corresponds to the salience of the policy or the action. It tells me the amount of uncertainty that I am reducing or the amount of information I have gained if I looked over there as opposed to looking over here. So this quantity has been used a lot in visual neuroscience found visual searches and salience maps in terms of the best place to go and sample the world from. It's the place that minimises your uncertainty or that's invited to your information gain that has salience, epistemic afforens. It's also mathematically exactly the same as the mutual information or the mutual predictability or the shared variance between the causes, states of the world and the consequences, the outcomes that are generated by those states. So effectively what we're trying to do is to move and palpate our world out of visually with eye movements, literally with our skin sectors by feeling for example the layout of a new hotel room in the dark. You're testing hypotheses to feed your way around. You're sampling out in the known sensations that tell you, ah no this is a table, not a bed. But you have to have those hypotheses in mind in order to reach into uncertainty and the hypotheses that you are entertaining. And in doing that you're increasing the mutual information between what you feel and what caused those feelings. So that's a very important aspect of this uncertainty reducing imperative, this free energy function of beliefs. Let's make things a bit simpler. So now I'm doing what I promised before, I'm going to get back to the value function. But if you remember before I said the difference between the value function and the free energy function isn't one is belief based and the other is not, I can actually convert the belief based scheme into a value based scheme by removing uncertainty. So the first central centre that you're going to be in is basically ambiguity. I can see there are creatures out there that can see every in state of the world. There's no sensory noise, there are no hidden states of the world. And what I see in my sensory organs, my observations, my mantras are the states that I observe. So esses become bones and bones become esses. And what we are left with is just the divergence of the difference between the predicted and preferred outcomes. This is just our risk again. So this is risk sensitive control in economics. Also known as KL control because this is a KL or called back lever divergence. It's a reductable control theory. This is known as KL control economics, this sensitive control. What it tells us is that this risk sensitive control is basically what is left if we remove ambiguity. Let's make the final move and actually take away ambiguity. So by taking away the risk what I'm saying is that I am equally uncertain what will happen if I do that in the future. And if I take that away we end up with just this term here. So I'll remove this now and now I'm just left with this. So what is this? Well it's just expected utility. So this is what economists use to score the probability of choosing this policy or that policy. In the absence of differential uncertainty both in terms of ambiguity but also in terms of risk. There's a deep history to the expected utility, expected value, both in economics and in behaviourism. Of course it's based on exactly the same idea and some reward or loss function that can ignore uncertainty. And then you will see policy of action selection being completely described by this value function. So the purpose of that was really to illustrate how in general belief-based formulation of the thing that we are trying to optimise, namely maximising evidence based on what evidence from all this in the world or minimising our uncertainty through active palatiation of that world are generalisations of things that we have all been working with for possible action. But you only get to these special pieces if you remove uncertainty. So the belief aspect should now to be pointed if we talk about value functions. Just to make it very clear for those people who haven't come across information gain or epistemic value before, I just want to give you an intuitive example of what it means to reduce, to choose actions that dissolve uncertainty even before you know what's going to happen. So imagine you're driving a car and you are looking around in the night time and you've got a choice. You're stopped at a traffic light and there is a filter on this traffic light that could be pointing right or left and you can choose to either look over here or you can choose to look exactly at the sign. Now if you're wondering about driving, you're going to have a 50-50 belief, posterior belief or pride belief before looking over here that the sign is pointing to the left or to the right. And if you look over here, then you're not going to change that posterior belief. So it doesn't matter whether the sign is pointing to the right or to the left, looking over here won't resolve any uncertainty. You will have a 50-50 posterior belief, whether the sign is pointing to this direction or to that direction. So this isn't the example of a policy that has no epistemic value at all. Concast that with the situation where you're looking directly at the sign and resolving ambiguity and getting very precise sense of information. So now if the sign is pointing in this direction, then you will be 100% certain it is pointing this direction. If the sign is pointing in this direction, then you will be 100% certain it's pointing in that direction. And you know that. And you know that before you've even made a high movement. So that's basically why this K-R divergence, this epistemic affordance, this salience, this information gain means. You can, if you know the way the world works, and you know and have a journey of what are the consequences of your actions, something about that world, you can work out in advance what the best movement is to make to reduce your uncertainty. And that's mostly what I'm going to say from now on, rests upon fundamental imperative, epistemic imperative, that that's certainly reducing self-homance imperative. So that's all the hard work done. Now we're just going to see some pretty examples and simulations to show what it looks like in simulations and hopefully convince you that you've seen a lot of this phenomenology in papers, indeed possibly in your own research. I should say, you know I made a joke about the mathematics and the formula before, and perhaps I should excuse why we use the mathematics so much. It's a simple reason that if you really want to understand something, as Richard Feynman would say, you have to be able to build one. I would be able to build a little creature that does the paradigm to be as per subjects or our experimental animals to do. You need to be able to write down the software and you need to be able to write down the mathematical formula upon which those software are generated. So that's our motivation. It's really to create people in the silicon regions that we can expose to the same experimental paradigms or regions as real creatures and then see what this belief-up data is active in and self-embedding looks like and then we can see the same kind of empirical phenomenology in real creatures. So that's the excuse or the motivation for it, but it does require you to commit to very particular and well-specified models