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>> It's my great pleasure to introduce drunkeness Meyer is a humorous professor in Young University reckons being. From NY thing I'm happy he's got his bachelor's at University of Cincinnati in 9993 and then the university type Carolina in science and I. Really hate being on there and very important from a journalist and very fact review and now you're listening and Mark Morrison g. 28 there you have.

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It he has received I Ming from a number of agents recently and stats and a half hours and today he got that I think are some of his more recent were a manic. But we've heard through your own economic Ok well thanks for inviting me. To today and let's try to give you my story.

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You know my. My research life's been a little bit complicated so early in my career I did a lot of work on what we call ran a lot if using models of of decision making you know these laws describe the deliberation process of the evidence accumulation process that leads up to a decision.

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But anyway I you know later in my life I had an enlightenment and I started working on quantum models of cognition. Now this quantum Onil they're not quantum models like a quantum brain model it's more like using the mathematics of quantum theory but applying it to cognition and actually there's a lot of the similarities between Markoff models and quantum of that I'm going to try to show you but there's some important differences.

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But most recently I've been happy because I've discovered I can put these 2 models together into one big model the physicist actually have created this model it's called the open systems model it actually puts quantum models a mark of models together in one big models and now I'm I'm happy again to put my split personality back together again so so let me tell you the story here.

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This is this is work I'm going with my collaborator take Peter qualm University of Florida and simplest catch is not universal Kansas. Now here's an example of evidence accumulation during decision making you know like if you're a path ologist then you're a radiologist or you're looking at an m.r.i. image of some woman's breast and you're trying to decide if she has cancer or not you know you have to you Can you kind of have to you know look around in your family information from this this complicated display and so you're trying to decide if a cancer is notice present and so there's a there's a sequential seed like there's a sequential sampling an accumulation of evidence that's going on and so the decision takes some time and so that's this that's an evidence accumulation process and of course the time it takes is important to the power to have all just because they probably have a lot of images that they have to get done in a day so there's a time pressure on these decisions as well but that anyway that's kind of an example of an evidence accumulation process of decision making Now there's also what we call.

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Value based decision making or a preference accumulation process and like here like here let's say you're trying to decide which motorcycle to buy and so here you not accumulating evidence you're more accumulating evaluations you're saying well you're looking at the style the motorcycle the speed of the motorcycle things like that so you keep accumulating evaluations in order to make a decision or the or the decision might be whether the whether or not you should even buy a motorcycle or use that I used to own a motor I used to ride a motorcycle for 225 years I got hit for same Ok now anyway those are tooth pulled i type of decision making tasks and any random walk models and the Fusion models have been applied to both these kinds of tasks and we've recently been trying to ply what we call quantum dynamics to these 2 different types of tasks song I tell you about that story now now what's the difference between a market model and a quantum model.

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Now this is a very simple diagram right here we actually use models that are almost you know approximately a continuous state model but this is just a simple diagram to. Illustrate the ideas and here's someone I love to have a kind of a stipple mockup Random Walk Model on the right have a was supposed to illustrate a quantum random walk in a difference now the idea of a random walk Mark Markham Random Walk Model is and it's this moment time you located some place right now like the decision makers located at 30 you know kind of leaning toward.

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Leaning towards choosing whatever is on the left are left alternative you know and in the market money kind and you jump around you know you move up and down these these states and it's it's a random walk because it's called a walk because you can only move the adjacent states you can't jump like a large distance you're kind of drifting up and down the scale but you're always located someplace and so and mark of Mars you're precisely locate some place and also it is assumed in these models that you know your location now the information might come from the environment that you can expect that to move you to a new the location but any moment time you know where you're located because when you hit it let's say when you hit a boundary of say this the top boundary if you hit the top if you can find a drift up to the top Bantry you decide Ok I'm going to choose the option on the right so that's a and you have to know you're here to make that decision so you're you're you're bouncing around and you're precisely located and you know where you are you might not know we're going to move next because it's coming from the environment but you know we are located.

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Now the word the way quantum walk works is different is you not know Katie anywhere so it's kind of it's called a dispersed state you know so there's some potential you have a potential for all these different states Now the interesting thing about. This called a superposition state an interesting thing and I like this because I feel like psychologically we have these kind of indecisive States not not well not well located States so when you're in this state at a single moment time there's some potential that you might give an answer like 70 that's above 50 or there's at the same moment kind of some pop potential that you'll give an answer that's below 50 like 30 and so there's that both answers are potential in the market model if you're located here and you're asked to report 30 but here you're not located in place and if you're asked you kind of have to locate yourself and so this is called the spur superposition state kind of like this idea that that your preferences are your evidence is kind of dislocated not well located now here's another diagram here to this horizontal axis is your evidence state different degrees of evidence that say for left and right and this is time often we often we rotate this diagram Tempus little These are make this diagram over here in this direction but anyway this year there are degrees of evidence in this time so you're starting out here neutral neutral degree of evidence and then you start collecting some evidence for the right and then you start collecting some evidence for the left and you're drifting around and so this is the mark of a model.

