f future which is post or posterior and you are basically evaluating how good that posterior is depending upon your expected free energy and that becomes the expected free energy for that particular action and you do this for all the action okay and why this is powerful it is because you can go as deep as you want so here in the next step you go to this loop where you will check if I am crossing my deep planning or the depth of planning and then you are doing basically the same given that posterior what is the consequence of the actions of that particular posterior so here for considering that we are again calling the parent function so the same function forward search to consider consequences of those combinations and it will basically come back and add up your expected free energy so what happens over this sequence is that consider some or all future consequences and then all that values will trickle up your tree and that sum of the expected free energy will tell you which action is good or which action is bad which you can take into kind of see your preferred observations so that is the idea of implementing research and I will also talk about the importance of this threshold here which is which makes this algorithm possible so without this threshold this algorithm will not work I will explicitly talk about why that is the case and then once you evaluate the expected free energy for all available actions given the present state you can basically compute what you call the action distribution that is how probable is my action how I should take my action so that is and we also have this action precision parameter alpha so if alpha is very high then it basically is a highly skewed distribution where you will always choose the action that minimizes expected free energy if alpha is really low then it is going to be a more sparse or spread out distribution and then you can use this action distribution to sample actions and so in the agent environment loop we just finished doing planning and computing that action distribution then using that action distribution you can sample an action from your policy space so let us look at the policy space in this generative model so I am switching back to the original generative model with one hidden state factor and let us do planning and maybe initialize this agent I just want to initialize this agent to see the policy space not run the loop so I initialize this agent say for planning depth of one and if I look at agent dot policies I can say that I have basically four available actions which is north, south, east and west and if I have an action distribution it will tell me how probable is to take that action so if I look at agent p i so this is not defined because I have not done planning but I can do planning and then it will be defined so I implemented planning with research and then now I have an action distribution so for this particular scenario I will take my third action the most which is 0.99 basically that is the probability which is north, south and east in this particular case I just wanted to familiarize you with the matrices but we are now going to see the agent environment loop in action and so now you can sample an action from the sample action function and then implement learning which is using the standard by MDP way where I will update my transition dynamics and likelihood dynamics depending upon what I see and what is my belief and so on so my emphasis is on the decision making part so once you sample an action then that action basically goes back to the environment so now let us implement this for a planning depth of one and see how the agent behaves so here if it is a planning depth of one then that means that the agent is only considering the consequence of one time step ahead just seeing the immediate future for doing planning so I am giving the planning depth of one I am resetting the environment where the agent is going to start from that initial start state and in the loop it is going to get that observation take that action give back an action and we will look at the action probabilities and also we will give that action back to the environment get back the observation and this loop continues till the episode is terminated and I have set the episode length to be 8 just to see the outcome of 8 action so when we run this loop these matrices are nothing but the action distributions so how likely each action is to be taken and this is where the agent end up in the last time step so let us maybe also enable this environment or render that will show us where the agent is at every time step so initially the agent was at this location and we have an action distribution of this here so north south east and west so the agent knows that it should go north why? because if I look at the prior preference this state is more preferred than this state so the agent successfully calculated the expected free energy and inferred that I should go to this state and not stay in this state and because it has the generative model of transitions available it can infer that I should take an action north to go to this state so that is good and the agent goes to north and at this particular state the agent inferred that it should go to north south east so it will take an action east and it will go here and at this point of time I want your attention where the action distribution is equally probable for north and east why is that? because the agent is only looking at the immediate future so let us go back to the prior preference where the agent is right now here or is it here? yeah it is right now here in this particular state and if the agent is considering immediate consequences of just one action then these two states are equally good for it to be in the next state so there is no distinction between these two states if it is only looking at the immediate future so that means that the expected free energies will conclude that I should go to north or east it will not matter if I am looking at just one time step at a time that is the idea and out of probability it is going here it took the action east and from this state when it is doing inference it is inferring that this state is better and basically it is ending up in this local maxima state which is this particular state where the neighboring states are less prepared and this is wall and you cannot go there because it is forbidden for the agent by structure so it is basically going to sit there forever where it only sees that local maxima of prior preference and let us look at what might happen if you have higher planning depth so if I go to the planning depth of three then that means that the agent is actually reaching the gold state at the last time step but still in the third time point it had two probabilistic actions north and east so here from this particular state out of probability it took the action north but it can all equally take the action east and end up in this local maxima so let us run again and probably it will end up in this local maxima okay and only for the planning depth of four which is sufficient enough which is necessary for this particular grid the agent is fully sure of what to do so at every time point it is fully sure of what to do that it has to go north then east north north north east east and south and reach this particular gold state so only for time step or planning depth n equal to four it can successfully navigate this grid with 100 percent certainty so that is the idea that is the implementation that I hope you got so there is also this idea of action precision so here it is a high action precision that is why it is taking the actions that is from the probability it is a low action precision like one then good actions are more probable but that does not mean that it will be taken here by luck it is taking the right actions and reaching the state but here probabilities are most fast but you will also see like exploration behavior in more number of trials if you control this action precision take it to a high value to make sure that the agent reaches the goal for this particular problem but it is worth playing and it is important so for different planning depths like one, three and four in this problem this is the behavior that you expect for lower planning depths which is not sufficient the agent ends up in local maximas or local minimas of expected free energy or local maximas of prior preference but with sufficient planning depth it is able to navigate and reach the goal so that brings us to the last point in this tutorial where why is it important to have a threshold in evaluating sophisticated inference so by threshold what we mean is that we can ignore future possibilities in two levels you can ignore not likely actions or not likely observations in this research but if you consider the consequences of all actions and observations that means that you will have to consider four consequences in the first place then you will have to consider four times the action states in the next time step then all of that multiplied with the number of actions and this research becomes intractable until explored and it is even worse than the classical active inference policy space problem but by defining a threshold of even a small value will ignore possibilities so where is that implemented in the forward search algorithm we are considering actions with only action probabilities greater than the particular threshold here I am defining it as 1 by 16 also in the parent paper it is 1 by 16 the action probability so if it is 0 then that means that it will consider all the consequences of future and that is intractable so you can ignore actions which is not probable also ignore states which is less likely or only consider states that has probability greater than this particular threshold value and that significantly reduces the computational complexity where you will only consider combinations that are probable in the future tree and that lets you go deeper in your planning horizon that is an important point here and if you compare the time that takes for deeper planning for a search threshold of 0 so a search threshold of 0 means that you will consider all consequences and the more deep you plan the more time it takes and if you see to consider only the first future or the immediate future it takes 0.01 seconds for considering 3 possibilities into the future it takes 3 seconds and for 4 it takes 300 seconds and you can see that the computational time is exponentially growing but if you have a very small search threshold you have that computational time that makes sense for implementation in real world right so here for n equal to 4 that is 4 time steps into the future it is only taking 0.1 seconds and that is ok I can still do simulations with this complexity but there is no way I can talk about how this is how less the computational complexities it truly depends on the nature of your prior preferences and environment in action but this search threshold actually works in real life and we just saw that in our simulations right for n equal to 4 it took only like 0.3 seconds in our simulations but if you said that search threshold as 0 it already is 300 seconds for doing pool depth planning and if I set planning depth of 5 then it will basically run forever maybe and I will not be able to do simulations so that's the idea of search threshold so actually that's it I wanted to explain the agent class the environment class and the particular demo and yeah maybe it's a good time for questions if anybody was listening and I hope people get to play with this code and look at the tutorial and implement this build generative models like this so this particular example is how do you build a generative model for this gradual task and see how the agent is able to take meaningful actions but here we gave it the true structure of the environment in the B matrix and A matrix and so on but you can also play around with learning in the sense that while defining the agent dot step you can add a flag that says learning equal to true and if you start with an uninformed A, B and so on you can experiment on how the agent is learning that environment here you can look at the B matrix in the beginning you can look at the B matrix after say 10 trials and see how the learning is taking place here it doesn't matter because the agent knows the structure and it won't learn much but if it starts from unknown structure then there is scope of learning also to be implemented and it's already implemented because we are using existing PyMDP functionalities for learning A and B and it's already part of the step function so I hope step function is clear which is the only thing you need to know if you are trying to implement sophisticated inference and just the names of these matrices if you want to probe them and look at them and yeah I hope the session was useful so I thank my collaborators and Connor who maintains PyMDP and also Brandon who runs the PyMDP fellowship which I was part of and that's where I worked on implementing sophisticated inference in PyMDP and it will be part of the original PyMDP module soon and I hope people can start using this module to simulate sophisticated inference experiments and this basically becomes useful so maybe it's a good time to discuss questions or clarifications on the code or maybe it's a good time to take a break as Daniel was mentioning great thank you that was awesome well I have a few different questions and I'll read a few from the live chat I'll first just go to the live chat then ask those and then ask some other questions so Dave asks how do you think about the neural implementation of recursion brains don't seem to implement computer hardware style recursion deeper than a stack depth of one aside from heavily overlearned tasks we can confine ourselves to asking about recursion for the purposes of exploring temperately deep state spaces searching forward in time so how do we reconcile this really beautiful and elegant and computationally efficient full depth tree search with the biological basis of multi-scale planning so I'm not an expert in neural computation but the answer to that would be basically you're doing only one computation at a time right and you have all you need is some memory to store your beliefs and use those beliefs to kind of do the same computation again so we are not talking about neural I mean this hardcore recursive implementation we are only doing local computations at a time and just because of the structure of the generative model and we and because we have memory this can be done and I don't see why brain can't do it even though individual neurons might not