that are used by creatures, living systems, by explaining their paradigm or their world. A very general one, again pleasing to all the equations we're going to walk you through with the graphics on the model, is called a Mark of Decision process. So with this single and same model, we have modelled an entire range of different kinds of behaviour ranging from waiting games to foraging in a team-aise, and so on. That's what we do to reading and seeing exactly what that is later through to active curiosity and problem-solving. So many, many different kinds of paradigms can be modelled with this one very general generative model. So I just briefly take you through to give you one worked example just to give you a feel for simplicity in case in your future work you want to use these kinds of models to simulate your paradigms. So the idea is we need to generate outcomes. Things that can be a creature or something like me would be able to observe, see, hear, feel. And these outcomes we're going to say are going to be generated by hidden states of the world. They are hidden because they are not directly observable. We can only observe our sensations. We can't see them directly because of their sensations. So they're often referred to as either latent or hidden states. And they have a narrative. They have dynamics. There are such sessions and transitions of hidden states. So if I'm in a particular hidden state in this point of time, I will be obviously in this state. The next point of time and so on and so forth. So we have this cascade of hidden states. Each one of these states generating an outcome as time ticks along. And the mapping between the hidden states and the outcome is just a line between the numbers. The probability of getting this outcome given this particular state of the world is usually less by hand. Now clearly the way the world unfolds these hidden states depends upon how I act upon it. It matters the hidden state of where my eye is pointing determines what I actually see. So we imagine that some states of the world depend upon policies. In other words, the transitions between this state of the world and the next state of the world at the next time point encoded by a probability transition matrix B is a function of policy. We've just said that policies are determined by our prior preferences and our added states. And eventually then the prior preferences by C can be done by any cost function. And they will have a certain precision, some confidence associated with that. We've not encountered a grammatical gamut. I won't talk about that very much but it is interesting because it looks very much like don't be the sponsors of the brain. I'll just show you a brief example of that later. And finally I just have to specify beliefs about the initial states or probabilities of the initial states and a few hyperparameters that statistically parameterise it. And with that model I can roll almost anything within reason. A toy model of almost anything. Furthermore, if I make some simplified assumptions about my beliefs about all the unknowns, the key unknowns of course being the hidden states of the world generating outcomes and crucial in the policies. So these are the two things I need to infer from good beliefs about my minimising that by optimising up free energy or that evidence you're about. I'm also going to think about optimising the confidence of my policies. The important thing here, notice that we're casting behaviour here in terms of forming beliefs about what I couldn't do. And then just selecting action from the most likely or the policy that I think I'm most likely to be missing in the moment. It's sometimes known as planning as inference. So it's casting action as a process of inference. So you can actually, if you subscribe to this formulation, then the choice on the selection of what to do next is an active inference. It's inferring. This is the most likely thing that something like he would do in this belief state. So I'm going to be trying to solve that kind of uncertainty over the work towards those sorts of preferences. And you can write all of these particular privatisations down as prize in this kind of objective logic. If you then just apply something that is called the infill approximation, just privatise these beliefs with normal forms of inverted distributions, you can then just go and get some shelf mathematics to describe the belief argument and the message passing, that having that sort of objective model, impedance will be you as a brain. And from my perspective, even if you're not a mathematician, that's possibly not from your perspective, but from my perspective, the results are remarkably similar. And more importantly, not very, very similar to the denouning of some belief update, as you can actually see in simplified versions of breadth. So remember before I say that we were just three things we don't know in this model. State of the world, policies pie and the position of confidence placed with those policies. And it turns out that the solution was to optimise that free energy function can be expressed here as a non-linear function of linear mixtures of beliefs about the past, of the future and observations now. And this starts with a very much like a very simple neural network model, a sigmoid firing activation function operating upon linear mixtures of activities elsewhere in the brain. A very, very simple expression that now starts to provide a metaphor for neuronal responses and belief updated as encoded by neural firing points. Here, an expectation of our belief in a state, one state or another state. Notice also, this implies expectations about the past and the future. So written into this gender model is an elemental form of memory and perspective, post fiction and prediction, memory from the past and the future. So there's a sense of time and progression implicit in this update. If we look at policy selection, it's simply a softmax function of this expected free energy of the goodness of a policy. And this is a classic softmax response rule used in economics and much of the workforce of learning. Interesting with the confidence one over gamma here, it's updated according to something that was very similar to a reward prediction error which takes us off in a very different direction and the direction of dopamine and the relationship with reward prediction errors. I want to move on to optimising the parameters of this model itself. Again, it's very nice because the update rules and solutions that optimise this free energy function are not exactly like them in the way. So you have these functions that have associated here. You can't see those here because this is the deep one. But if we were looking at the A1 and CB, I would come from the states carrying together as a product a decade back here. And we just accumulate it by building a connection sense and then decay again as a function of time. And then finally we have our action selection here. And with these very simple rules, you can start to engineer or propose a very crude or coarse function of natural wear. Observations can take the visual cortex, they are used to update the lease of our states and the worlds, hit a campus at a time. And these release them and use to evaluate the goodness of our policy in terms of expected free energy, the risk of non-reduity. You can