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But the idea in a market model is you have a trajectory like all classical dynamical systems you have a trajectory you're located at some flight point in time you're kind of jumping around getting bounced around but at its moment trying to locate it so that you produce ejector you like this.

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Where the quantum model it doesn't have a location you have a wave so you just just your dispersed across the states so you might have a wave that's it started here and around the ritual and then this wave might being pushed to the right it might get start push to the left and so this wave is travelling across time so instead of having a trajectory you have this kind of dispersion that's a wave like movement across time now in the market model you know you know you know where you're located any moment time so if I stop to it let's say So you're processing evidence and I stop you at this point 4 seconds.

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You would report an existing location so you would report let's say you know point 25.25 evidence because that's where you are located when you're asked So the measurement just records an existing location or isn't in a quantum model you're not really located anywhere and so if I stop the airport point 4 seconds you know right the 4.4 seconds are kind of spread out I mean maybe you're leaning towards the right there's more potential for the right but you know well located convinced located but if I if I ask you to make an exact probability judgment let's say then I have to come out of I have to leave this dispersed state and report an exact answer in sight what happens as the measurement creates a location than a quantum model you're not located in term measurement take place is the measurement creates a location rather than just recording existing those cases so that's how the quantum of work I mean I think human beings like that we're very sense of the measurement so before the measurement you're kind of in this in the size of the spurs to dislocate it's base but the measurement force you into precision and change of state now.

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Now and when you talk about a mark off model we were going to be talking about the probability you know the probability that you're located someplace. So when you so mark of one of the problems that models but the probability refers to an observer you know my is a fear of my my uncertainty about where you're located so you're making a decision I can't see inside your mind I don't know where you're located you know where you're located that I don't know the observers this is like an f. what we call an epidemic uncertainty it's the observers uncertainty about a person's existing the location so the person has an existing the location but the observer doesn't know where it is and so we put a probability that you're located here and we put a probably that you located here so the the probabilities are coming from the observer or as in a quantum model the probability refers to an internal uncertainty the person him him or herself.

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There are unsure about what answer they're going to give they don't they're not really well located and so if you ask them before you ask them they're not really welcome located and so the probability comes from them trying to resolve the uncertainty and make a measurement make a response and so that's a difference in kind of a that's what we call an unsecure and certainly it's an internal uncertainty this is a post I'm servers uncertainty so that's how these models psychologically differ and I kind of got attracted to these quantum ideas Now here's another illustration of these models now that the market model you know we're going have a probability distribution but this probability distribution reflects my own certainty about where you're located you know so I think whether some probably most likely you're located at 50 at the beginning of the trial the blue curve represents initial probability distribution for the market model and now let's suppose the evidence is pushing you to the right.

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So this is the this is the probability that I think you're located in different places and then the evidence starts pushing this distribution to the right and if it's a reflect well this is I'm using right here I'm using reflecting down market model because we've found that skills and or it we're going to be looking at down the scales but anyway the part market model is going to be the say the evidence is pushing you to the right is going to pile up here now the market model I like to think of it is like wind blowing sand so there's a pile of sand right here and then the wind started blowing the sand and it's pushing this distribution over to the right and then the wind piles the sand up into an equilibrium this division so that's how mark of my models work it's like wind blowing sand and you know and you push to the right and you hit the wall and you pile up sand piles up on the wall the quantum models are different now this is this is that what we called the squared amplitude.

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Had to make a distinction between Anyway this is the property distribution from a quantum model and with this a proposition so you starting out like the mark of mana maybe with a distribution it's located at 50 but if your own uncertainty you kind of spread out you don't know where you're located and most likely the most potential that 50 but you're kind of spread out you're dislocated and then the evidence is pushing this wave to the right and then this wave moves to the Right now quantum model the analogy is like when blowing water up against a wall so winds blowing this way and what happens in a quantum model this water this wave water water of wave hits this wall and it'll bounce off and still it awesomely now the when to push it back that will bounce off and they don't come back and so you get oscillation in a quantum model now many for many years my Markoff buddies like Roger reckless or somebody will make fun of that oscillation property I think that that doesn't happen in evidence accumulation of preference accumulation the work well we're going to investigate that later.

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So that's a difference between these models what's going wrong direction Ok now this is the slide let slip it's scary but. I'm not going to go through the whole this in detail but what I want to show you here is there's a lot of similarities between Markoff processes and quantum processes and I just try to locate the critical difference so it's not terribly important you understand all the slide but the one of things I want to mention or try to get across it was this so a market model to see represents the probability that you're located in some state like some state of evidence that probably located in a 30 to one a market model does it if there is a probability distribution across the states so let's say if you had 100 states instead of the thing I just had like 7 or 9 if you had 100 states more of a continuum you might have a probability distribution across those 100 states where the quantum of what it does is it puts an amplitude on its state so instead of a probability which is a number between 01 quantum model to use an amp that's called an amplitude and an amplitude can be a complex number but if it's squared met modulus is less than one in magnitude but anyway the quantum models has an amplitude empathy addition across states this represents your dislocated diffuse state across the evidence scale now the squared amplitude is all have to sum up the one so like an a in a mark of one of the probably this news now is up to one the problem to sum up the one but the quantum of the squared ample to sum up the one so it's kind of a different norm the norm here is a like l. one Norman is like an l. to norm now the mark of models the way they what the way they move this probability distribution evolve it is a transition matrix to the start of a transition operators of the transition operator are to move those distributions we're talking about.