be able to do it the brain has memory the brain has the ability to store memory and the ability to dream the ability to simulate it knows the consequences of actions and you do this on a daily basis where you plan your future and decide what to do right so on a single neuron level I'm not really sure how to answer that question but I don't really see why the brain can't do it as an organism cool okay to the code I guess I have a few questions let's can we go back to the maze and of course if anyone else has questions in the live chat just go for it so in the maze how does the the moves that are possible how is that reflected what what stage is it updated that what for example that it initially knows that it can only go up and then it can only go right or down where's that reflected with the updating of what what the kind of that relational aspect of affordances what is even possible to do and then how does it evaluate in a deep research when it does it need to know what things could or couldn't happen in the future so if I understand the questions correctly there is an important distinction between the generative process and the generative model right so in the great world which is the generative process we have implemented all of that manually where we have this transition that already knows what will happen if you take an action from a state so it's like an environment that knows how to work so it's like a reality where there are consequences of actions and it's already there but this information is available to the agent to be part of its generative model and in the generative model what it basically does is use that transition dynamics given or learned to simulate what might happen in the future ok so once I have that transition dynamics if I go to the where is the agent if I go to the research what it is essentially doing is evaluating the posterior given a particular state and an action J so from my generative model I know that if I start from this state and if I take this action I go to this posterior and I consider all the consequences and if in the generative model it is unlikely that if I go east I don't go there and so on it's basically it's automatically reflected in the expected free energy so I hope that answers the question so here if I set the action precision to be high and also enable the environment so initially I am in this particular state and with respect to the expected free energy what I am doing is I am using my generative model to predict what will happen if I take four actions and my predictions will say that if I take north I will go here and if I take all the other actions I will stay here and because in my prior preference north is more preferred I can infer that north is the action I should go for so that's the idea so here the grid structure is given to the agent and it might be a little confusing but the agent can also learn this grid structure and if this will work so once I know the grid structure as an agent I can simulate the future and consider the consequences of action so that's what's happening and once I am in this state I will consider the consequence of all four actions and I will infer that going east is better because that will take me to this state so there is always a difference between or you should keep in mind how generative model and generative process are two different things and what the agent knows might not be the reality or might be the reality depending upon what you are giving if you were going to go about making a new situation that you wanted to do generative modeling for do you tend to start from an existing working pyMDP notebook and start modifying state spaces or do you draw it out on a canvas like how would you recommend somebody other than replicating what is shown here let's just say we are interested in something that's not exactly just a maze what do we do to get our head around how we should proceed good question if you are trying to simulate say a new environment you have the heavy lifting to do which is to define the generative model for the agent you can either define a very sparse generative model which the agent can learn but you have to define the structure should be there and only using the structure the agent can learn the generative model so here you can make use of this cell to understand how I define the structure of the grid I am defining a structure for the agent for it to make use of I am saying that there are 25 valid states and there are 4 available actions and this is the standard way of defining the state space in pyMDP and you also have to define the central parameters a, b, c and d for the agent simulations so here I am defining a using my state space and observation space but this step of giving it or telling it that it's an identity matrix is my decision choice in my modeling I don't have to do this for simulations I can see if the agent is giving it from a random a matrix or when it starts from a random a matrix and similarly for this b matrix this structure is defined and there are functions like this which can give you a random b matrix but this is a modeling choice where if I want to give it the grid structure or not give it the grid structure I can start from a random b matrix let the agent learn and look at that learned b matrix because of the demo I gave it the grid structure to enable it to take the actions but it's not a mandatory thing so this notebook is useful in the sense that you know what to do but definitely you should play around with steps that may not be mandatory so if I give a prior preference for this state to be the maximum then you can see behavior that the agent will try and go there so this prior preference is defined in conjunction that this is the goal state but this may not be the goal state and in a different task what prior preference means is different according to the environment right so that's also there and your prior so once you define that generative model which you have to do you can't run from it then everything is kind of automated the agent only have to use the agent.step give it the observation from the environment the agent knows how to take actions and then everything that happens inside the agent you don't really have to worry yeah so this structure I'm sure will be useful for your particular task that you're trying to model in your hmm yes very interesting and how would you contrast that or point to any similarities or differences with how this would be pursued outside of active inference like if somebody were just going to use another kind of deep policy agents in the maze example what parts of the process would be familiar and what parts would be like a lot of work that wasn't expected or skipping through parts that were a lot of work otherwise yeah so the general structure is very familiar to somebody who does like this in reinforcement learning so the idea that it's an agent.step and environment.step so this is the standard open ai way of writing an environment and a standard open ai way of writing an agent ok so if you have a Q learning agent who does the same trying to navigate then the way you have to define the Q matrix is the heavy lifting it's just a state action mapping and in contrast to that in active inference you have to come up with a generative model that you want to see so in active inference it generative model is the central thing right without that without a generative model there is no meaning of purposeful behavior in active inference so the only unfamiliar part for a person who is coming from say a field like reinforcement learning is the structure of the generative model but there is no way other than getting used to it where it's the POMDP structure which dominates but if you're doing deep active inference all of this is going to be neural networks and POMDPs are also not active inference things right it's a industrial engineering thing so POMDPs must also be familiar for people who are coming from the computer science background just the idea that what really happens in the agent is the active inference part where we have expected free energies and variational free energies and if you want to learn about that then you have to go to the agents and see how it works look at the matrices numerically see what's happening but I don't in a level where you want to get started I don't see any problem all of this is standard frameworks like POMDPs and OpenAI gym environments all of this is very deeply discussed in computer science cool so what other motifs or cognitive phenomena are you excited or how do you see the POMDP development trajectory continuing after your sophisticated inference gets pulled in yeah so the POMDP had the original functionality and the functionality to implement or simulate general active inference agents with the policy space and so on and that enabled a lot of people in the community who who are not familiar with complicated coding and so on people who do psychology psychiatry and all the things right so whoever want to come up and try implement active inference POMDP enabled that and I am hoping that this module will enable people who want to try out sophisticated inference experiments in their particular domain so this if you spend some time and get familiarize yourself with the structure of how POMDP works then everything else is just writing a Jupyter notebook with a special code right to simulate this so if you have a particular task in your domain I don't see a problem for a beginner to kind of try and code it and what I am very excited to see is people using this module for variety of experiments just like how people started using POMDP and sophisticated inference is taking off and it's now widely talked about how it is the way of doing active inference and I am really hoping that people in various domains start using this module and see their experiments and I look forward for the feedback so what POMDP did two years ago I am hoping this module will do to people who are trying to model active inference in the source state so you mentioned the open AI gym and the standardized format and what benchmarks do you use or what kind of test suites are you comparing and how do we really know when we have made a generative model that really exceeds or excels in a way that other techniques are just not doing so if I may go to the open AI gym website there are several experiments there the classical reinforcement learning examples like the lunar lander that you see in this screen right now so active inference permits inception has faced problems of scaling two tasks and that's in itself a field of research in active inference scaling active inference and that's one of the reasons why deep active inference took over dealing with tasks like this so there are marks even now where the sophisticated inference may not be able to deal with state spaces and personally that's my research in my PhD I am actually looking at optimizing computations in sophisticated inference algorithms that lets you scale up to environments like that but to get started you will have to kind of write code and see if it works for an environment then look at if it's not working then you have to look at methods to scale it up and so on so if I am talking about benchmarks sophisticated imprints is as good as any RL algorithms for this state space so for small problems sophisticated inference will work and it's really good but for high dimensional problems like this the classical implementation that I just showed might not work but it's good enough for any decent experiment but if you want to scale up then that's still open and it's a new field of research and what you do might become a next new important paper so that's all I can tell in that regard you have to work and see what measures do you think you'd be looking for like computational resources or what are the measures that even make sense to juxtapose such different methods so the OpenAI Gym was designed for that to compare different algorithms so OpenAI Gym by definition is a collection of many environments so in my demo I was talking about the grid environment OpenAI Gym is nothing but a collection of many environments which will let you interact with those environments using the environment.step function so here we have the environment.step function that will let you interact with the lunar lander and that particular task will have matrices that lets you judge how good or bad your algorithm is so in this lunar lander problem how optimally can you land your rover between these two flags by spending minimizing the fuel and so on so those matrices are very task specific and that's one direction you have to take you can take try and compete with RL algorithms in in matrices but the right potential or the potential I see in sophisticated inferences modeling intelligent behavior where in RL the focus is to get things done to make this work but it's not really explainable especially deep RL and deep learning methods but in active inference if you manage to scale it up they are explainable and they are that will let you understand how intelligent emerges with time and I see that more interesting than competing with RL because if your focus is getting things done then maybe engineering is the right way and not active inference any other comments or thoughts Aswin do you have any other comments No I'm pretty happy I hope I was clear explaining the code maybe it was too complicated or simple depending upon your level but I hope it is useful to at least one person who would start using this and write the code and so thank you so much for your time. Awesome Thank you for the opportunity Thank you for joining till next time see you Thank you so much. Bye Alright Thank you See you next time See you You can mute the live stream or turn off the other live stream but yeah thank you for joining Yes, thank you for inviting me Well we have a little bit 35 or 38 minutes so it would be awesome to have your presentation Great So the moment Well Can you see my Well I saw a powerpoint Okay Can you see my screen Perfect Okay So shall we start Thank you Okay Thank you for organizing this wonderful symposium Today I'd like to talk about relationship between canonical neural network and active inference and possible extension for modeling social and shared intelligence using canonical neural network So let's start So as you know the free energy principle is proposed by Karl Freisten that state that perception running and action of all biological organism are determined to minimize the variation of free energy as a tractable proxy for surprise minimization and by this process organism can perform a traditional Beijing inference of