code it in the front, off the brakes of the Basil Gangler Court of Life Loots where the confidence in these policies may be mediated by safety only in the ventricic mental area. And then they generate the next action, change the world, gives you the next observation and serve the cycle of the continuous. The very crude, but relatively simple understanding of the covalentation strategy that you get to. I'll close down with two examples, one of the very simple examples of origin in the maids. And then we'll come to a proof survey of advances in deep genealogy models of the sort that have been used to construct things like language comprehension and reading. So this is an example. I don't need to go through it in detail. In brief, all we have is a little rat on our house in the team maids. And it lights rewards. It's got two moons. It can make two moons. And it doesn't know whether the reward is on the right or on the left. What it also knows, though, is that there is an instructional cue at the bottom arm of the maids that tells it whether the reward is on the left or the right. So it presents an interesting choice for us. It can go to one arm, and once it goes to one of the two rewarding arms, it has to stay there. Which means that it can go there and get two rewards on 50% of the time, or it can go there and get nothing on 50% of the time. Or it can go down here to find out where the reward is and then get 100% on 30% of the reward for half the time. So the expected value things that people say. But by going to the instructional cue, the epistemic cue, it can immediately reduce the epistemic part from the expected financial. Which means that if this mass was minimising its expected financial or minimising its ambiguity in this, it should go, if we simulate those equations on the previous slide, when the journal took on which I've written down here to the appropriate for this parallel, it should go and get the incentive and then go and get it to reward. And indeed that's what it does. So it starts off, what I'm showing here, is behaviour over 32 trials in terms of where the reward was when it was on the left or the right. Policy of the terms, the outcome, the amount of reward it got, and the use of that when the reward is on the right or the left in terms of the additional students. What I've done here is after switching the reward up to the first couple of presentations, I then left the reward on the left-hand side. And I want to see what's going to happen. So initially, as we might anticipate, the mass goes and finds the epistemic cue as well as its uncertainty about what to do and then enlarges in its risk of those behaviour. So then chooses the pragmatic preferred option by going straight to get the reward and it's as happy as it could be. However, as time goes on, it now learns that it found the reward is delivered there all the time. So now the epistemic value of that instructional cue gets less and less and less. It's resolved with less and less uncertainty because it's increasingly certain that the reward is on the left-hand side. The left-hand side changes on its experience with head-on learning, learning about these English mistakes through evidence of cue generation and that head-on style of epistemic. So at one point, it changes its preferred policy and jumps to a pragmatic, exploitative policy. So it's got some natural progression from expiration to exploitation, but it's purely a reflection of the fact that we are using a belief-based function. Because the goodness of the thing to choose depends upon my beliefs and my uncertainty, whether I need it to get right back to you or as a search. It depends upon the need of a search and of course they are very familiar with that, but there is no need to search. It has to be a strain for that expected value and to engage in that exploitative behaviour. This slide summarises that in the same point that I've been making. So basically learning underwrites confident policy selection and that confidence is reflected in this precision parameter, which is very much a lot. I don't mean that it can, indeed, really simulate time-to-time updates of this parameter here, but it's always exactly like that. We can also look at the simulations of data brief updates during a particular trial. So it makes a move that sees this, makes a value, but as it sees anything, it has to iterate these equations in order to find the days optimal solution, the stuff evidence solution, and that looks a lot like an adventure-related potential in a geological research. An interesting what happens is that it is less belief updating when it's more familiar and confident about the environment and you get an attenuation of these responses, but an increase in the confidence because it knows exactly what's going to happen. What it expects to happen does indeed happen and how it goes, and it's strong inside about where the reward is. So using that different example, you can tell all sorts of stories. You can tell a story about the representation of the future and the past, so this is the beginning of the trial, the first and second move, and of course, as these beliefs are updated, what are beliefs about the future consequences of action now become memories of our past. So there's an interesting shift of time in the table frames of reference. Things that were once predictions become post-pictures. That feels very interesting when you accumulate beliefs from trial to trial. It also allows you to think about the approach responses to the things that you would ultimately choose as opposed to things that you are not going to choose. There was a nice literature in the empirical papers showing exactly this form of solitary divergence as time progresses in terms of selective responses shown by these expectations in COVID-simulated neural populations that mirrors or reflects exactly the empirical results. We can even plot these responses as a function of where the mouse is, and what emerges from this kind of architecture are place numbers, that sometimes are very unartiguous, for example, the two rewarding locations, sometimes are a bit more unartiguous. We can also perform simulated on-board experiments, especially negativity experiments. So, these are the same results that I showed you before, but I'll now tell you a different story about them using a different language, as if I were an electric physiologist doing popular paradigms. So, what I'm going to do is look at the belief updating when this little mouse sees the same stimulus when it's familiar with it and when it's not familiar with it, does the same response, selects the same policy. So, the only thing that's different between the perception and the action is its beliefs that it has accumulated through experience. And if I associate this with a standard stimulus and this with a normal, a bold policy stimulus, we can comparatively update and take the difference, and indeed we can reproduce the phenomenology of mismatch negativity. Do the same thing with those dem-stimulated domain sponsors and show a classical phenomena in single-unit energy physiology in domain cells, namely a transfer of phasic responses from the rewarding queue, the ad-condition stimulus, to the instructional and systemic queue, which you can think of here as the conditioned students. So, again, nothing's changed here. Other than