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You know kind of moves this is what's moving that the distribution over time whereas the the quantum model has something called a unitary operator to correspond to the transition operator and so this this unitary operator it moves the amplitude distributions over time it actually rotates them it's a rotation operator and then finally the probability for your Markov model is you you take all the states that are associated with an answer and you sum up the probabilities of the states associated with an answer in a quantum model what you do is you square the amplitude so you get the squared amplitude and then you sum up all the squared amplitude associated with an area anyway so you can see that there's a lot of similarities here but the main difference in the market models operating a probability is the quantum model operates on amplitude at the end you sum up the probabilities but the squaring is produces a non-linearity and the quantum models that you don't get in the markup model is a produces a big difference in how that models operate Ok let me take a look at some evidence why we started thinking about this point the models for evidence and preference evolution so this is the paper that we published in p n a s.

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Several years ago 2015 so we did this task so this is about motion tasks so the stop motion has a kind of popular in neuroscience and cognitive science. So you know you see the basic idea is that you see these gods jiggling around in on a screen and they're kind of jiggling around at random but some proportion of them are jiggling in a certain direction that say some proportion are jiggling to the right the proportion of their jiggling in a certain direction systematically is called coherence anyway so your job as you stare at the screen at these dots you going around and then you have a side of the jig they jiggling mostly to the left or mostly to the right.

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Now and what we can also do then is like you know you watch the Dutch jiggling around you decide if they are moving to the left or to the right but then we can allow you to continue watching as dots to going around think and ask you to rate the probability later on what's the probability that they're moving to the left or to the right sort so we can get a choice followed by a probability rating this this path here but in this experiment then we want to compare a choice followed by a probability rating to another condition or you just made just made a probability rating there's no choice so you see the dots jiggling around and it's at the point in time that you know you would have made a choice you don't make a choice you just put a pre preplanned preprogrammed button so there's no decision making here you're just still watching the dots going around and then you continue watching the dots you going around and then you make a probability rating so so we got these 2 conditions a single rating condition down here we just watched dots to going around and to make a probability rating and then we have a double condition here we make a choice and then make a probability rating and so this allows us this is allows us to study what we call interference interference effects this kind of like a in quantum theory a to slit experiment if you're you know a thing about quantum physics.

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Now the critical thing that we want to do is we want to look at the marginal probability rating that you give at the end. Now if you make a choice and you say it's to the right you know then you can have a probably have you can have a like a distribution of ratings that's on the right side but if you make a choice and you say it's on the left you're going to get a distribution of ratings on the left side but more instances pulling those who dissed distributions the ones that were going to look at the poll distribution the marginal pulled across the choices like averaged across the 2 choices and so then you get a distribution a single distribution here called across the 2 choices and we're going to compare that to the marginal distribution where you didn't make a choice so we're going to compare this marginal distribution when you did make a choice but we ignore the choice to this marginal distribution we didn't even make a choice and the way you see these dots jiggling around and this path here this is the choice followed by probability rating you see the dacha going around you decide if they're going left or right make a decision you see the dots to going around some more and then you make a probability reading where in this condition you just make it a probability rain and no choice you see the Duchy going around at the same time when you would have made a choice you just click a button just the control for the motor response anyway so you see you just watching the dots are going around the whole time and then you make a probability rating so we want to compare the single condition with the bottom panel we only make a probability reading the double condition now we're into knowing the margin of probability So what's the you know when you pull across the choices you know average across the choices what's the marginal probability distribution across.

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The probability ratings and compare that to the marginal distribution here now the thing about a market model is that satisfies something called the Chapman Kemal graph equation so it satisfies like a total probability so it says like let's say this left hand side represents the in the no choice case where you just make a probability reading this is the marginal distribution of probability readings on a no choice on the right here we have the total probability where you made a choice but were were pulling across the choices so this is the probably that you made a particular choice then it's the probably the probability rating given a choice and we're summing across those and so the mark of models says that these 2 things have to be equal and so that's from the Chapman Kemal graphic way Jeanette's from the yeah anyway so the market model predicts no difference between a single condition and a double condition no interference effect now the quantum model predicts that they're not going to be the same and the reason why this happens is the mark of a model when you calculate the probability that a summing the probabilities everything stays linear but in the quantum model you're you're summing up amplitude but then you get to square the amplitude and when you square a sum you get these cross product terms and that gives you this interference effect so we predict interference with the quantum model but no interference for the mark of low Now this is one subject so this is the horizontal axis is the problem different confidence range called Conference ratings but probability judgements so here's a 5050 percent probably judgement here the 70 percent probably judgement so these are the different probably judgments in this example to the evidence of pushing it to the right this is the relative frequency of giving a probably judgement so you can see that like.

