Measures of Consciousness From the Viewpoint of Information Geometry by Masafumi Oizumi

you hi my name is Massa who mio is me I'm from I am in Japan and Monash University in Australia so so today's talk about I think mathematics of integrating information and a measure of consciousness defaults the basically integrating information and I will give you the kind of details of how we can qualify integrating information and my framework is based on the you know information geometry which I'll explain later so here is an outline of the Facebook are first briefly review there are kind of most important concepts of individual information theory of consciousness and that explain how to mathematically define integrate information this is kind of a unified framework so today's main objective is not giving the kind of best measure of integrated information but laws are given kind of a framework mathematical framework to you know define integrate information and the finally I'll explain the relationships between the integrate information and the other can be well known Connery's so first i'll start from the probably the most important concept in IIT which is a distinction between the extrinsic bus's intrinsic information so IIT states that title system must generate information to generate consciousness when I teach sales information to the first two are intrinsic information so let's just compare other you know brain or brain and you know just a camera digital camera which consists of millions or billions of just photo diodes actually that when we consider just extrinsic information which is the information for some ideal external observer we qualified just you know some info let's say mutual information between the some external stimulus and some response of the system actually the plain terms of this extrinsic information we cannot distinguish the brain from the digital camera this camera generates a much of extrinsic information when we see are the states of the billions of photo diodes we can extract much of you know information about external world in this sense the brain and the camera actually the same but in the camera actually there is no intrinsic information because that inside the camera there is no such a thing that can accumulate all of the you know information generated by our photo diodes just inside of the camera these four diodes just independently work regardless of other photo diodes so there is no communications between the you know four diodes and there is no sort of intrinsic information so intrinsic information is something like information for the system itself and the information that system can exploit for itself which does not depend on external observer but only depend on just causal relationships in the system IIT tries to quantify this kind of concept intrinsic information and you know conscious system must generate intrinsic information not extrinsic information and also the important thing is that you know concept of integrate information so integrate information clarifies actually the difference or information loss after some cause or inference inference inferences between the parts are cut so let's see the digital camera again this constitute of just a bunch of photodiodes independent photo diodes even if we cut the causal inferences between the photo diodes nothing basically changes so in that case we say integral integral differential 0 so if nothing changes or no information is lost after the you know causal inferences are cut we say integral function is zero therefore we say that they their camera cannot generate consciousness but in in the case of the brain if we cut there are you know causal inference between the neurons millions of billions of neurons the difference will be a lot and lot of information is lost and also the IIT tries to solve sort of boundary problem of consciousness so let's imagine that you know two people are talking actually we can consider you know integrate information between the two people it's it's probably a detail but there is something something from integrate information between the two people but we say that there is no such a thing of you know two consciousness of two people we say there is just two consciousness in each person so IIT excludes that you know the other are consciousness only entity that you know generates the local maximum fight exists in that case the interior information inside this person is much much larger than the integral information in the whole to part two people so this leads to consciousness exist and also in the case of the brain actually there is a left brain and the right brain and due to the you know strong connection between the you know left and right brain the our consciousness is one so in this case the whole integrative nature is larger than the you know integrating information in the parts of the brain so in our brain you know integration is bound because because that the whole integration is larger than the part of the integrating information in this way we can exclude you know consciousness and the only there you know introduction is a local maximum exist so in this way we can make the boundary of our many many consciousness okay so let's move on to the you know how to mathematically quantify integrity information so the important thing is that we cut the system and we compare the original system with their you know disconnected our system so in this case that we we use was a full model for the you know original network which is described by this probability distribution P and this connecting model is represented by the probability distribution Q and we qualify the difference between the you know this P and Q and we say integrate information just difference between P and Q so to tonify integrate information we need to first define the operation of cutting cause our differences between the parts and we also need to define the how we can measure the difference between property distributions so in IIT previous version of IIT we just use you know well-known harbor cry blood divergence which is kind of easy to analyze but we use we change that this difference into a swivel distance which we live probably it's better for understanding consciousness so there are some options to you know for the difference between property distributions but in my talk I use carbon fiber diverges for the ease of you know explanation and most most important contribution of the kind of my are what is that we also have to minimize the difference between P and Q which corresponds that are finding the best approximation of P by using this Q this works in Mali and also max also proposes this operation for defining the interior information so let's just consider the specific just a simple system which constitutes of just two neurons two units x1 x2 and I represent passed via X and the present state of the system by white and there are actually two types of kind of interactions in the system first one is the interactions at the same time and also interactions