that, I've told a slightly different story about the results that emerge from this little simulated rat, and all of it lend a degree of concert validity to its overall thesis that everything is in the service of self-evidencing, maximising evidence from my turn to model the world, and selecting actions that minimise uncertainty, namely this phenomena theory. So, I'm going to finish now with a very quick run-through of exactly the same technology and ideas that apply to slightly more sophisticated joint models of a sort that people might use to understand language and generate language. Now, I like this graphic, not because it's educational, but because I've probably spent a long time drawing it. Again, that was a joke. It's a nice graphic because once you bring down formally what you think is driving message-passing belief updating and behaviour, you can now just extend that forwardism by generalising it to hierarchical structures. When you do that, you start to see lots of emerging behaviours that now look a lot more like the kind of behaviours that psychologists study in human beings. So, all we've done here is taken our standard little MDP model, states team over, time on, time to two, generating through the lightning matrix, and now we've come here out with the transitions encoded by the B matrix, depend on some policies pie, that itself, that are informed by the expected theology gene that comes from those policies. What we've done is put another one of these on top. Crucially, it operated a slow attack scale. So, the app comes from the process at the higher hierarchical level now cause things that don't change on a faster attack scale. There are lots of things we could have chosen. We could have chosen the lightning matrix seats or we could have chosen the lightning in particular policy. We've actually chosen here just the initial set. It means that the outcomes from the generating models point of view of the higher level are in play for the duration of the same transitions at the lower level. And you can imagine putting a faster level below this in a faster, in a faster one. So, you're writing in, you're baking in to your generated model, not only a high model depth of abstraction, but also a deep diachronic on time depth, a separation of temporal scalars over time. And of course that's what we need to understand language. I will have a representation of a sentence or a phrase at one level and that's the same sentence of phrase from the beginning of the first phony to the end of the last phony. It's the same object. But at a faster attack scale, that this current word will change. But this current word is the same word from the beginning of the words first time frequency died phony possibly to the last one. And as we keep going lower and lower and lower, we now generate faster and faster dynamics using this kind of model. So, you may be asking, and that's all that these equations say, that they're just a hierarchy generalisation of the first method used for the rat into this deep diachronic structure. This is exactly the same model. And the reason I show this, and the reason I like this model, is you can generate this graph automatically from this graph and this graph is those of factograph. Now, it may not mean very much to psychologists, but if you're a computer scientist and you want to design the message passing in the most efficient way, this is the design. So, what we're saying here, or what this figure says, if you can write down the form of your geratin model, you have automatically written down the message passing graph, and at some level, a brain has to be using it in terms of connections and passing messages over these connections. For those of you who are interested, these factographs are interesting because they place the variables on the edges and the probability distributions at the nodes. That's why we call factographs. So, the probability distributions are the factors of my geratin model, the margins. You can forget that, but it wasn't interesting. What is interesting to remember is you can generate these things automatically, and once you've done that, you can start to make little brains in software. That could actually be, I don't know, systems or very large-scale silicon integration chips, for example, or classical computers, pure computers. Anyway, so, once you've written down the factograph and you've learned the architecture of the message passing, you can actually go to neuroanatomy. As we're on the isomorphisms in terms of the structure of the dynamics, the temporal scattering of those messages in real brains, and it's an interesting geesal problem to solve, but there are lots of immediate parallels that we can evidence when you just look at the factograph and you look at the textbook neuroanatomy. I just sketched out some ideas here. We don't need to talk about this. The point is that there's a very interesting opportunity. Whilst you understand what has to be the computational anatomy, if you commit to this geratin model approach and the self-evidence formulation of belief updating behaviour, if you commit to that, then you've got that necessary computation anatomy, you've got the empirical neuroanatomy that we presume does this computation, so now you can start to look for parallels and assign different roles to different parts of the brain. So, for example, in this instance, it looks as if the Gerbers paradigm contains labels for policies, for example, just on the basis of the connectivity in reference to that factograph of previous stage. But let me think about this by taking you through conceptually a genetic model of a simulated agent as being a very simple form of pictographic reading. So here, there are no letters, but there are little icons. The position of these icons depends on a particular word. So, an icon can comprise each word if you like, comprises two icons, that are the seeds, a bird or a cat. If the cat is meant to the bird, that means the bird will flee, so that's the word flee. If the seeds are meant to a bird, that means the word fheen, the bird can fheen on the seeds. If, however, there's nothing next to the bird, so the seeds are down here from the diagonal corner, that just means weight. So, it's a very simple little language that we've arbitrarily invented. And the reason for using this pictographic form is that the agent has to decide where to look. If he wants to read this word, look at the letters in the word, it has to decide where to look at. Now, that can look over here, over here, over here, over here. Has it been noted by the locations 1, 2, 3 and 4? From the point of view of the genetic model, what does that mean? Well, these are the states, the hidden states that you would need to generate an alkan. So, what would be a sensory alkan? Well, a sensory alkan would be feeling that I put in a position 1, 2, 3 or 4, 4 would have actually sampling or foveating at that time, which would either do nothing, seeds, a bird or a cat. But to generate those alkans, I have to know the configuration of these pictographic letters, where I am looking, and I've introduced another hidden state here, which is feeling, like presenting words in upper or lower case. So, with those three causes, I can generate any particular outcome in a visual modality and a proprioceptive or feeling where I have currently pointed my