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In this choice condition right here the relative frequency of giving a really high well relatively high probability judgement the real different frequency is pretty large. And same thing for the no choice here is the choice and no choice but what you can see here is the date is the blue line here you can see there's a big interference effect the choice yes person is big bump right here in the middle and is no bump right here and so we get this kind of interference effect going on produced by the choice that the market model cannot predict also the quantum model kind of captures this wave property of the probability ratings or the market model prisoners monotonically decreasing.

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Probability distribution and this is like this is represented as wave I mean this represents a stylus and building up to the equilibrium distributions or this the the dotted just dashed curve here that of the quantum model reflects this water wave hitting the boundary and in kind of. You know sloshing around it could hit a lower boundary and slosh back and he could hit the top batteries last back so that's that's this anyway the main thing is we're getting this interference effect as predicted by the quantum model not predicted by the Markov model and we also did a quantitative comparison of these models and use a base factor to compare the models for the individuals and we found 7 out of 9 individuals of the base factor favor the quantum model over the mark of Moses the 1st kind of nice strong piece of evidence that we had for the quantum dynamics over the market dynamics Now this is another study let's try to go for briefly because I don't want to run a time delayed a little bit but we did a 2nd study with a similar kind of study where but instead of making a choice in response you see the dots to going around and then you make a probability reading at time one then you continue seeing the dots to going around and you make a probably reading at times too so you're making 2 probability readings that's a different times and we have 3 conditions and one condition you know they made a public reading of point 5 seconds at 1.5 seconds.

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We get probably right in here and probably reading here another condition you made a reading it 1.5 seconds in 2.5 seconds and we get those 2 rating and then a 3rd condition you get a rating a point 5 seconds and 2.5 seconds and so the key to the critical thing that we want to do in this experiment is we want to do a quantitative test of the 2 models so we fit the market model in the quantum model to the 1st 2 conditions like these are calibration stages and so and but then when using the 3rd stage is the generalization test we're trying to see whether or not you know the premise estimate if in the 1st 2 stages how well can they predict then you know using the same parameters we use we think the premise in the 1st 2 stages reuse a same parameters to predict performance in the 3rd stage so that provided a quantitative test these 2 models.

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It's model had what you might think of as 22 parameters to keep parameters of a drift in of the fusion parameter for each coherence condition and we estimate the Premier's by maximum likelihood and I'm just going to summarize the results here so we don't run out of time for that what I get one of the study I have to show you and basically what we find here in this experiment is that the quantum model this is these are g. squared so we're getting a g. force lacka fits are getting a g. squared like a fit and this is for the generalization test the square lacka fit on a generalization test with a quantum model versus the mark of multiverse the quantum model and you can see that you squared if it's positive that means you know because of lack of it that if it's positive the quotes we favor the quantum model of the market model and you can see the g. squared are definitely favoring the quantum model except for something interesting here is the coherence thing creases the mark of lost art starts doing better in fact you know another some other analysis that we've done we find that you can actually build a market model that outperforms the quantum model at the high coherence levels but the quantum outperforms at the local here is levels to the start of making us think that actually you know like when the lee evans is really strong you get night pretty consistent really high probably reading the low probably reading some arc of model works better but when you have like a lot of uncertainty the quantum other works better so we're we sort of started thinking that we really need both of these models so now let me turn to this.

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Summer here both the quantum of predict is interference factor in the in the market model to not you could it you could add ad hoc assumptions but we try to rule out a lot of these ad hoc assumptions in our papers. And we found interference for these effects which kind of give the support for the some quantum model we found evidence for the quantum on this generalization test but we did find some evidence that the mark of model starts working better at the higher coherence levels so now going to talk about this most recent study this is the most this is a really interesting study I think.

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I hope everybody. Ok you can see my pointer Yes Yes Ok we did 2 experiments let me just talk about one of them so this 1st experiment you were giving coupons these are real coupons you could choose like a coupon that's got more money for for a restaurant that's got a certain rating and a certain distance away from your home so here's one coupon and then here's another coupon and so had to make a choice between these 2 and also a preference rating so that basically what we did is we turned on a display and showed the choice between a coupons now we have different coupons so this is just one example but we don't you know variety of different coupons that we're looking at but this one coupon here but we turn on the coupon and they're looking at the coupon and so they they study the scoop on for 5 seconds and then it's time to see one.

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We ask them to either make a choice like we talked about before where they had decide which coupons you want you want they want to left or you want to one of the Right that was one condition but the other condition they didn't make any choice they just push the button so the 2nd condition they're just looking at the coupons still thinking about the coupon and then finally we had to make a preference rating so they made a preference reading like house if there is a move on our to the right there strongly prefer in the Q coop on the right where they can move the left a strongly for the coupon a left so so we can study interference effects again we can compare we're going to compare the marginal distribution right here.