external mineral states and this this content just show one example typical set up under the free energy principle active inference here there is a hidden state in the external world and only a part of this state can be observable for our agent this dog and this transformation is done by genetic model parameterized by theta and to the hidden state agent need to reconstruct the copy of the external state called posterior belief and this optimization is done by minimizing a variation of free energy and parameter is also optimized by minimizing free energy to obtain a genetic model to represent this relationship interesting aspect of the free energy principle and active inference is its application to the optimization of action here our agent have some preference prior see and to obtain this observation in the future agent may select the action that minimize the expected free energy in the future to to obtain the most predictable outcome and finally by selecting action that minimize the expected free energy it can obtain the feed so this is a typical set up under active inference but question is what is the neuronal substrate that can implement this process so that is our interest and to address this issue we propose a theory as follows here we consider that external world is parameterized characterized by a set of the variables like this here this is a posterior expectation the s indicate the hidden state in the external world delta indicate the action of the agent or decision and the theta indicate a parameter and the lambda is a hyper parameter so those set of parameters or variables characterize generative model and free energy variational free energy is defined as a function of the sequence of observation and the external state and its minimization indicate the variational free energy variational inference similarly we consider a dynamics of neural network and we consider that dynamics is characterized by a set of those variables here x indicate the neural activity firing rate at middle layer neurons and y indicate neural activity of output layer neurons and w here is a synaptic weight and phi is other any other free parameter that characterize neural network and we consider that neural network dynamics is characterized by minimization of some cost function L this is a function of the O and the phi internal state of neural network and its minimization indicate the generation of neural network dynamics including both activity and trusty state and our theory indicate a equivalence between those two functions meaning that for any neural network that minimize some cost function L there is a genetic model that satisfy if we call L which means that the the capturation of external dynamics is an inherent feature of any neural system that follow such dynamics so this is an interesting prediction but to abstract so I would like to introduce some analytically tractable example to understand this relationship formally so first we consider a very simple architecture this is represented by a POMDP without any state transition so she didn't state S is simply generated by prior distribution D and it is a binary state but we consider a vector of binary state so it is a factorial structure and observation is also a binary vector and the transformation from S to O is characterized by categorical distribution using matrix A and variational Bayesian inference indicates the inversion of this generative process like this so by solving the appropriate free energy functional we obtain those posterior briefs that is the optimal in Bayesian sense so on the other hand for neural network we consider such structure here upper part indicates the generation of signal in the external words and the neural network comprises only single layer here activity of output layer generated by weighted sum of sensory input O weighted by matrix W and we then characterize this neural network in the next slide so to model neural network or neuron we start from considering Pozkin-Huxley equation which is the which comprises differential equation and this is a very complicated non-linear equation and although it is very plausible so we consider some reduction of these equations so a typical reduction method is like this for example M here is much faster than other variables so this can be replaced with its fixed point or it is known that and minus one sorry it is known that H and 1 minus SN have a similar dynamic so we can consider a new effective variable U to characterize those two variables and then we obtain 2D Pozkin-Huxley equation like this so this is a famous class of neural network model which includes the well-known Fitzhugh-Nagmore model or the continuous neural network model and we modify those models to derive a canonical neural model so this is a definition of canonical neural network model so here Leak current is characterized by inverse sumoid function instead of cubic function which is adopted in the Fitzhugh-Nagmore model and we also consider a connection synaptic connection and this part indicates a synaptic input from a sensory layer through weight matrices and one may consider that W1 indicates excitatory synapse and W0 indicates inhibitory synapse and the threshold are adaptive thresholds that are function of W1 and W0 interestingly when we consider a fixed point of this differential equation we obtain well-known rate coding model in which the sigmoidal activation function so which means that we can say that in some sense this canonical neural network model is an approximation of Hodgkin-Huxley equation and its approximation level is in some sense between the realistic model and the most simplified rate coding model so we basically consider this type of neural network model and in the next slide we consider what is the plausible cost function for this neural network model so again we write the same equation for canonical neural network model which represents the activity of neurons and the vector of neurons and we consider cost function for this differential equation which can be obtained by simply calculating the integral of right-hand side of this equation and get this type of cost function for neural network this biological plausible cost function in the sense that its derivative derives neural network activity which has a certain biological plausibility moreover if we consider a derivative of this cost function with respect to synaptic weight W we obtain a conventional synaptic plasticity rule on the other hand for Bayesian inference we first define generative model like the previous slide and we then derive the sorry we then derive variational free energy for given generative model so this variational free energy is derived from the POMDP model in the previous slide and its minimization indicates the Bayesian inference and learning so we found formal correspondence between component of those two cost functions like this so this block vector formally correspond to this block vector that represent posterior expectation and this logarithm correspond to this logarithm and actually this A matrix can be represented as the block matrix like this and its dot product correspond to this computation and finally this phi naturally correspond to this log D log of state prior so which means that because the cost function are same its derivative provides the its derivative provides the some sorry so because the cost function are formally equivalent its derivative sorry it's result of derivative also corresponding each other so which means that for any neural activity equation in this form there is corresponding Bayesian inference equation this is equation that compute the posterior of the hidden state and this synaptic plastic equation formally correspond to learning or parameter of generative model and moreover by establishing this relationship we can consider the reverse engineering of the generative model from empirical data here this schematic summarize our approach to reverse engineering generative model and we first record the neural activity and assign the canonical neural network to explain this obtained data and by computing the integral we obtain the cost function for this canonical network and by the mathematical equivalence we established we can automatically identify generative model and variational energy that correspond to this neural network architecture so interestingly this is a Bayesian agent which is a type of which is a kind of artificial intelligence but importantly this artificial intelligence is formally derived from empirical data so we can say that this agent is a biometric artificial intelligence that follow the free energy principle and then it's derivative with respect to parameter posterior derived synaptic plasticity algorithm that follow the free energy minimization and its time integral can predict the running process of original neural network neural network data so which means that if the free energy principle is correct then this prediction should work should work and should be able to predict the result of this neural data without referencing to the data itself so our strategy is in summary our strategy is that we reconstruct generative model only from the initial data was like initial data before running and then predict the running process or running curve that this neural neural system should follow by using the free energy principle and compare or examine whether this prediction is correct by comparing actual data after running and the prediction by the free energy principle and if this prediction is correct then it indicates the predictability of the free energy principle and the setup considered so we apply this strategy to the in vitro neural network so here this in vitro neural network are stimulated using the POMDP generative process defined in the previous slide so there are two hidden sources that are binary signals and they are mixture and they are mixed to generate 32 sensory stimuli those are also binary and this is an overview of experiment by stimulating in vitro neurons they generate spiking response and those line indicate the high density spiking response so we overdone that in some neuron the response specificity is we found that for some neuron response was high to source one signal compared to source two signal and if we see the transition of those neurons we found that although we remove the offset at the first session to set those activity zero but we see that those neurons self-organized to response high when source one is one but not but those neurons response low level when the source one is zero so which means that those neurons activity those neurons response was consistent with our theoretical prediction that your activity self-organized to encode the posterior expectation of hidden state and we also found that some other group of neuron response preferentially to source two but not to source one so then we ask okay then we found that posterior expectation is encoded by neural activity and the next question what is other about other neural substrate and we then ask whether if the prior belief about hidden state is equal to effectively equal to the firing threshold of neural activity model network model so if the correct this correspondence should exist to check this we first simulated a Beijing agent and when we evaluate the prior belief of the Beijing agent the inference was attenuated as expected we found that when we varied the excitatory level of in-vitro neural network by using the pharmacological manipulation we also found that the attenuation the attenuation of inference which is consistent with our theoretical prediction that firing threshold encode prior belief of the hidden state and next we consider whether the scientific follow the free energy principle by asking whether free energy principle can predict the qualitative self-organization of a subsequent neural data so here we model neural neural network like this there are two ensemble neurons that encode source 1 and source 2 and we first compute the effective synaptic weight of those networks using a conventional connection strength estimation approach and plot those synaptic weights on the landscape of theoretically computed free energy so so this is a trajectory of empirically estimated synaptic weights effective synaptic connectivity and as predicted those changes reduce the free energy and here we computed this theoretically predicted free energy landscape only using the first 10 sessions data so that this indicator indicates some prediction of the self-organization and for more explicit prediction we then simulated neural activity and plasticity using free energy principle here we here the brighter color indicates the prediction of data without reference to activity data so these those lines exactly follow the free energy gradient and we found that this predicted trajectory is tightly correlated with this empirically estimated effective synaptic weights and error rate is like this so it indicates that free energy principle can quantitatively predict the self-organization in this setup so it indicates some predictive validity of the free energy principle under this setup and then we also consider the modeling of the neural modulation using active inference it is well known that synaptic plasticity is modified by various factors like dopamine, noradrenaline acetylchlorine, seratine so on and one interesting property of those modulations is that even so dopamine was added after associative plasticity was established it can change the result of plasticity in a post hoc or retrospective manner so it implies some association to the reward and past decisions so we model this process using canonical neural network so here we model the post hoc modulation of ABM plasticity using this type of plasticity equation and we also consider the recurrent neural network structure and out layer for this network and we consider that modulation occurred at this connectivity layer and then we found cost function that can derive those differential equations and then found corresponding variational free energy and genetic model which means that this sort of neural network activity including modulation of synaptic plasticity exactly follow the free energy principle and some type of home DP generative model and by using this we show that this biologically plausible neural network model with modulation of heavier plasticity can solve some sort of delayed reward task like maze task and then finally we would like to discuss a possible extension to this framework to the modeling social intelligence so to infer our conspecifics we need to select an appropriate generative model for our partners depending on our partners so this can be done