Branching Time Active Inference: the theory and its generality

hello and welcome everyone it is September 1st 2022. and we are here in model stream number 6.1 we're going to be discussing branching time active inference the theory and its generality we're going to have a presentation followed by a discussion so thank you Ali and Jacob for joining and anyone else to be adding their questions in the live chat without further Ado over to geophilia Champions and thanks so much for joining really appreciate it hello thank you very much for the kind introduction uh and thank you for inviting me to present today I'm very glad I had this opportunity so today I will be speaking about branching time active inference um basically it's really different version of the of the the approach the first reason is Dash passing so second using Belgian filtering and the third one is using believe propagation and allows the model to contain several observations and several item States this works has been realized in collaboration to we've lost Acosta Mike Josh and Hogwart Bowman so first of all I want to speak a bit about the action perception cycle which is a core ID in active inference and the second is the agent which is all of them the environments provide observation to the agent for example an image of the environments and then the agent need to take this input and perform inference on it and the goal of the entrance process is to extract high-level iron states such as the position of black man in X and Y or the position of the ghost or whatever information may be relevant then based on those States we can perform planning and action selection and action selection how it puts the action to perform maybe the action going up which is fed into its environment which produce another observation and this cycle continues until the Trail Ends now that we have the core there is a core idea of Arctic inference which is action perception cycle I will be speaking about active inference in a bit more depth so basically active inference is about an agents which is equips of a model this agent makes as I said observation which are represented here at the bottom of the screen and those observation depends on the island States through the a matrix so that it is a matrix provide a distribution of the observation for each possible Latin States we also have the G Vector which contains the parameter of the prior over the initial item States as well as the B Matrix which explain how the transition of the environment works so basically it explains how given a state and an action we get the new state at time t plus one we as I said uh have an action or here is a policy variable and this action variable or policy depends on the Precision parameter which is called gamma and as we will see influence how stochastic or deterministic the policy of the agents will be so here we see how the prior over action is being defined so it depends as I said on the game parameter and it is and it is defined as a soft Max function of minus the gamma the Precision parameter times the expected free energy and the expected free energy for particular policy is basically a sum of all future time steps so from t plus 1 which is the first time step into the future to uppercase team which is a Time Horizon and for each time step the expected free energy is defined as the expected Cost Plus xiaomi equity the expected cost is the K Divergence between as a predictive post trial or the future observation and the prior preferences but the prior preferences defines which observation the agent want to to observe and this the predictive posterior defines How likely its observation is and so what we want to do is to minimize the Divergence between the distribution so that we actually observe what we learned okay and the second term is about the entropy of the likelihood mapping uh expected under the directional posterior of a state so I'm speaking about directional posterior I will explain what this is in a minute uh that's that's the definition of the expected…