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Whether you made a choice or you didn't make a choice and as before the mark of mana predicts no effect of choice vs no choice on the marginal distribution or as a quantum of a prediction effect but but another thing that the quantum model predicts that I mentioned at the early the beginning of this talk so the quantum model predicts oscillation and so we looked at the we looked at this preference rating at different points in time here's a day like like here's a choice that after 5 seconds but then 3 seconds later or 6 seconds later 9 seconds 830 and 45 seconds later we ask this preference ready for work or we want to see is there any kind of oscillation going on in between during this period of time and people have never really they like people like Roger rock I make fun of Roger but he's friend of mine but you know they always made fun of the fact that they want to model predicts oscillation but they never tested it so we tested it and what we find is we don't get off leash and now that the stage is the bit busy because I got predictions on here but.

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This topical for the 1st experiment and these blue these blue crosses represent. The no choice condition and the and the red plus is represent the choice condition and what you can see is both of them are giving oscillation the Blue Cross they're giving oscillation. And the red pluses are also giving oscillation this is systematic I mean so in other words this oscillation was systematic across all the subjects or else if it was if it was oscillating different for different subjects it would average out to nothing but we got signal you know statistically significant and also we did Beijing and now this confidence that we get it we're getting some awful ation right here so 1st of all we're getting oscillation that the quantum on a project mark of model does not predict that like here out here the predictions isn't the best buddy Mark of model it just grows monotonically like Roger thinks everything should grow monotonically I make when I want you to tell me but them anyway this is the mark of modern predictions this month on the these lines here the quantum of production now so the quantum of predicting is oscillation also though the quantum model is predicting dampened oscillation there's a choice effect that the red plus is our choice the oscillations been dampened by the choice.

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And the no choice has a wider angle I mean it's sweeping out wider so we predicted so the quantum model of. The quantum model actually predicts that the choice is going to dampen oscillation and we get that effect now the only thing is is that this is pure market model projections these lines right here this is a pure quantum model predictions and it's kind of off and so what we discovered is well we discovered what these open systems models that I'm going to briefly describe next and that the trouble is that the the Quantum the mark of models are bad because they have no oscillation it have monotonic growth and the mark the quantum although a little bit problematic because they predict oscillation but you know what we find is often is that the we get off lacing but the oscillation tends to dampen out eventually doesn't keep us going forever where the quantum out of will and so what we develop now while we were barred from physics actually it's called Open systems model the open systems model Priss oscillation like a quantum of the beginning but then it starts dampen down act like a Marco model and we also get this choice choice versus no choice difference in the open systems model so that's that's the model that we're working with now we're really happy because now we can put these 2 things together the other slides pretty complicated and I'm not going to try to explain all of this to you but I'm just trying to show you it's made kind of briefly how this works so that the Sultan's really kind of real anyway.

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And this is this is an open system quantum model this is what's actually they using quantum computing actually these models because they're going to try to dampen when they have to worry about quantum noise damping the system anyway this is called density matrix is a matrix now that there is thinking about this matrix so this is representing the state of evidence this matrix and reason why matrix is interesting is a dial entries can represent classical kind of probabilities but the off diagonals represent the quantum what we call the quantum coherence so you get the quantum nature in the op diagonals.

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You have the classical on the diagonal to this density matrix and then this part of the open systems model this is the or this what we call your Schroedinger equation in a density matrix warm so this and this is giving you the quantum dynamics and then over here is a called Linde let operators but anyway these are giving the market dynamics and so we get we're getting quantum dynamics and markup dynamics combined in one complete model and we have a parameter weight parameter can adjust how important each one is this comes from Physics and what this model does then happen the way this model works is that early on in time this quantum regime is operating in dominating the system but later on in time the the the Quantum the markup part of the system starts dominating so you've get early oscillations but then it dampens out converge to the mark up model so you get in both systems in one dynamic and so we were really excited about this model.

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And this model captures the at the stem a mark of kind of uncertainty on the diagonal and it captures the the ontic uncertainty in the off diagnosis and so we capture both kinds of uncertainties in these models dream just as the equipment occasion question which at the superscript Eggerth there is that the conjugate transpose Yes that's concentration Ok thanks yeah.

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I mean yeah. Yeah I don't want to go through all the details as questions of a complicated and for yes I find you want to make sure yeah it's a death a conduit transpose Yes thank you and if it's down here to you know this is how weak how we form the density that like this vector This is a vector right here this is a vector Vampa distribution and then this is its conjugate transpose and the this outer product forms a density matrix that's how we form this image Well I'm probably getting close to end of time here I suppose.

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How am I doing on time. You have to do what I could for you I'm. I think I really see that stead through this thing then I can't believe well time for questions. I thought I was going to run out of time because of the screen problems we had and I guess I went maybe I went too fast Well anyway so the conclusions are well the mark of models they have a strong track record for predicting choice of response time and past research but but but we've been accumulate some Perkel evidence that that the mark of laws are not the complete story you know that's that's these interference effects that we found and he's also now these oscillation effects that we're finding that we think there's you know the mark of one of the not the complete story there's there's something like quantum dynamics going on in there too now and and so now there's open systems model it's not necessary to choose one versus the other because the model provides an elegant integration and including a parameter that describes the comp and the contribution of each type of dynamic so these models you know they're not really want to compete with each other what we have is like a super model that incorporates them both a unified theory if you want and.