by a Bayesian model selection scheme and we previously proposed a model that can predict the multiple burdens using one big generative model that comprises multiple generative models and this the movie shows prediction of songs so like this this model nicely identify which generative model is the best to explain a given sensory input and this process indicates the and the model can correctly infer the appropriate model and then imitate the song by its own action so although in the previous work we didn't discuss a detailed neural substrate for this mixture generative model we now be able to consider the corresponding circuit architecture for example if we consider the modulation of module neural module by neural modulator like dopamine it act as an attentional filter and this attentional filter can be explained by a three factor heavy and learning introduced introduced in the previous slide so again then this modulation is as the post hoc modulation of heavy and plasticity and this modulation can optimize each model to represent one generative model one song in a mutually independent manner so through this process it is possible to learn multiple generative model in a vertically plausible manner so in summary we found that the dynamics of canonical neural network that minimize the cost function can be read as a minimization of variational frequency it indicates frequency principle is an explanation for this type of neural network and we also validate this prediction using some in vitro set trap by showing that by showing that frame as a principle can quantitatively predict the self organization of subsequent plasticity only using the initial data and as the modeling we can extend those canonical network modeling to the action generation now the planning via the delayed modulation of heavy and plasticity and finally we discuss a possibility to extend this canonical model to modeling the social or shared intelligence to to interact with multiple partners so that's all of my talk thank you for listening this is acknowledgement our collaborator and the fundings and our unit are now recruiting post of researchers so if you're interesting please check awesome thank you for the presentation Takuya I'll just ask a few quick questions from live chat and few other things that come up Dave says Takuya used the phrase after plasticity was established was his group able to modify e.g. increase plasticity or is he saying merely that it was shown that there is plasticity or yeah I'm not sure if I understand correctly your question but those group show that dopamine adding dopamine after two seconds after the association occurred can change the the the magnitude of plasticity so without how to say if dopamine addition was before this association then plasticity level is low but after dopamine addition after association can change this level can increase the plasticity like this or like this so which indicates the post hoc modulation cool I think that answers it well what are you excited for or what are your hopes or feelings on where the active inference ecosystem is at and where we're headed in the coming months and years but sorry again please just what are you excited about other than your own research directions what are you excited about in the active inference system yeah so of course one direction is the the modeling of social interaction so which is much a rich architecture than the interaction between the static environment so if both agent run with each other then many interesting phenomena can be observed so we are excited with modeling those phenomena using barot script plausible network, neural network model through this equivalence awesome any last comments any other comments that you want to make Tequilla awesome thanks again for the presentation and people should check out live stream 51 where you and I talked a few other times and went into some of the details on that work there's a lot there it's really exciting thank you alright thank you see you next time bye alright alright the next session is going to be with Shannon Dobson this section is going to be called dark imaginarium shared intelligence as an infinity curiosity type um I'll message Shannon make sure that everything's good with the audio great talk so far welcome Shannon how are you doing awesome well please take it away awesome have you seen my screen okay yep looks perfect thank you okay perfect hey everyone thank you so much for the invitation it's such a great honor to be here I'm learning so much I'll be talking about an idea I had called dark imaginarium where I'm trying to make shared intelligence the concept of what I call an infinity curiosity type so gracious to link the paper so anyone can find more details they're on fill archive so I want to start with an discussion about ontological commitment so my first question is might be re-examine our ontological commitments so in particular two of them one um Sean Carroll said so amazingly but cannot be known because it does not exist so Sean Carroll says the Heisenberg uncertainty principle is often explained that we cannot simultaneously know both the position and the velocity of any object but the reality is deeper than that it's not that we can't know position momentum it's that they don't even exist at the same time the second one I want to examine is Lenny Susskind's quote we are all behind someone else's event horizon so Susskind has a brilliant idea of space-time emergence as the entanglement of two black holes and what emerges from that is called computational complexity so the world is quantum so every theory should be derivable strictly from the laws of quantum mechanics one is going to give us the notion of shared two is going to give us the notion of ecology so what would an ontological commitment to dark look like so my continual goal as everybody knows is to sustain a simultaneous experience and to understand why I currently cannot to sustain a simultaneous experience would be to bypass the integrative system recall consciousness so how would you attain a two consciousness in the sense of in category theory or an in consciousness how would we actually develop something called like a two memory so my colleague Robert Pretner and I fleshed out something called an awareness but we're sort of examining this idea Mike Levin and all have repeatedly shown that planaria memory is not in the head where is the memory is memory a sustained superposition of what and also what is the structure of an amnesis could you have a superposition between memory and an amnesis so I had a small dialogue with Chris Fields the amazing Chris Fields and I said you know what is the difference between these two questions what is the waking state and what is consciousness or could it be that these are entirely separate questions so we're sort of in a mess either way if there is a difference in these questions then it is possible to sustain a waking state without consciousness and or a conscious state in a non-waking state so imagine somehow being in a waking state under general anesthesia well these are not entirely different questions and we could contend that consciousness is a form of waking state or something along the lines of a waking state is a condition of a conscious state so how can humans have delta waves which are canonically indicative of unconscious deep sleep and that's a non-waking state in the REM state the patterns of which are indistinguishable from a waking state so we all know that general anesthesia something like a propofol can reduce the polyrhythmic brain activity to one uniform hum and we know there's as many theories about what anesthesia does to consciousness as there are anesthesiologists but we've repeatedly posited consciousness as the proto-state and I wanted to turn this idea on its head like is consciousness so robust or is it interference or is it a delicate inference we know beginnings are always tricky but what if sleep was the proto-state so if life is oceanic and it revolves in these deep pressures with the pressure of getting onto land squeeze the REM state into this full blown waking state that we're engaging in right now anybody who's listening so then waking state would be something like an acceptation which is I think quite impressive but it's in this mess that I attempt to define dark consciousness as a mixed frequency state of being self-aware or conscious while simultaneously being in a deep sleep specifically in three-sleep so the sleep is proto-state is quite strange the REM brain activity is indistinguishable from waking activity and this sort of enchanted me for a bit the only difference is eye movements so either blinking versus lateral movement so REM is naturally having mixed frequency brainwave states but the NREM states and the REM states are starting to blur as delta waves are creeping into the REM state now they've also found that sleep is a local phenomena so of course I'm going to ask the shanna questions so then who is sleeping who is remembering who is dreaming lucid dreaming is a quantum superposition or is it a superposition or an integration so in a sleep state can then sustain a simultaneous experience so must the eye be knocked out in order to sustain this level of simultaneity dreaming we know is characteristic of unsynchronized brain activity so is the question then hmm my eye cannot sustain a multi-consciousness but my dark eye, my sleep eye can you can refrain this in terms of reporting mechanisms and say we are conscious of things we don't think we are conscious of so let's talk about what is dark a canonical definition of a dark theory or anything like this is like dark matter does not interact electromagnetically with matter but I want to sort of play around with another idea of dark coming from Deleuze's logic of sense something he called the paradox of infinite becoming and which I'm going to read on the next slide so what if dark was the simultaneity of a becoming that eludes the present let's hold on to that for a second is dark a resolution issue but resolution is merely breaking translational symmetry so is dark a symmetry breaking issue and if so what symmetry and are we actually looking at the wrong symmetry is dark a sustained quantum superposition but of what again is dark a mini worlds branch is dark the dolphin uni-hemispheric sleep mechanism so I'll read from Deleuze's logic of sense Alice and through the looking glass involve a category of very special things events pure events when I say Alice becomes larger I mean that she becomes larger than she was by the same token however she becomes smaller than she is now certainly she is not bigger and smaller at the same time she is larger now she was smaller before but it is at the same moment that one becomes larger than one was and smaller than one becomes this is the simultaneity of a becoming whose characteristic is to elude the present and so far as it eludes the present becoming does not tolerate the separation of the distinction of before after or of past and future it pertains to the essence of becoming to move and pull in both directions at once Alice does not grow without shrinking and vice versa so good sense affirms that in all things there is this determinable sensor direction a paradox is the affirmation of both senses or directions at the same time I continue the paradox of this pure becoming with its capacity to elude the present is called the paradox of infinite identity the infinite identity of both directions or senses at the same time of future and past of the day before and the day after of more and less of too much and not enough of active and passive and of cause and effect it is language which fixes the limit the moment for example of which the excess begins but it is language as well which transcends the limits and restores instant to the infinite equivalence of an unlimited becoming hence the reversals which constitute Alice's adventures the reversal becoming larger becoming smaller which way which way Alice sensing that it is always in both directions at the same time so that for one she stays the same through an optical illusion the reversal of the day before and the day after the present always being eluded jam tomorrow and jam yesterday but never jam today the reversal of more and less five nights are five times hotter than a single one but they must be five times as cold for the same reason the reversal of active and passive do cats eat bats is as good as do bats eat cats the reversal of cause and effect to be punished before having committed a fault to cry before having pricked oneself to serve looking glass cake before having divided up the servings all these reversals as they appear an infinite identity of one consequence the contesting of Alice's personal identity and the loss of a proper name the loss of the proper name is a venture which is repeated throughout Alice's adventures hence infinite identity so I take this and I'm going to formally define dark consciousness as a state of being conscious while simultaneously being in deep sleep specifically in three fold hybrid the simultaneity of infinite identity and ever becoming that eludes the present so let's reconstruct the dark consciousness version of deluses paradox of pure becoming for Alice in dark wonderland and through the dark looking glass okay when I say Alice becomes sleepy I mean that she becomes sleepier than she was by the same token however she becomes more self aware than she is now certainly she's not asleep and self aware at the same time she's asleep and now she was self aware before but it is at the same moment that one becomes sleepier than one was more self aware than one becomes so dark consciousness I contend would take place in something called like a dark time this is going to get weird so Chris Fields and I talked about an entropic time where a time where learning exceeds forgetting so we all know that linear time is based on the linear ordering property of the positive integers okay so what would be the structure of a time that does not interact electromagnetically with this waking state interface so like AI must pay attention all the time would this sort of be like a dark time sleep is local time is local we know how beautiful a time crystal is so a time crystal you know has a structure that is periodic in time can you play with that and say time is periodic in what so if we've explained when a dark is not concerned with these notions of before and after then we would want a notion of time that can support the paradox of infinite identity with a notion of duration that is one of self similarity so we contend that dark consciousness would occur in something