eyes modality. And because I have written down the genetic model, I can use the standard message passing scheme of previous slide to simulate inference. I can simulate what this is a creature would do in terms of foraging information by trying to understand what word it is looking at. But what I really want to do is to do that with some of the deeper temporal structure, so diacronic aspect. I want it to actually remember the words in the seed. And from the point of view of the genetic model, generate sentences or sequences of words, from the point of view of subvenancy, inverting that genetic model to recognise what this word is in the context of beliefs of our own sentences. So to do that, I now have to put together four words on four different pages, if you like, and the four words are basically sequences of these three words here, typical of Zeus, a sentence, flea-point, flea-point. I'm not going to show here. So now, if I know the sentence, I know the sequence one, flea-point, flea-point, and I know where we are in terms of which page we're looking at. I can now generate the word, I can generate the word. If I am now looking at information about where I'm looking or whether I flip, or not, I can now generate the outcome. If I can generate the outcome, that means I can invert the outcomes to make inferences of how beliefs about the sentence. So I'm going to take that factor graph, that computational anatomy, and this genetic model, and then simulate reading in terms of where this page and law is to try and accumulate evidence to build post-geofilies about the sentence it is reading. The actual sentence it is reading is flea-point, flea-point, and these are the expectations of the lowest level about what is actually there at the lowest level. And the key point made in these simulations is you can have very precise beliefs about what you would see if you looked over there, even though you never actually looked there. And these precise beliefs come from this deep structure. So, for example, you can see that in the first room of the first academy room to the second word, and no point because it actually samples a stimulus that it either sees or burns. It sees nothing of either sample, and yet it knows because it knows what could possibly happen in terms of the alternative structure of the sentence. The solution has to be, sees up here, and burns up here, and indeed its posterior beliefs is hallucinating effectively in a very positive and base-optual way. The existence of these per sets, even though they never look there, and you see evidence of that if you look in detail at the sequence that's accounting by movements as they form beliefs. They resolve uncertainty, they respond when it's done in accordance, and you'll get the next sort of information that will resolve uncertainty about what this agent is looking at. I share the same results here in a different format, just to emphasize the separation of templates. So, these are beliefs at the higher level about one of six sentences that this synthetic agent was looking at, and notice it's going to be right at the end. It actually resolves uncertainty about the sentence because these two sentences share everything apart from the last word. So, in those words, immediately it must be looking at one of these two sentences because the first word is unique to these two sentences, but the last word is ambiguous. So, this uncertainty evolves slowly, and it maintains slowly, and it's only resolved by the last word. In contrast, the beliefs about what particular word I am currently looking at develop much, much more quickly. So, these converge to a particular posterior belief, and then that is evidence for the higher sentence based belief, and then we start again with a new outcome, a new outcome, a new outcome. That is hard to select between visual impressions, and I try to indicate that in terms of this separation of temporal time scales dictated by and only by the belief uptoting. Just want to make a point again that what you might actually see in these cynical creatures is very similar to what we see as a letter of physiology. So, for example, pre-secadding delay period activity in the prefrontal cortex, shown here in a raster format, looks very similar to the kind of responses observed in the view of recordings shown here in terms of a bar chart. Furthermore, when we look at the deflections associated with the belief updating on a stimulus by stimulus basis, we see that they've looked very much like a parasympathic evoked potentials during anti-vision in markets. And I just want to close by pursuing that, but by focusing on the responses to stimuli towards the end of the sentence. And I'm going to play a trick on this little creature. I'm going to teach you some violation or two violations of a different sort in the hope of reproducing chemical responses you find in cognitive neuroscience, namely a pre-attentive like this much negativity at about 100 to 170 seconds. And then a reorienting novelty like response, a later more endogenous response. So, how do you go to a P300 associated with semantic violations by changing stimuli so that there's a surprising mean to the work? So, I'm going to do that just by presenting it under case. I'm going to present it in lower case. So, this is if you like the stimulus manipulation at the lower level. I've shown the results of the lower level in blue without the manipulation. And then, part of the difference there may be not very much like this much negativity of the sort that you would see if I played you at what more stimulus in a stream of standard stimuli without any differences, but the same number on the more semantic representations. If I now do the same trick with this type, instead of just changing up a case for lower case, I now have to change the mean of the word to use the same stimuli. I now have a much more semantic high level violation. And now the thing that recognises the surprise of the reorienting here is, first but also now, the second semantic level. But of course, it's had to wait longer to get the evidence from the first level to be surprised, to do with the belief updating to a spot on that surprise, which means that the difference waveforms are not expressed in the perisynthes time. In a regime that would correspond to the EP300. So, it's a very particular specific example, but I use this just to consider how far you can get in understanding classical results that are used, and I've been using it for decades in cognitive neuroscience research and physiology. That can be understood in terms of the computational architecture and message passing, under the simple imperative to minimise uncertainty about the way the world works, and indeed how it might work in that world. And this conclusion, I think, is nicely summarised in relation to my movements by Helmholtz, who was the partner of many of the inferential interpretations of the scheme, where each movement we make, which we alter, the appearance of objects that we thought of as an experiment designed to test, and test everything about us to correctly the invariant relations of the phenomenon of the forest, that is the existence of indefinite spatial relations. And with that, it remains for me to thank the people of whose ideas I've been talking about, but most of all, thank you for your attention, thank you very