across the time which is represented by our red arrows and what we are interesting 4:25 integrity information is just a you know causal inferences red arrows and especially these two arrows Belinda you know units and the example of the this kind of dynode system is for instance at Gaussian distribution case which is just deepened by just a linear equation of Y and X the part present and past and actually that that is you know interaction at the same time comes from just I know noise sort of noise for you Asian okay so with this setting first we need to you know define the operation of cutting cause our inference so let's consider cut the cause our inference just from X 2 to y 1 in this case we imposed some constraint for the disconnecting model which is represented by the cube Y 1 given X 1 X 2 it's just Qi Bank of extra which means that you know the state with y 1 only depends on just X 1 not depend on X 2 by imposing this condition we can cut this connection so by using this definition of cutting cause our inference we can derive many from rates many well-known qualities as well as integrating fashion first let's consider just you know cutting all of the you know cause our inferences from the past state to the present state this is done by imposing you know four constraints right this which is just so you know kill Y given X is just Q by 2 y does not depend on X by imposing this constraint for we need to do is minimize the difference between the full model and the disconnection model disconnect model is constrained by this and I introduced framework of information geometry so information germ theory considers a no space of probability distributions so let's consider this is the space of the probability distributions and a point in this space represents some particular property distribution in this case P here and this constraint are sort of forms some sub manifold or somewhere praying of praying inside that this space so this blue and praying represents our you know this constraint so the point any point in in this praying satisfies this constraint and from the theory of information geometry actually the closest point chiusa which is the best approximation is the orthogonal projection of p to the sub manifold and actually that in this case this sub money for this sort of flat manifold like a plane so we can use the Pythagorean relationship like this like a bit among P and the closest point to star and any point inside the money for some Marshall Q and this relationship holds so by using this relationship we can easily find the closest point which is actually if we can find that the Kerr divergence is minimized when Q star of X is actually equal to the actual you know property this marginal distribution of X and the case of wise action is equal to the axial you know marginal distribution of Y and if we substitute these you know minimize point in this equation we can get actually mutual information which makes sense so - you know summarize if we cut all of the codes our inferences between the past and present and then we minimize the difference between food and disconnecting model we can get mutual information between x and y which is kind of an upper bound of information that is available in the system and if we cut only the one closer inference actually that we can derive transfer entropy right if we minimize under this constraint the Kerr divergence become just I know transfer entropy which just only qualifies are you know inference right of X because it is represented by de you know entropy of y1 given only x1 - interval y1 given everything so this actually quantifies the effect of x2 for predicting y1 further integrating information we want to quantify the cause our you know in interactions between the parts so we cut both directions and we impose two constraints and then we minimize the you know difference between P and Q we can get the major winter great information so the important thing is that this in this way the integrative information is less than the mutual information total amount of information because that lets say that this is the space of the constraints for integrating information this under let's say this green one the you know the constraints for mutual information which cuts all of the quarter inferences actually this blue space is Russia than this green manifold so there are you know distance minimized in larger spaces always of course smaller therefore we can easily see that this integrative venture is less than the mutual information so this unified framework based on minimization of the Kerr divergence between the flow model and you know this collective model clearly shows the relationships between among many Connolly's so first if we cut all of the cozaar inferences we can get mutual information between x and y and if we cut only causal inference from X 2 to y 1 we can get a transfer entropy and then if we cut the both causal inferences we can get our integrity information so in this way we can get this clear relationship so transparent mutual fashions are per bond and the transfer entropy is less than the fine also that we can compare these countries with the other previously proposed Connolly's the this one is actually previously proposed as a measure of integrity information but right turns out this major qualifiers also simultaneous sort of interaction non Kosar interaction between y1 y2 so therefore I believe that if we want to just quantify causal inferences this measure is better than this so let me summarize our trace so first you know I proposed you know no other measure of integrate information from a unified framework the important point is that I I'm not claiming that this is that kind of best measure but this framework is kind of general and that is utilized for deriving other measures as well so far we did is that first we define the operation of cutting causal inferences that is given by this and then we codify the difference between the full model P and some disconnected model q and I use car back tribal divergence for the ease of analyzing their measures but we can of course use other measure Riker earthmovers distance which is more difficult to deal with but I think it's an interesting or future research project and then we minimize the difference the p and q and they will get you know measure of integrating fashion and also I think that it will be very interesting to derive integrating measure from physics viewpoint like Marx did in 2015 paper which conveys a kind of super ability of the you know Hamiltonian and also probably I think that for instance information thermodynamics can contribute to this aspect I think but I have not yet time yeah that's all

Channel: FQXi

Views: 2,045

Rating: 5 out of 5

Keywords: Masafumi Oizumi, fqxi, Information Geometry, Measures of Consciousness, Consciousness, max tegmark

Id: vwjwI6G2_bQ

Length: 19min 35sec (1175 seconds)

Published: Thu Dec 01 2016

Reddit Comments

[u/blowaway420]

What's it about? IIT?

Or woowoo? Why down voted?