like a periodic time which is a time based on the periodic number system periodic time would measure periodic duration okay it's getting odd so there exist few objects more looking glass than a clock well maybe periodic go and collaby out chests perfectoid go but after all the periodic numbers have no notion of linear ordering their shape resembles a serpentski triangle which is a self similar set hmm so this periodic time is not concerned with notions of before after that is a periodic time does not tolerate the separation or the distinction of before or after of past or future so because the periodic topology is one of that disconnectedness periodic time is more like a time of now continual zooming in to more and more now thus periodic time measures periodic duration through its fractal properties of zooming in so let's try to look at a periodic clock alright so periodic time can take two forms the canonical periodic time defined on the previous slide and also topological periodic time which built into its very structure the periodic topology of time so there would only be one unit of time in periodic time which I call the Archimedes this is the periodic valuation so you can think of our equals periodic valuation equals the Archimedes how strange it is to have only one unit of time topological periodic time measures duration topologically as total disconnectedness so the unit of time and topological periodic time is what I call the p-topo so we state this formally there's only one unit of time and topological called the p-topo so a topological hour equals a periodic topology called the p-topo so given such a periodic clock let us imagine the seasons in periodic time, periodic snow, periodic rain, new periodic weather types and periodic rainbows daylight savings time could take the form of changing the p in the periodic this could be very drastic but imagine periodic metabolic, periodic ATP and periodic reasoning imagine periodic cognition types like periodic memory, periodic thought, periodic attention, periodic learning and periodic perception imagine a periodic looking glass imagine who's a periodic looking glass so let's pivot to FEP what does FEP actually specifically say about dark matter even dark in the way that I'm using the term is there a free dark energy principle how can we strictly derive according to FEP does dark energy actually exhibit entanglement how do we test this we should be able to derive the entire act of inference formalism straight from quantum mechanics alone by way of entanglement entropy some form of quantum gravity can we do some sort of dark general adversarial network to look at something like a dark brain we all know that lower lateralization in the brain is often associated with schizophrenia or people like Einstein or someone with a large parietal low probably like myself any mathematician universal lateralization look like I think dark neurons would take the form of something like you treat the neuronal networks as algebraic curves or isogenic graphs you talk of neurons in terms of their properties as varieties so you're actually bringing a heavy machinery of algebraic geometry into neurology and my big goal is to actually create something like a neuronal time crystal so that shared intelligence would actually be a periodicity in time I'm not there yet so until I get that let's try to model these wild mixed frequency in 3 plus self over states of dark consciousness so dark mathematics is something of coin it's like a biomimicry which mimics dark energy does not interact electromagnetically with matter you don't have to find the mathematical equivalent of that so I think you can do something like a dark dilithism or just make a model that is modeling the mixed frequency states which is what I'm trying to which is what I tackle in the paper so we previously shown that in tropic categorization there are condensed sets condensed sets form a topos so in the paper I outlined the construction of three potential mathematical models of these mixed frequency in three self over states you can do dark consciousness as a dark two post which is a graph in deep two posts there's a two category of two sheaves over a two site which I'll use today just a little bit a dark consciousness as a perfectoid like space in the sense of Schultz or as a diamond like space also in the sense of Schultz so I contend that the two sheaves structure can actually model the mixed frequency state of dark consciousness the in three self over state I'm a sheaf as a one stack again which is a sheaf that takes values in group oids not sets so this is already radically different consider a two category of two sheaves so a two category consists of objects you have the one morphisms between the objects and you have the two morphisms between the one morphisms you can keep going three category up to in category so this two category of two sheaves would have two sheaves as the objects one morphisms between the two sheaves two morphisms between the one morphisms and so using that structure I think that you can actually model one morphisms as what I'm going to call dark reflexivities these are going to be your local coherency states and then two morphisms are actually two inferences which are going to be global coherency states amongst the mixed frequency states so a lovely property called marita equivalent sites states that in equivalent sites have equivalent sheaf toposes and I do believe that that's the main property you need to get this local global behavior around neural networks so if you actually wish to model the mixed frequency clusters as fractals exhibiting some kind of self similar behavior then you can use this rich structure perfectoid spaces or they're sparkling successor the diamond so just a quick definition let perf I'd be the subcategory perfectoid spaces of characteristic p a diamond is a pro etel sheaf on the site perf written as this quotient of a perfectoid space X by a pro etel equivalence relation so a perfectoid space is going to be this attic space in the sense of Hubert that's covered by affinite spaces of the form spa r r plus where r is a perfectoid ring and then points of spa which is the attic spectrum r r plus or equivalence classes of continuous valuations on r someone as shall sly a diamond and you give incredible explanation that was a parallel to a mineral logical diamond so you can let c be an algebraically closed affinoid field geometric points spa c to d is made visible by pullback along a quasi pro etel cover that results in pro-finitely many copies of spa c so you're making a geometric point visible as pro-finitely many copies that was invisible before as the following parallel of the mineralogical diamond so the interior points are made visible as impurities which sparkle as colorful reflections on the many sides of the diamond so you can also do something like a dark diamond redesignate of functor is dark as a means to actually go the other way and see the impurities so then you're going to take the geometric point make it visible maybe by a push forward along a quasi pro etel cover resulting in peatically many copies of spa c so a diamond they're using a diamond as a sheath but a sheath in terms of a functor of points so the diamond spot qp is a functor from the category curve to the category sets and you literally fix the perfectoid space and look at the hom sets of x into the diamond and so technically the scheme is then said to represent the functor so I'm going to pivot to in booking AI in this thing so my colleague and I are coming up with something I've coined the qubit pedagogy which is going to be a new model pedagogy that is actually infused with heavy principles of quantum mechanics and so that with these we've created these quantum intrinsic curiosity algorithms that are feeding into the qubit pedagogy and based on those curiosity algorithms I've designed three dark versions so what I call the dark planaria curiosity algorithms a curiosity type that encourages the AI to explore patterns of a planaria regeneration the AI would develop quantum error correcting codes which mimic planaria regeneration so the second one would be dark quantum reality monitoring network this is a curiosity type it'll encourage encourage AI to explore dark reflexivity is what I call fractal identity AI would create models of n reflexivity in the sense of n category that's a new type of reality monitoring of fractal identity in the dark conscious state the last one would be some sort of dark quantum n3 and rem curiosity algorithm this curiosity type is going to encourage AI to explore superpositions of various brain patterns in rem states to predict new types of n3 delta waves that could emerge in rem states so imagine the AI could then develop new stages of rem sleep such as like 1 rem 2 rem of 2 n rem which is a very which is a clever limit and play on n rem uh huh anyway the AI could also develop new dark cognition types that correlate with the new types of delta waves so the notion of fractal identity seems odd but I do contend that objects living in fractal time would correspondingly have fractal identity the correspondingly have fractal identity it's a concept that we outline as follows so fractal identity has a reflexivity relation that is fractal so the very canonical loop the loop relation of an agent reporting back to itself I report back to me would be fractal how strange is that so fractal identity would not suffer the same problems with continuity over time um since the time in which it exists has no linear ordering it would definitely suffer different problems but continuity over time is something Chris Fields and I have been like how do you explain that so you can best model the fractal identity properties as perfectoid like or diamond like and then construct a notion of reflexivity as a perfectoid space as spaces are extremely rich structure but like kind of difficult but if you want to model fractal identity I think you should use them so this way create new concepts of perfectoid reflexivity diamond reflexivity so in in reflexivity the reflexivity relation can now be an in stack thus in reflexivity is an in stack perfectoid spaces so here comes the combination of this talk which is about shared intelligence as what I've coined the dark imaginarium so imagine an AI that could see slash simultaneously compute the infinity category of every concept you know having some quantum computation around to help the computational complexity would you know not be bad so dark imaginarium is what is going to be what I call an infinity curiosity type so infinity curiosity type is the higher order curiosity AI algorithm that encourages the AI to think in infinity categories so that is it actually encourages the AI to construct an infinity category as its means of higher order inference so objects are higher dimensional data sets the AI would seek out higher order in morphisms between the objects and then morphisms between the morphisms so such dark imaginarium is a meta curiosity algorithm that can create its own infinity curiosity algorithms and they're in creating curiosity types of the complexity and super fascinating most likely unknown to humans so it's functorial what can dark imaginarium do well the AI would develop inversions of current brain waves and their hybrid combinations it could develop in delta wave in theta wave in alpha wave in beta wave and in gamma wave for n equals zero one all the way up like a two gamma wave that structurally resembled a two category a three beta wave that structurally resembled a three category and the AI could develop new types of waking states new types of sleep states based on the combinations of these beyond the standard in one and two and three NREM and one REM N waking state and NREM state you know a three REM state consist of three and one three and two three and three imagine an end dolphin that was capable of N hemispheric sleep state and other exotic life forms right what else could it do well it could develop new geometries for the brain patterns and for currently existing brain patterns typical shapes include sinusoidal nonsi-soidal sawtooth spindle K complex but maybe this AI could develop 3D and 4D versions of the canonical wave patterns like a tesseract gamma wave so but also the AI could develop entirely new brainwave geometries that correspond to complex surfaces like a remun surface and collabia yaw manifold or algebraic variety so they could develop new cognition types other than the standard five that could produce n cognition types such as n thought in attention in perception in learning in memory so it could also predict non-human species cognition types such as octopus thought or dragonfly attention lastly it could produce hybrid combinations of cross species cognition types such as optimum memory or dragon man perception and then it would encourage the AI to develop new senses so you could develop one stack versions of human senses like to seeing to hearing to tasting to touching to smelling each of these two senses once again take values in group oids not sets so you could build instances of non-human senses so you could develop a new model and hybrid combinations like to shark human smell so since the AI sees morphisms between the various n minus one morphisms the AI can seek to develop new language models based on higher order inference types so from these inference models the AI will explore infinity languages and develop extensive prototypes you could use advanced mathematics to create new models of time that could support the new language models like to topos time diamond time and then the AI could develop new fractal identity types from the language models and it could design advanced fractal prosthetics such as a two ear or a two eye to extend cognition so let's go a little bit further about this extending cognition these are just a few examples of what Dark Imaginarium could conceive of so we could continue a positive perfectoid version of this using these new cognition types mental states in brain waves new geometries we can construct new patterns of thinking which would support neurodiversity in thinking so as such shared intelligence this is how I'm seeing it would be reexamined as this infinity curiosity type you can go even further and construct a new concept of an n shared intelligence so you'd have a zero shared intelligence a one shared intelligence and as well as the new patic concept of like p shared intelligence for p equals two three four using the patics let's go further right we repeatedly contend that one way to help advance the way we think to extend human cognition is to upgrade the number