much. The first example, the first one, is how in terms of, you know, how can you describe in your theory the hundredth of the oral, why is O'Chamryd, and why the bird has very different, the prey should be catched. It's the first question, and another one is related, and maybe it's how I'm trying to resolve this problem, is the question is how is active inferential in the inferential section? And because testing hypothesis is risky, it's time and energy we're consuming, I mean that you are resolving uncertainty, you invest something in toxic energy in your time and so on, and what do you think about how nature isolation shapes these prior beliefs to make them more efficient in terms of survival, a lot more in terms of companies and jobs. So, to answer your questions, that were probably three questions there, so I think we're far less fancy than that. So the first question, how do I account for context-specific drives? What determines the best sort of behaviour for me when I'm very hungry as opposed to when I'm just eating? So, in this field, that all of the answers usually result down, rebound, reduced to the form of the character model. So here, another big nice example of having a kind of character model where your prior preferences will now become conditioned upon different states of view. So, if I were to, and you are now registered that we are entering the interesting world of active infants applied to home spaces and spaces at the intersection, then let's say I have evolved, creating the next question, to have a gender model under the grave that was able to recognise certain states of hunger. So, these were good explanations for particular gut feelings, particular particular inputs from, say, receptors measuring your blood sugar, and also my beliefs about when I last have something to eat. Then, if I have those representations, I will be able to do two things. First of all, I will be able to contextualise my prior preferences about what I think I will be doing in half an hour, which could be in a restaurant, or it could be continuing to work, or it could be continuing to socialise. So, you can contextualise any behaviour simply by conditioning a parameter of your gender model at one level, on both slowly context dependent states at the high level, if you have a sufficiently deep gender model. And that leads to all sorts of interesting issues, you know, the distinction between home spaces and other spaces. So, I would imagine that a virus, unlike the apple, doesn't worry about whether it's hungry or not. The apple just won't let us take an eco-life. The eco-life doesn't worry about whether it's hungry or not. It just pursues chemotaptic reagents. Who can I apply them in? It's very discreet to me. Let's assume that a thermostat doesn't care whether it's hot or warm. So, it just immediately minimises two of these policies of a very trivial sort, which is just the very next thing to do, based upon fixed fries that they've changed to the homey stack at that point. That's very different from having another level above, which recognises a different state, though would then actually change the set point. Now, at that point, if we move from a homey static reflex to other spaces where we now start to anticipate the causes of our behaviour for our spaces. So, I will go on and eat something before I need to have a clinical watermelon reflex to fill my very, very low organs. So, I think it's a great question because what it speaks to is a fact that we're not dealing with simple genoclogicals or the sort of pre-preparation for a thermostat or a virus. We're dealing with very different structure. I repeat diachronic in the sense of separation temporal time scales, which are the kinds of models which would be necessary for you or me, possibly even a bacteria. But then the question is, well, where did those come from? Because then I answered that by answering your third question. The model is just the price. So, the price could be of a formal or a structural sort, how many levels does my model have, how many hidden states. So, if you were doing machine learning and deep learning, so you're using a variation of encoder, you have a prior basement. So, yes, there are 12 hidden layers. Hidden layer 6 has 270 hidden units. All of these are formal prices, you believe, are fitting of purpose and appropriate to the kind of data that you want to classify. Then, of course, you actually have the parametric price, the actual prior expectations, distributions, anything that you would normally associate with a prior leader. So, by model, by mean price. And, you know, obviously, there is a lack of an execution by tree because the lack of adjustments at the bottom of these models. So, if we go to that, this graphic here, all of these are products. The only time a liner becomes evident is right in the bottom here. More the interesting structure in terms of depth and publishing and contextualization is a prior structure and the actual cost of a parametric price you apply to all of these variables. So, that means you need to, or you, to your second question, where do they come from. And, again, you appeal to hierarchical difference, but now over a more extended timeframe. So, from the point of view of statistician, the way that you would learn the good price for a particular environment or a particular sort of data, via manifold learning, for example, or structure learning, will be created by model selection. So, now, you are selecting the form of those models, then maximise the model there, that's an average term of time. If you look for the physiological form of that, lots of static could be things like life or this or see. I will be giving a lecture. I think it's shaped that point towards the end at some point. There's not so many opportunities to discuss this further. But probably more interesting, I think, is during the government, to the next level, as you've hinted, all of this takes place at an evolution timescale. So, the way mathematically we bring all of these things down under the same principle is to interpret natural selection as Bayesian model selection. And that's actually very easy to do. But not only that, but in the past 10 years, people have now started to interpret the theoretical biology of the models or the dynamics of natural selection in terms of Bayesian filtering. So, for example, the replicator of dynamics or the replicator equation, or the price equation, these are very easily shown to be spent with the use of simplified assumptions to make Bayesian filters on output filters. So, what you're saying is that evolution is just nature's way of doing basic model selection to change or to select those models that require structures and is phenatised. That's how the greatest evidence. What do you mean by evidence? The likelihood that they are there. The likelihood that they are out of order for that environment. So, from the environment's point of view, it is testing the hypothesis that this is a good fit for being the environment, or this phenotype, or this phenotype. The evidence that it is a good fit for being the environment corresponds to the fact that fitness is stored by the time interval of the variation of the energy because that's the bound on the probability of that model being the right model given the experience provided by the environment. So, the answer