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And so we think that the evidence accumulation and presence accumulation seems to have both kinds of uncertainties this ontic uncertainty which which reflects the uncertainty about the state of the system and then I'm sorry I'm sorry epistemic uncertainty epidemic uncertainty there's uncertainty about the state of the system and the Arctic uncertainty is the internal uncertainty about the decision maker is to his dispersed indecisive state and so this of a systematic captures both like the epidemic I as I said it's on a diagonal this density major x. in the Arctic and the off diagonal so we're where we think this this is a really exciting new development and and so that's that's the end of my story then I hope I didn't go to I felt like maybe I was going to run of the tides or started speeding up a lot anyway thank you for your attention will answer questions at this point.

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Thank you so much. Clothes and everybody. You know sorry about the pointer problems. All right. You have questions and you're. Going to chat. I have a question you put on my camera here. So I'm curious did you choose a quantum model so that you could. And I said So why did you choose a quantum model over like a control control systems model where you have transit and steady state sorry about this.

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You can have a you know you can have a classical. Deterministic dynamic model for example but well you know those. The reason why we like a quantum model let's say is because why would it if it's a classical that dynamic that's a non-linear off letting the terminus tick model why would that choice versus no choice why would you get interference you'd have to you'd have to make up some story about why the choice is now produced any interference about the interference effect this is critical for you know and we also get this kind of dampening effect in the oscillation you can have a non-linear dynamic model that also leads but that non-linear dynamic model doesn't a primary predict any kind of dampening produced by the choice.

[00:38:44]
Of the mean that would affect it. Depend on the state batteries and how they are controlled right like what I mean yeah you'd have to make something up I mean you could make something up. Now we are and we win and when you make something up then you have to go back and seal accounts for some of our findings so when we published the piano yes paper we made up 6 I don't know maybe I can remember maybe 17 ways you could do that 17 and we will do everyone else now maybe you can think of another one that we didn't rule but you can look at the p. and ask paperweight where we like the mark of more you can say well you know when you make the choice then to change the system like for example here's an example of a change in the system of the markup when you make a choice let's say you choose that you think the dots are going on the right that starts to bias your evidence accumulation so now you start focusing more of the evidence for the right and you discard the evidence the left I don't produce a change but that that's change that's like we call it.

[00:39:49]
What you call confirmation effect it's kind of a confirmation you made a choice you said it's all right so now you try to look for confirming evidence that explanation predicted the opposite of the results that we've got that doesn't work the interference effect we got of the opposite direction but anyway there's that other explanation like that but we tried to rule out a lot of them.

[00:40:10]
Course you can always try to think of another one but yeah I mean we we can this is never going to prove them prove the mark of you can't prove anything or to be true fact all theories are wrong but. But we like the quantum model we think we have evidence for the quantum model because we we design is experiments before we looked at the data so we made a priori predictions in the quantum model supported We were surprised fact what we did is interference studies we never thought we get interference because then we thought you would get interference nobody people working with the mark of models when they asked for choice in conference readings they never thought of anything about the choice interference with the interfering with the conference ratings they say they thought they had no effect but we started it we did with the quantum of predicted it so we're I think events of the quantum model is where we're predicting things a priority so I can have a dynamic system of dynamic system doesn't have to operate it does it are slight It could be it could be monotonic or could be oscillating I mean could be the one but we have to protect our solution that's for her and that's a good question no I mean if that's a legitimate question I mean there's always alternative explanations I guess that's Ok.

[00:41:31]
So you you sort of spoke to us in the beginning and maybe I missed this but I was just wondering when you were talking about the just differences between like a decision like a preference decision. Versus like is this moving right or left decision is like do you see a difference in which type of model is the best for those is there any difference at all well I mean we we've applied we've applied the quantum model to both both of those types you know I mean you know so we found.

[00:42:09]
I don't think it's I don't think it's like we played the quantum of this perceptual this is an evidence accumulation past here but then the last one I just showed you with the eyes with the also lation that's a value based decision making so we found evidence for the quantum model both those kinds of tasks I think but but I think what the.

[00:42:29]
Where the quantum model probably operates better is when there's a lot of uncertainty you know like if you have a cleared preference decision I mean if you have a really strong preference probably the mark of model to start working better but if you have a really difficult preference decision I think the quantum level might work better or if you have a really difficult evidence accumulation problem like it's coherence is low that that's where the quantum is working better but if the coherence is high that's where the market model starts working better that's what we're finding so far Ok so it's more about the uncertainty then that's on the type of the decision yeah that's what I think thank you.