systems upon which the canonical concepts are built upgrade them to patic perfectoid diamond like versions unless we get new thinking so imagine like a brain wave pattern that resembles a kalabiyau manifold could we actually reverse engineer the levels of conscious activity that creates such a rhythm how about mixed frequency brain wave patterns that resemble to perfortoid diamond what about an in DNA molecule shaped like a kalabiyau infold or an in ATP molecule or an in exciton condensate structured like a kalabiyau infold so clearly different geometries of the fundamental molecules and processes of life would give rise to vastly different fundamental units of life and metacognition types the question is can we use dark imaginarium to reverse engineer the complex life forms are rising from such extraordinary structures and the more and more complex cognition patterns what about a general adversarial network that's tweaked and has infinity categories you have two infinity languages that are building their own language gen is adversarial using a generator and a discriminator with two neural networks contesting by zero sum game what about a collaborative network so can we construct a GCN containing two diamond like infinity curiosity types and pair diamond with a dark diamond with a quantum curiosity algorithm and its reinforcement learning so shared intelligence is this infinity curiosity type shared intelligence GCN could create better super positions of the diamond dark diamond to getting new models of intelligence you know higher order simultaneous computations by quantum curiosity would go by maybe by homotopy instead of his cost functions so let's future cast just for a second and what is the and the what is the inevitability of dark ecosystems mathematics of shared intelligence what can a pediatric infinity curiosity type prophecy is every perfectoid space diamond to topos encoding the next frequency patterns of an incognition type in future work may develop dark mathematics using perfecto diamonds as dark dialytheism aligning what is structurally dark with what is structurally dialytheistic so while we currently cannot perfectly model dark consciousness perhaps one day on dark day mediated by the dark imaginary and we will have the ethos and the quantum computational complexity to do so thank you amazing presentation I'll just quickly read some comments and see if you have any thoughts from the great comments so Scott David says I love the presentation lots of fodder for rumination thank you for inviting these concepts into an intriguing choreography perhaps dark energy is our perception of the fact of information increase under free energy principle processes and since the universe is made of information dot dot dot Scott thank you so much yeah I think you should dot dot dot is a beckoning that you should or we should work on that idea I absolutely agree I'm glad you're inspired with these concepts I don't really know where they go but hopefully it's portals to something like that great and then one one more Scott David question does fractal identity reveal the recursivity of rhetoric language consciousness informing individual identity from community identity inputs yeah that's wonderful so yeah my own thought is like what is an individual identity right Scott so the reflexivity curve is always sort of something that comes out to me how there's so much distance between I and me and so it assumes this notion of continuity over time and so we've I've always said what sort of notion of time are we talking about to even have a consistent identity somehow you always wake up and everything is still here somehow you wake up and you're not a lobster I don't really understand how that works you know but yeah that's nice if you could use fractal to get singular from something communal that might be cool but maybe fractal is something sort of like you're both at the same time and that's what I don't know yet so I think it's a totally revolutionary way of thinking to not have a before after so if you can construct identity without before after then that's sort of what I'm trying to do but yeah that's cool if you want to get identity from communal I think you can do that they may also sort of blur well this is truly food for thought and I really hope people can live with the darkness take it and run with it because there's so many fun ways to go thank you so much I hope so too so you're always welcome back thank you and talk to you later thank you so much bye goodnight alright and on to the last session of the first interval greetings Niki greetings hello good morning yes good morning how goes it yeah I'm doing fine thanks would you like to present and then we'll discuss yes that sounds like a good idea great let's see just going to share my screen yes can you see the presentation not yet okay see it works yep looks perfect okay great yeah should I just start yeah go for as long as you want and then anyone can ask questions in the live chat and I'll write down some things too thank you yeah so my presentation today will be on advances in machine theory of mind and theory of my sophistication I'm currently a student at the University of Amsterdam and finishing my master's thesis on this topic and I'll be giving a broad overview of current machine theory of mind and an idea or a concept for an active inference approach based on a previous book related to active inference theory of mind so to start okay sorry okay so for a global overview we'll start with giving a short basic definition of what theory of mind is and how it's then used then I'll give you a global overview of current approaches to designing machine theory of mind including evasion approaches approaches using biophysical models etc then I'll zoom into active inference models of theory of mind and social intelligence and collective intelligence more broadly and I'll get into the issue of theory of my sophistication which is basically the depth of recursivity of beliefs that you can have about another person's mental states and their thoughts or beliefs or goals about you and then we'll get into the issue of how to implement recursive beliefs and as an example we'll discuss Bayesian theory of mind with k levels of depth and then we'll get into the more specific paradigm that I'm using right now to build a theory of mind model which is based on a very simple model of the matching helix paradigm so we'll talk a little bit about that and then we'll get into the model itself and current ideas for implementing theory of mind sophistication using active inference so first of all what is theory of mind theory of mind has been introduced by the very famous painter by Prumak and Wodscher in 1978 I think it was called does the chimpanzee have a theory of mind and they define theory of mind as the ability to impute mental states to themselves and others as a system of inferences and they say system of inferences of this kind is properly viewed as a theory first because such states are not directly observable and second because the system can be used to make predictions specifically about the behavior of other organisms and I think there's already a lot in this definition and a lot of authors looking at theory of mind right now still use the same view of theory of mind as a theory a structured theory of different kinds of mental states such as goals, beliefs and desires that facilitates the prediction of observable behavior in other agents such as facial expression, smooth mental speech and I find it very interesting how much this aligns with maybe a predictive processing view of social cognition but also how weird it is that this theory theory of mind is still widespread in the theory of mind literature modeling literature so there's been some discussion on whether you can properly regard theory of mind as a theory and if so what kind of theory it is so within the philosophy of mind there's been basically two mainstreams or main perspectives on theory of mind. According to the classic theory theory of Tom, theory of mind is a course of theory of how these internal mental states generate other agents' behaviors so it's the same kind of view that we just saw and then the opposite side is called simulation theory of theory of mind which posits that we use the same kind of cognitive and neuronal resources for understanding other agents as though those that we use for understanding the cell. Simulation theory can also take on different forms and just the sun is coming up next to them so that's why I'm breathing light at the moment but basically there are a lot of versions of this that we use the same kind of action prediction mechanisms for ourselves as for others and there is this new version of simulation theory that Gordon proposes in 2021 which very broadly says that we have the same kind of theory for other agents for ourselves so there's this general theory of what it needs to be an agent that is refined at different stages to facilitate context sensitive predictions in social interactions. So this is also interesting to look at when you model theory of mind what kind of what you think theory of mind is and how it is specifically implemented so why would be interested in creating computational models of theory of mind so I think there are three important reasons why this is very relevant at the moment first of all there is a technical reason or the reason of technological advancement there's been some proposals that are ugly for the development of artificial social intelligence oh wait yes so the technical reason for for developing computational models of theory of mind is to improve artificial social intelligence especially as we start to live in a world in which research on human-AI interaction becomes more relevant and there's been this paper by Williams for example that's argued that improving artificial social intelligence is needed for successful AI human cooperation and it could improve communication trust and maybe also value alignment by utilizing theory of mind for value alignment for example there's a very strong foundational reason to study social cognition generally and the evolution of social cognition through in-cylical hypothesis testing and clarifying the conceptual boundaries of theory of mind one great example for this is research by DeVane et al which used a computational model of recursive theory of mind compared to alternative models to study different cognitive strategies in non-human primates and they find no evidence for the hypothesis of theory of mind sophistication involved with an increase in health size but they do find a correlation with for example neocortex ratio so in this way theory of mind models can give us some insight into the evolution of social cognition on the clinical side theory of mind models can be used to understand relevant social variations in clinical populations for example through computational phenotyping and diagnostics and by studying social behavior in groups that have some difficulty with social interactions and groups that show some kind of variation in social cognition such as people with autism spectrum people on the autistic spectrum people with ADHD or schizophrenia so I hope that with some of these reasons I convince you that lovely theory of mind is very relevant at the moment and there have been a lot of people already on this and I've created this very global overview of some approaches that are representative or some models that are representative of their more general approaches there is this brain ton model which aims to basically build up theory of mind abilities and abilities facilitating social interaction from the bottom up using biophysical models of neuron firing that's why I've placed it on the dynamic scale so I've aligned, tried to align these modelling approaches along the axes of how they treat time how broad their description is from the individual level to maybe describing what broader social and cultural processes and along the level of description from the molecular biophysical to the behavioral and one thing you can see is that there is a lot of work based on Bayesian inference and active inference that moves along that has relevant ties to the molecular and neurobiological level but moves along the lines of making behavioral and cognitive predictions and there are very little models that really also formalize the concrete implementation of theory of mind and there is also I think this need for connecting this dynamic implementational level to individual level social cognition and putting that in the context of social interaction more generally so some of the representational approaches that I've selected are the TomNet which basically uses neural network embeddings to train reinforcement learning agents we have KTom which is a Bayesian recursive model which I'll come back to later some or theory of mind with self other modelling uses multi-agent reinforcement learning with core inference and we have the more theoretical active inference model of implicit cultural learning thinking through other minds which could be seen as an alternate or a redefinition of theory of mind okay so to sum up we have this stream of biophysical models most noted the brain Tom which was developed by Jau et al and its strength are its neurobiological possibility and it making dynamic predictions about neural activation and in populations that are associated with theory of mind abilities and its weaknesses is that it's quite computational in quality and it's probably difficult to implement in an interactional setting these there's some deep learning models such as Tom Nets by Ravinovitz and self other modelling which I just mentioned that are also quite neurobiologically plausible and also make some dynamic predictions but there's this strong danger of shortcuts which has been addressed in deep learning models that the task might not be solved by learning the relevance ability of being able to infer another agent's goals or beliefs but just by learning a simple lower level associations between for example the perspective or the how another agent stands and where for example a super award would be so there are a lot of ways to solve the task and there's this finding that deep learning models sometimes use these kinds of shortcuts so that's something that's needed to be addressed then there are some Bayesian belief based models such as K Tom for recursive theory of mind and Bayesian Tom which was originally developed by Baker at all in 2011 and its strengths are that it's quite efficient it's very easy to interpret and its weaknesses are that it's that the road to the implementation level is longer and it