is, it all comes down to evolution, but it's exactly the same process of operating very, very, very slowly. And in that context, you wouldn't think about the phenotype as being the individual thing about cost specific, it's a cycle of life. So, we've got a selection here over a developmental cycle. Thank you very much for the talk. I have a small question about, is there a small body about human evolution? Is it possible in terms of your theory to describe, just to describe and explain, the huge quality difference between humans and other animals? And is there, maybe in that relation, any hint that your vehicle has solved this problem? Thank you. That's a difficult question. I think it's a short answer because I think it speaks very much to what we were just talking about. I think it's just the depth of the German model that distinguishes the kinds and structures that either associate with me and you, as opposed to say a dog, as opposed to say a fish, as opposed to say an insect, as opposed to say a single cell organism. So, just the distinction between single cell organism and multicellum organism between species of a hierarchal aspect and nestling aspect. But if you take that further, I just think what kinds of hierarchal extensions would make you, you as opposed to a bacterium, or me as opposed to a bacterium? I think the answer is in the span of death in time. I think that's basically it. I think it almost reduces to the very simple observation that you and I plan and the bacterium doesn't. We can argue about whether the beetles or the dog does. The bacterium doing its chemotaxis does not plan. It does not plan to go to school or to find birthday presents. Whereas we do. So what do you think to plan? To plan to select a monster various policies. Which means you have to have a judging model in the future. The consequences of those policies. So that's just simply a statement about that we infer our world under judging models that have a temporal depth. They have a horizon that goes beyond the present. It enables us to plan and to think about what would happen if I did that. Now because as soon as you have that capacity, you've now got to make a choice. So the bacterium doesn't have a choice about what he does, but you and I do. And I think that sort of qualitative distinction, which again is just a structural fire, is a thing that would distinguish higher order life from lower order life. It's not to say that we're better than the bacterium or the virus. For any particular economic or environment, there will be a free energy expiem. So viruses are great for fitting and inferring their environment, just if you add a person's cell on another cell. We'd be very doubtful at that. And after compressing down very, very small, you would not do very well outside a cell, but the virus would not do very well at the university. So it's all in relation to the way that your sense of input is from your environment at your time space. And once you acknowledge that, then there are lots of global minima or unilateral acts of that that correspond to all sorts of different ways of being, both in terms of species, but also in terms of inner species. Then you can see now an easy taxonomy in terms of higher level death and sophistication, and particularly temporal death. And I think it comfortably separates us from other animals, other animals from cats, cats chasing certain reasons. Mr Prysen, thank you very much for the lecture game, as I said at the very beginning. I would like to go a little bit away from, let me say, scientific point of view towards the theoretical future prediction. I think it is possible, first question, to the current state of psychological outlooks towards personal belief motivations and beliefs into this key that you are describing. Like saying that those beliefs that are totally wrongly, you know, totally to the person, and they could also be in the state to the person which is not recognising you. And if so, is there a possibility of point of view to create, kind of like, a human impact software which will be possible to predict behaviour of each kind of certain person in certain conditions by that human kind of enormous power, I would say, to manipulate those people? Thank you. Right. So, a fascinating question, I just want to give you an aspect to differ with some. Perhaps I'll just take a practical one and take your question as a psychiatrist, because then it becomes very important in terms of understanding made beliefs, false beliefs and the remediation of that false influence. That may or may not be a good thing or a bad thing, but certainly being able to do it and understand what you're doing is practically very relevant in a few different ways. It could be psychoanalysting or it could be biking by advice. So the idea here is that this psychiatric syndrome can be thought of as a form of false or a buried influence. So, a lucidation will be basically believing in this theory that something is there when there's an accessory evidence for it. A delusion is having a conviction in substating affairs, usually interpersonal, for which there is no evidence that a ball does, would accept as evidence for that delusion. You can even tell the truth to things like anorexia and dysbondrophobia, holding beliefs about myself, which have no evidence when I look at myself in the mirror, for example. I see myself as fat, like a scene, like a bird, but I'm fat even when you like a scene with everything very thin. So you can certainly get an enormous variety of posterior beliefs. I would say that, when accountable, you could bring them to a certain number of fears like death hunger or whatever, which is why I'm asking. So those of you who are not accountable to me there can be brought to, maybe be, but to a final number of accountable factors. I agree with that. There will be mathematical reasons based on competitive evidence that will make that true. I guess what I really meant was that the number of ways in which I can deviate from you are large, but the number of dimensions may be quite astute. So if that's the case, if there is an opportunity, indeed, that's clinical evidence for a better belief updating, then people have been focusing on how that could happen. It seems that the most important synaptic mechanism that enables that sort of false inference is in the precision afforded to various sources of sensory evidence relative to priorities. So if you're a psychologist, you think that it has retention. So now we're getting to how it's shifting from how we form our beliefs or our data beliefs to how we attend to different things. Now we were talking just before about this being the same mathematical problem that I obviously think is worth an awful thing to any millennial society when it uses social media. It becomes big data, but the real problem is really to select what you accredit or assign in precision that enables that sort of information to update your beliefs. So I think in terms of understanding the mechanics of belief updating and intervening in that either therapeutically or for commercial reasons like in advertising for example, it's probably going to be all about how you can get attention at what you need by attention and the physiognomic mechanisms of attention. And also just gaining some high level control over attention to be able to mentalise it. So