[00:43:14]
John I've got kind of a similar question with regard to the math. The weights in your open system they were static I'm not time dependent right right so are they really operating off the amount of coherence in this just don't know if yes so the flights are static they don't change across time but the way this dynamic works is so let's let's go back to this density here I mean this density that on a diagonal you have kind of like classical probabilities on the off diagonals you have like the quantum quantum stuff you know the quantum amplitude and what happens is is that it starts out you have you have off dial entries that makes the system in quantum computing and call it coherent the off diagonal entries are important for what they call coherence it starts out coherence.

[00:44:07]
In a quantum but but this this this mark of part this this Lynn blood it's called in blood and quantum field but it produces a mark off it starts driving it starts driving all the off diagonals 0 so it's it slowly starts you know anything else off diagonals and so it diagonalize what they call diagonalize is this matrix starts out a full matrix with off diagonal but then this thing the k's all the off diagonals becomes diagonal once this becomes diagonal then the classical is quanta I mean it's classical Markoff So it starts off with off diagonal that's called that's called a coherent quantum state and then it's driven by this term to get rid of the diag to get rid of the op diagonal it becomes diagonal and it becomes more classical Markoff So like in quantum computing this is what's causing the trouble this is like environmental environmental disturbances coming in so this is this is what's the quantum state that they want to keep They don't want this term here they want to try to reduce this emphasis they want to reduce this wait here because this makes the system to go here but for us to say this hatches the the the market part so you start out all sliding and you kind of the all slaves and starts to dampen out and so that's what that's what we use this for yeah anyway yes so these are constant but it's just the the mechanics of the dynamic is you know so the changing from quantum regime to mark of regime is is coming from the ballot the balance of these 2 types to different kinds of dynamics Ok I think I see thank you.

[00:45:53]
I know so thank you for all the talk I'm so I'm a research her interest in individual differences and correct me if I'm wrong so on one slide you. Would think that So 7 out of knowing subjects preferred a quantum although so which means that 2 of them prefer.

[00:46:14]
Markov So I'm interested in so this any liking to be told different is I think the majority of people may favor quantum but like this any. Good to be told phrase that could predict which model people she was yeah I mean we got this and here tonight these are different participants right here and some of the participants rashly best said by the market model and then some others are best that by the quantum of like here's one fit by the market model Here's one here's one so yeah you get these individual differences and you know now we know we can find nothing predictable we can capture that that individual difference could be this prem or Omega right here so if I said if I set a maggot here to one so this goes to 0 so this goes disappears and so we just have this part of the model is pure Markov and you get exactly exactly the same answer as there is a random walk to fusion model.

[00:47:18]
But if I said if I set a maggot to 0 then this becomes one and I get a pure markup model you know so I think the individual difference would be as a mega parameter. And we've just started fitting this model so. In fact this the state it was the 1st time we tried to fit the the open systems model I think the you know the parameter turned out to be.

[00:47:41]
This was like around point this article point 8 This is point to the most so it's like mostly Mark often but still healthy part on the quantum but I would put the individual difference here but now why would some people be I mean it might reflect some people are more like.

[00:48:01]
You know clear let me say clear really clear the term maybe clear an earth and their inner state you know the state of mind clear where some people are like let's say more in the term allow more determinant I mean not a bad thing but you can be like that morons in some kind of an uncertain indeterminate state where someone has to be always in it it's a terminal state that could be an individual difference I mean some people don't like uncertainty for example they like to be sure about things in a mark of money or you're definitely one state of the other for example you're clear in the quantum of your kind of fuzzy you know you have this kind of fuzzy superposition indeterminate state so that could be some people are more like color fuzzy reasoners I'm not advancing maybe just because quantum computing they have to take care they take advantage of that fuzzy reasoning that's how they can speed up the computations the superposition state is needed to do faster quantum computing so the fuzzy is not necessarily bad but when you're in a fuzzy reasoning state it's kind of like your pet you're thinking about hypotheses in parallel so some are some way the quantum computer is speeding up calculations because if it can compute hypotheses in parallel.

[00:49:15]
And so this fuzzy state you're you're you're you're maintaining many hypotheses simultaneously and you know in a sense the kind of the sense that you're kind of in a fuzzy state so it could be that kind of an individual difference thank you sorry sorry but we're fine. I think you spoke to this just a 2nd ago it sounded like you're saying there might be individual differences in the Omega parameter right.

[00:49:48]
And so you could kind of elaborate on that more do you think you could have say you know there's really regression style predictors of those individual differences in the Omega parameter. Yeah the bottle has kind of the structure of a mixture model and yeah right modeling the typical thing you do is you've got kind of individual predictors of the kind of mixture probabilities such that one person is much more likely to be in one class and another person is much more likely to be in a different class and you could kind of change the tuning of the mixture components between the kind of the quantum dynamics and the markup dynamics you know but yeah I mean I may agree on that in the me make a couple of points yeah play one well one point I want to address is a little bit of a difference you're talking about then I'll come back to your point but this model it's kind of a mixture but it's not like it's this go back to this picture it's not a mixture in a sense that.