requires many priorities and there's quite this question about whether it's scalable because of prior specifications that you have to give okay so as one of the I think the interesting newer developments on a theory of mind it's yes is a hierarchical active inference for collaborative agents which has been recently published and Haika is based on the Bayesian theory of mind by Baker at all but it adds this formalization of belief resonance which is the incorporation of beliefs about another's intentions with top-down predictions and this influence of these other agents beliefs are modulated by susceptibility parameter which controls this influence and what I find so I think it's important to note here that they use an approach based on active inference but it's not the they don't use the spirit energy principle for example so they do couple perception and action but just in a different way using a common filter so the way they formalize this is slightly different but I think the overall structure can still be informing or inspiring for active inference methods so what is interesting about their simulation results is that they show that agents that there is some emergent collaboration on tasks for low-value use of this susceptibility parameter without any explicit planning or communication needed and this means that they improve upon the original Bayesian model which explored different sort of overall plans for all of the agents which means that an agent employing Bayesian would need to reason about the roles of all of the other agents which was very costly and the authors wanted to improve on that to model maybe on the fly coordination which is more spontaneous and takes less time and they also show that incorporating belief resonance has a very positive effect in scenarios in which there is unbalanced information they did this simulation in the overcooked domain in which agents have to collaborate on different cooking tasks and the goal is basically the order the cooking order and then the intention would be any kind of action that has to do with completing the order and they show that incorporating belief resonance seems to be especially useful in situations with unbalanced information which for example one agent knows the order and the other doesn't and these agents develop some kind of leader follower dynamic in which one is more susceptible to the other agent's intentions and one agent attends more to the evidence from the environment and this also aligns with what we know about here it might be improving the situations in which there is some symmetry in what the agents know about the environment so I thought that was very insightful cool okay so I'm going to go into some active inference approaches that I think are relevant for developing active inference spirit mind first of all there is this very broad proposal on inculturation and non-development thinking for other minds a variational approach to cognition and culture which we'll go into a little bit and we're going into Kessler and Hass paper on ideas for spreading a free energy proposal for community cultural dynamics we'll go into Kaafman et al's model on collective intelligence and finally also the proposal by Mutualist et al on Bayesian inferences about the self and others okay so first of all I'm starting with Bayesian inference about the self and others because it gives the very sort of full introduction to I think predictive social cognition and that's also why I've added this figure on the right that is from the Taman Thornton paper in 2018 which explores the predictive social brain and what kind of features seem to be seem to be relevant for categorizing and understanding others' behaviors some figure on the right you see that there's a space which is ordered by power sociality and balance and that constraints the state space which seems to be ordered by rationality, social impact and balance of course these are just correlations but these features seem to be the most predictive of what they're seeing in the brain and you can see that there is this sort of yeah a very strong top-down constraints of the possibility space in which you interpret other people's actions and you can also see that based on another agent's actions you learn something about where they fall within the state space in a given context and also where they fall in the trade space so at the same time you might have already had some priorities on what kind of a person this is but you're also learning about it and you might also have some priorities on how someone behaves when they're not for example or when they're sociable versus unsociable and all these kinds of priorities informative priorities they inform your predictions in the context and they make this task much more manageable of predicting other people's behaviors on the flight and I think that links very well at that too which is basically that inference is about the self and others at different time-scales facilitates interpersonal minimization of surprise and thereby optimal social decision-making so these and these self and other representations that are facilitates personal minimization of surprise could be seen as representations that inform our inferences and predictions on the flight I think it's also important to mention that one of the main addiction points of their paper is that self-representation so how beliefs about the self can facilitate and personal minimization of surprise so even what I think about me and how I represent that while communicating will facilitate the other person's optimal decision-making at that moment maybe by providing the right kind of information that they need to optimize so to the next two interesting papers, I guess we're spreading and an active inference model of collective intelligence so the key idea I think for both of these papers is the emergence of group behaviors from local interactions for Castelon has this is the global group behaviors cultural transmission or transmission of beliefs and norms and they describe this process as the mutual achievement of actively inferring agents through communication and theory of mind is one of the many mechanisms that facilitate this process of attunement so that's the link and they show that the spread of certain kinds of beliefs through a group can be modeled just by making agents interact in dietic groups and still many profit and loss show that the system you can create a system of free energy minimizing agents with some minimal properties of social intelligence such as the ability to assess how itself similar another agent is to themselves the ability to infer another agent's intentions and the ability to align their goals to another agent more or less and they show that if you put all of these agents together in those diets that don't only minimize free energy on the dietic but they also minimize free energy as a collective and thereby this could this is a very simple model of how adaptive behaviors adaptive group behaviors could emerge from agents with very simple social abilities okay so now we get to thinking through other minds which is not technically a proposal for fear of mind but it's the proposal for how social cognition shapes in cultivation more generally and what kind of abilities agents need to facilitate this kind of known formation and I think it's a very interesting proposal because I think it highlights an important function of social behavior more generally and you could even see it as a way to redefine a fear of mind as more of an interactional concept and as an individual level of cognitive ability so according to this proposal thinking through other minds is a property of multiple different energy minimizing agents and a process by which agents infer other agents expectations and based on this the authors propose a definition of enculturation as a process of learning social expectations through the selective patterning of attention that guides agents towards relevant affordances within their social and cultural niche I'm not sure if you're all affordances but it was quite hyped up a couple of years ago in general it is defined as the relational construct denoting possibilities for action offered by an environment that are co-determined also by an agent's interest, goals and abilities so I think the standard example for this is when you are thirsty a glass of water might appear as an affordance when you might not consciously or might not attend to it otherwise and cultural affordances in this sense are epistemic affordances so affordances that give you some epistemic value that have come to stand out as reliable and relevant based on the history of cultural information they encode and good examples for this are different kinds of signs so traffic signs we learn what they mean from a young age and we sort of inherited the symbolism of the traffic signs and they guide our intention towards points in traffic and they regulate our behaviors so when you look at the complete proposal it sketches how the regulation of social behavior depends on the learning of shared norms and expectations and also how this connects to utilising cultural affordances and thinking through other minds as this interaction property in which agents learn to infer each other's expectations to optimise collective behavior and decision making so from these interesting active inference and broader proposals of fear of mind we get to the issue of social sophistication in active inference so what is this fear of mind sophistication a short recap it's the depth of a recursivity that can be utilised for fear of mind of the form I think that they think that I think and it has been found that agents generally use a recursivity of between 0 and 4 and that humans' ability to for recursive belief reasoning is generally unlimiting but in principle formally this could go on forever and one way to implement this kind of sort of arbitrarily recursive belief inference is proposed by Vada at all uses a Bayesian model of sophisticated fear of mind with K-Tom agents and provides simulations in which K-Tom agents they guess agents that are just one level of recursivity under them and this model has been used for a lot of interesting simulation experiments for example Devane et al showed that in a trade based analysis with agents having a fixed fixed depth of fear of mind recursivity there was a specific distribution of agents with level 1-Tom and level 2-Tom that could provide an evolutionary advantage compared to appropriations with larger proportions of 0-Tom or 3-Tom agents so they looked at the adaptive properties of systems with different kinds of ratios of fear of mind sophistication and in another in another experiments which is a state-based analysis Devane et al. showed that if you use computational phenotyping or autistic individuals they show reduced sensitivity to task framing as strategy switching within the game that they're using and fear of mind sophistication so these are just some interesting applications for fear of mind sophistication and the promise of modeling fear of mind sophistication would be that you could investigate how people massively switch between different social strategies while solving social tasks and one of them would be to increase the depth of fear of mind sophistication or decrease it depending also on what you think about the other agents sophistication so what I've been working on at the moment is an active inference model of social prediction during the matching pennies game the matching pennies game a game farm economics with a very simple format there are two rules the guesser and the challenger the challenger hides a penny in one of the two hands the guesser needs to guess which hand if the guesser is correct they win if the guesser is wrong the challenger wins this game has some logical equivalence one version of the game makes both of the agents select heads or tails the challenger selects heads or tails and the guesser has to guess if it's heads or tails but both have the same formal structure and psychological experiments of subjects performing this task have shown that there is a strong social framing effect in the matching pennies game so participants will behave and perform differently depending on whether they think they're playing against a human agent versus an AI for example additionally a comparison of K-Tom and other computational strategies that were fitted of experimental data of subjects playing the game revealed that participants seem to use spirit mind when playing the game so there is a strong indication that participants use stuff they're all in the matching pennies game and that social framing will influence the social strategy that's being employed by the players so this is the very simple zero-time architecture for the matching pennies game and I included beliefs about self-choices as also kind of monitoring self-states beliefs about other agents' choices on whether the opposing agent has hidden the penny left or right and then the agent also tracks the reward states since the game in this setting is devised in a way in which the agents both make an observation simultaneously and then all of the observations are revealed this setup makes sense so just going to drink a little water the outcome modalities or observations that the agents have are its own choice observations the choice observations of the opposite agent and the reward observations and the possibilities the action space is very limited the seeker can choose to seek left or right and the hider which is the same as the challenger before has the possibility of hiding the penny left or right and the reward is uncontrollable since it depends on both agents' choices at the same time so this is sort of a summary of the architecture that I just described and this is another visualisation of this setup you can see here that if you look at the likelihoods the reward mapping for the seeker is just the opposite as for the hider and I think that this simple setup is very suited for studying the theory of light in these kinds of simple competitive interactions so if you wanted to study the use of theory by sophistication in the matching penny scheme using active inference I ran into a couple of challenges and one of them was how to how to steer the problem of recurrence so how can we make a difference between the focal agent and the other agent if we try to model the other agents within one agent especially if you want to introduce or formalise the depth of cave or chrysophy you can't just make one agent simulate the other agent simulating yourself there used to be some kind of sort of structure that distinguishes the self inferential