there are certain forms of attention that we have known, not because I don't have any control over it, but which it may be possible to learn to control with suitable mindfulness for example. So that's a chaotic suppression. So this is the phenomenon when I move my eyes as I look around the room. During the motion of the minds, I do not see the optical flow. I don't see the words sweep past them. All I see are the static samples that I then integrate into a coherent theme. So that's a chaotic suppression. It's a very interesting example of temporarily ignoring or reducing the precision of the lighting mapping here in a very, very tentatively precise way, which you cannot affect by the least higher in the model. I imagine that you now have a connection in the generative model. So you felt hungry to talk about contextualising it before. Say there's some higher level representation of yourself or myself, say yourself at this point in time. You can actually get in and then suspend that's a chaotic suppression. So you can choose whether to see the world moving when you move your eyes or not. If up to a certain you can, this isn't the old hand on this trip, you can see what it would look like if you'd push the side of your eyeball and you'd see the world shift. So there are ways of getting around it if you have a sufficiently deep generative model. So my studio question, I am not sure what the implications were in terms of the ethics of it or the weaponisation of that which is another issue of course. Just in terms of practically what you would be looking at, have you been looking at the processes, the medium, the precision and the degree of the message passing between these hierarchical levels that would look very much like what you think isn't useful or what you ignore. If you get control of that for yourself and for the patient, then you may well have a normal strategy. Thank you. I wasn't talking about therapeutic aspects like improving the situation. I was talking about the domestication of this system which is still being bad. Can you give me a concrete example? Well, it is the same thing, like as you said, advertisement rate. So it's not about changing human attitudes, explaining how bad and fast are bad or whatever, you know, advertising. But it just predicts what kind of disorder will react to this kind of like, what will be the way that people will be so that kind of these other non-psychiatrists will be able to kind of, you know, continue to this sort of message about, like, the non-hygrif aspects of that. So will they still buy? Will they still like? Will they say no? Will they say yes? I'm talking about kind of like prognostication models, not improvement, but just improvement of the management, not improvement of agents themselves. So what was in the economics context then? Some should have politically, whatever, because it's a digitising only, whatever I'm saying. I don't know because this particular mathematical formulation hasn't really gone that far. It's penetrated theoretical biology in terms of multi-agent gains of eucanical structure and anthropology. So there are simulations of how multiple agents eucanical structure and constrain their own conversion behaviour. And there have been sort of multi-agent simulations of a number of cells organising before parents and clinicians. But nobody to my knowledge has taken these variational free energy solutions to model markets of advertising or gene political events. So it has been really exciting opportunity. But to my knowledge, it hasn't been done. It's only been initially addressed in the past couple of years in ethology and in the literature in psychology and in all the genesis. Thank you very much for your interesting presentation. I would like to ask several questions concerning Markov processes. First of all, the principle feature of Markov processes is that the future is determined by the past only by the present. Is this factor resulted from the application there or is only the simplification to be able to solve mathematical problems associated with problems solved? The second question is, on this slide devoted to equity gain and currents, there is two molecules, entropy and energy. Energy is non-dimensional, energy is dimensional. How do you explain that? That's your question. We're really a source of ordinary differential equations to predict the area of Markov markets. Thank you very much. So a few easy questions there. Do you think we want to answer your mind a part? We're probably a new physicist. Can I answer your other criticism? Read into the question the first one. What extent are Markovian independence or Markovian process assumptions implicit in the Markov decision process for covenants? Or do we think or is one thing that these are the only kinds of genetic models that are fit for the universe in which we live? I think, technically, all of this maths inherits from the treatment of random dynamic systems. Cassett is a large model of the system in which case the Markovian product is going to be true and fundamental. That's where you start. So my answer would be they are not a device of mathematical convenience. They are actually dicting to the underlying premise. And that also enables me to stress the third question. What we are basically solving here are not ordinary differential equations that would follow from a stochastic differential equation that you can treat along with others. They would be applied to the density dynamics. For example, a Focke-Pac equation on the density dynamics on a straight wave equation or a master equation. So much of this really, all of these simulations have actually created a sense on functionals where there's a function of probability distribution very much like the Focke-Pac equation. So that's the belief-based aspect that would be a way from gradient flows on functions of states or gradient flows and how functions of states. But in terms of gradient flows, there are functions of beliefs and coding by states. If you might have discussed that further in the email, I'll send you something which I've never done and it's a bit of a peer review that takes you through those arguments very precisely. The interesting thing though is coming back to the first question because clearly this particular MDP is semi-markovian. I have written a Markovian property because I've now got two pi zones in place here. So in practice, what happens with these immensely complicated, itinerant, captive sets that we use as a mathematical model of self-organising systems like biological systems when you summarize it in terms of a Markovian-like process with a discrete time. It looks like it has now acquired a semi-markovian aspect. So it is interesting that from purely Markovian physics of it due to the complicated nature of the systems that we like to study when you find the free-engine optimising models that turn out to be hierarchical with that breaking of simple Markovian to make the same Markovian. At that point, I think that the discrete model of decision process has become a mathematical approximation to what is actually a continuous time Markovian process that looks as if it's lost its simple Markovian property because it's just become so itinerant, so complicated, so structured and so interesting from a biological perspective. Is that a reasonable answer? Thank you very much.