[00:50:45]
Some proportion of people are doing this and then some proportion of people are doing that and you average the 2 or or let's say on some trials a subject doing marked your mark off another child the subject of impure quantum and we've averaged across trials that's not what the model doing the fact that that model is continued all Slate's is amiss when presenting else listen but as we continue oscillating we're getting dampening So this mixture is not a mixture of like sometimes you do this and sometimes you do that this is like a mixture of 2 different dynamics you know so it's a new dynamic that's a mixture to dynamics but yeah would be kind of interesting like for thinking about a mega like say a person who likes.

[00:51:29]
You know comfortable with uncertainty or an indefiniteness or you know allowing possibilities exist in parallel you know we have like in the vision different measures we try to use as individual difference measures to try to predict the mega because we haven't done that yet because this is all pretty new but if it there might be a lot of individual differences that could predict this so we have like a regression model that predicts a mega and that will allow us to predict you know an individual dynamics better rather than just fitting the parameter to them.

[00:52:02]
Thanks I know you said that you haven't done that but where you try and start researching that what do you think the m. from ation in your data would be that would drive good estimation of those individual difference parameters so what is simply being more trials would it be certain types of trial certain task types of tasks or was because often you can think of a mixture model quite easily but that the rubber meets the road when you try to estimate and you end up giving $100.00 items you know when each one takes 2 minutes and things like That's so it's not it's not feasible in practice what what do you think would drive this.

[00:52:50]
Well I think that. It would have to really get a good estimate of these the magazine 1st of all you need to have an experiment where you can maybe see reveal some kind of quantum effects like you know if I just that are. We have that just plain old choice response time data if it plain old choice response time data you know like a typical experiment.

[00:53:18]
We're not going to see the quantum effect you know you think the extra parameter right here is not going to be the actual parameter right you're not going to need it you know we could probably just define Well we we have to we have compared a fit of a pure quantum model to a pure Markov model for choice response time now actually the pure market model when I did it did a little bit better than the quantum model for predicting response time but anyway so I think you know if you just do a simple choice response time experiment you know need going to get this estimate because you well you probably won't need it so you're going to have to do an experiment that or you can have to collect data where you you're kind of kind of exposing these quantum effects then you can start estimate as parameters so it might not just be.

[00:54:02]
Sufficient to add a lot of trials or things like that it might be more important to make sure you. You kind of have the conditions for exposing what that are uniquely quantum aspects you know without that you know probably probably won't need the quantum model so we you know we deliberately design experiments where we kind of try to discover you know that we predict these quantum effects and that's where that that's where the quantum model will shine if we didn't deliberately design in these conditions that we probably wouldn't get strong evidence for the model and actual Our sense thank you.

[00:54:41]
Yeah that's a quick question about transitions face transitions so we are starting and I want them. To a going from a quantum state like system to the mark up system which of the Paramor you think is driving that transition at Hitchin is a mego do you thing it is a gamma here yeah no it's the gamma as in these it's the get with now the gamma like this gamma right here is your mark of transition probability So basically this is going to be the probability you go from say from state j. to state I So that's the mark of transition probability.

[00:55:22]
In these things this thing this complicated thing is I know it's like enough that's called a limb let operator this is this thing is what's driving the off diagnosis 0 so it's not the a mega I'm course of a magazine or you won't have this but if you get your fix the Mega this is over time making off diagonals go to 0 which changes it from quantum to markup when one of the when this becomes diagonal matrix then is classical Markov So this it's just these Lindland operators that are dampening out the op diagonals This is called These are called decoherence terms and in quantum computing it with Esther this is the one of the changing the regime this one right here and as you look to what that looks like at the transition what's how those parameters behave when at the face transition it's not like it's not like an abrupt transition it's more of a gradual transition so you can't you know I mean yeah there's no like it's not a jump in the system or anything like that it's more that it's becoming more is starting out quantum like and then becomes more Markov like eventually becomes your more God at the end because it's more of a gradual change so there's no abrupt change now you could look out early in the.

[00:56:46]
You know if we look at early in the decision process where it's more in the mark up a quantum area versus we can look at later in a process where it's more in a mark off area you know if we then will you know we could look at the parameters at the early stage or later stage.

[00:57:04]
But but you know we think well these these primaries are always operating all the time and not just turning on a turning off at different stages or. Megas constant This is called a Hamiltonian this is this is constant course it's the dynamics in the row right here this is where the dynamic is these are constants these are constant So all these other things are constant across trials in the this operator that's changing.

[00:57:31]
The dynamics into changing the dynamics in the market off thank you. All right so I think we should probably end here. That next well that was probably some of the most involved discussion group have read your program heard of our great I was Jeremy. If you can I'm yours and I'll just get one more round about your own.

[00:58:04]
If you got to him. Directly you Acme already read your own terms yes yes and I have my comment before next meeting and then you have a half hour or actually an hour break between 130 interview here what are things like if you if you get interest in this quantum cognition we have a book so you can study it's kind of a you know interest you know it's a it's a it's a designed to teach you all of the ideas of quantum cognition you might if you like you might take a look at that book.