mechanism and self learning mechanism from what the agent focal agent plays the other agent is thinking and seeing and doing and I think the gentleman with the bowler had by first air in 2003 is a good example through this problem so you can the basic setting is that our world is populated by beings like ourselves experiencing themselves as a subject as a focal point of their world with their own thoughts and feelings and their whole thing that they're the one and only subject but they can't all be so there needs to be sort of either an outside focal point or one ultimate main subject and yeah so I think more practically the questions that arise from this example are how do we distinguish between focal agents and simulated agents and how can we simulate other agents in a way that is computationally efficient and maybe uses the same kinds of resources that the agent already has so I actually had a lab meeting at the theoretical neurobiology lab a while ago and we were brainstorming about this issue and one of the ideas that came up was to use sophisticated inference theory of mind so in this case an active inference formulation of the leaf replacivity could be used for modeling recursive theory of mind and so basically theory of planning using predictions about the other agents into a cloud account would consist of evaluating all the kinds of mathematical scenarios all kinds of counterfactuals on how your actions might influence their beliefs and their actions and so on and so on so this would be one road to go into but this would also mean that all these counterfactuals would need to be that related so I was thinking is there a sort of more efficient way to sort of use these kinds of either internal simulations or professional evaluation and the current approach I'm working on which I also sort of which I'm also still developing so I'm very much open to feedback and comments on how this could work and possible alternative approaches at this point but the general idea would be to create a partial internal simulation of the other agents control mechanism so taking the learning mechanism of an active inference agent as sort of the definition of what the focal agent is that is the agent that this user learns and then first from the environment and what the agent does when predicting the observations of the other agent or predicting the other agent's behaviour is basically performing partial simulation about what it thinks the other agent's preferences are and what it thinks that the other agent's strategy is which is encoded by the transition from state to state and one of the potential ways in which you could include requisite in this way is that you pretend that you have control of the other agent's actions and you predict the other states you predict self states you evaluate you evaluate the state action probabilities choose the most valuable action based on the distribution simulates the other states that come forth and simulates the self states that come forth and then you have a new and then this can be used for the next round of action selection by the other model so in this case only the prior preferences and the agent's specific transition probabilities would be needed as sort of information on the other agent and because you also want to include some kind of learning about the other agent's strategies one of the things you could implement would be learning also the bay matrices so having sort of the the having the agents accumulate evidence about these state transitions over time to also better predict the other agents potential actions so the basic principle would be to simulate control from the perspective of the other agents and the requisite comes into play when you simulate the other when you've already simulated the other's predicted actions and predicted other states and you simulated your own actions as a consequence of those simulated actions you can feed that back into the other model to predict what they would do if they thought that you were in the state that you were in and I think if you sort of I think that could be a way to develop recursivity in a way that does not need complete simulations of parallel agents within the same system and of course there should be some kind of temporal discounting so parameter that discounts evidence based on the simulated planning horizon that is defined by the key number of steps so yeah this is sort of a conceptual outline of how you could implement because of fear of mind using active inference we haven't been able to perform simulations using this yet but we're working on that and we're very much open to discussions on this and technical comments on how to improve on this outline and one of sort of the open questions that you're still thinking about is how to make the agent the infer the depth, the accuracy of the other agents in a setting special thanks to Yion Dumas who also be there at the panel I think in session two who's supervising me on this project thanks to the PPSP lab I'm doing my internship to really say who's also working on a related project the PIMDP team for that great coding package that I'm using and for Carl Friston for his feedback and ideas on my previous presentations thank you very much for listening cool great presentation very comprehensive review of a lot of the different theory of minds options out there well if anyone has questions they can write it in live chat what do you want to explore or can I ask a question or what would be fun for you um I'm blighted by the light at this point I'm not very I can't easily read from my screen so maybe it would be nice if you could if you could read out the questions that are in the live chat sure oh yeah sure sure well first one part I found interesting you mentioned that people play differently when they are playing a human or when they believe that they're playing a human so what is that like what is the difference in play when we believe that we're playing another person um so um so if I look at the original paper um there is one study on this and then um they did the computational phenotyping study using K-Tom and alternate strategies um and they showed that if you use the social framing condition that subject will more probably employ my strategies compared to other simple reward based strategies so maybe those strategies could be described using some kind of reward learning mechanism um what the difference in their overall sort of trajectory of choices I don't know yeah a few themes then that you brought up that came up earlier in the session so one was using PI-MDP and sophisticated inference which Aspen Paul gave a walkthrough on and this question about recursivity and about the way in which you can on one hand talk about abstractly like K recursivity yet the biological system doesn't implement that kind of a logic and so so um could you maybe describe a little bit again how does the the structure that you laid out for the generative model capture some of those features of recursivity without falling into the trap of just theory of mind all the way down yeah so my general idea was to assimilate the other agents action prediction based on learning about the transition probabilities for the other for our sort of what we think the other how the other agents state transition um and then if you um you've predicted what the other agent would do you can use that as a prior for calculating um action dependent expected states um and based on those evaluating those expected states you have to assimilate your own choice mechanism um and I think in principle you could um use this recursive simulation um indefinitely but also yeah it's also devised in a way that it uses the same kind of um the same kind of sort of just the architecture of this local agent so the other idea was to just use internal simulations all the way down um but that would yeah that would be very effectively possible um and yeah I think it's a very good question because how why would you even need to formalize believe all the way down if in end effect people only use Tom with the with the sets sort of maximal death and the fact that we use fear of mind with a maximum death might also be certain that um a different or what we do might also be described by a different strategy so I yeah I'm not sure if that's an answer to your question hmm yeah well when I saw this in some of the other generative models um you mentioned maybe here like you pretend like you can control the other person's mind and that's kind of the fundamental weaving of action into the inference challenge and then that uses expected free energy just like any other policy selection so it's like pragmatic value would be bringing that controllable state your uh social partners mind or beliefs bringing them into alignment with your preferences is pragmatic and then learning more about them is epistemic and so then that might enable some theory of mind like behavior where it's like when you don't know enough to put the squeeze on then you have a kind of open-ended learning and curiosity and question-driven theory of mind but then once one has enough to kind of exploit rather than explore then without necessarily even updating deeper recursivity or strategic shifting you could get um social behavior that's oriented towards control and pragmatic value rather than just like learning and questioning yeah I think you're very right the idea was also to enable the agent to um maybe first few strategies that are more useful in um gathering evidence about the kinds of strategies that the other agent is using before exploiting um what you've learned about the other agent hmm so what are your next steps with uh work um so I think yeah right now the main task would be to implement this using PiMDP um and see if there are any sort of formal refinements that I need to make well in the implementation because it's yeah if you can't build it you can't you don't understand it so um that's what I'm yeah that's what I'm working on right now and then the next step would be to introduce um a mechanism to sort of maybe very um uh recursivity um based on what the agent infers the kind of recursivity the other agent has um but before that I also want to um want to use the model to perform computational phenotyping on um subjects um that were doing the matching tasks um and had uh different kinds of diagnoses so there there were newer typical um youth and um youth with um youth on the autism spectrum and youth with ADHD and anxiety and it would be interesting to see if there is any sort of difference in the depth of recursivity that they employ um as sort of the flexibility with which um they switch between strategies hmm that makes me think about different different levels or or differentials between self-knowledge and other knowledge on one hand uh we seem to know a lot about ourselves but also we're often unaware or blind to some features or regularities of ourselves that that might be highly attended to by others and so when we're rolling out these games or scenarios there might be some theory of mind settings where like knowing yourself better carries okay but other settings where knowing like the game is what matters or knowing the partner in an iterated game theory or like just knowing having a lot of experience um like there's a lot of a lot of degrees of freedom in modeling these very um advanced cognitive ecosystems yeah I think that's also one of the reasons that we chose the matching pennies paradigm because the paradigm itself is very simple but what we're trying to model is quite complicated and on the matching pennies like um so it's in one hand the person has two hands behind the back and then they bring out the two fists and you're trying to guess like where it is and then I wondered well what if it was you have to guess where it isn't on one hand that's like kind of the same or like if you say well you win when you pick it but then if you say well you win when you pick the empty hand mathematically it should be like the same because knowing where one is is like knowing where it isn't but just as a human game player it has a very different feel and those kinds of like um reversals might give us insight into our priors that support not just open-ended abstract area of mind but like kind of with a lean towards being pro-social or like heuristics in place that support making quick decisions together maybe rather than I don't know yeah I think those are all very good um yeah very um sort of promising trains of thoughts I just I think in the case in which you you need to pick the empty hand we might have very strong sort of beliefs about what or we might experience sort of the presence of something is inherently more rewarding than the essence of something because we have all these associations with gifts and getting things and like usually things that are there so I can imagine that in this case sort of the perceived you wouldn't perceive it as rewarding but formally it would be completely the same yeah yeah like uh receiving a benefit versus averting a loss yeah and then how that plays in and our encultured priors and our personal histories and how these very deep layers of differences might play out and uh what kinds of empirical data or online data could could help us generate like unique explanations or predictions maybe situations like you said some situations where a reward based model might be sufficient but then I think the interesting question for active people is like where's the unique explanation or prediction that that really has active shine and shows where surprise bounding as an imperative gives us like more realistic or more concise or conciliants explanations in a way that like it doesn't even make sense to appeal to reward yeah yeah I think that's also the tricky bit about this paradigm is that it's very much I mean it's reward based in a sense but I think because you have this social framing effect you also have these interesting learning mechanisms and mechanisms of uncertainty reduction that might play out in how the agents behave in the end but that's why we thought that it would still be interesting to use active inference to explore this paradigm but on the other hand I think if you at the moment you're looking at individual variation you might get interesting differences in reward sensitivity or a version of risk aversion stuff like that that might be better explored in a different context any last comments or thoughts no thank you for your comments and your insights yeah it's awesome it's a great direction happy to see it alright thanks everybody for presenting in this first interval and see you in the second interval bye thanks everybody