[User] Please transcribe this text

[Assistant] Then you can see that that's a negative number, that's a negative number, the whole thing is negative. So α- is definitely, uh, let me see how I wrote it.


[User] Please transcribe this text

[Assistant] These are called just plus and minus alpha. Alpha has two roots.


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[Assistant] And I have to write them as they are. Okay, I'm sorry. So please remove this unwanted sign there, because they are the two answers for α. So I put e to the α plus t. So again, I should change my answer here. I'm really sorry about this one.


[User] Please transcribe this text

[Assistant] Now I'm going to write it below so you have a second chance. So here's what it looks like. A, e to the minus.


[User] Please transcribe this text

[Assistant] E to the minus, gamma over 2 minus,


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[Assistant] I think I did mean this. Or did I get it wrong?


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[Assistant] So they both have the first number to be minus gamma over 2.


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[Assistant] And the square root comes to the plus sign for one of them and minus sign for the other one. I probably have A and B mixed up. Let me check that.


[User] Please transcribe this text

[Assistant] Yes? I'm willing to be corrected if I got A and B mixed up. I know these are correct. I want to make sure this is what I call B.


[User] Please transcribe this text

[Assistant] Let's see if that works out. This should be B e to the alpha minus t. B e to the minus gamma over 2, uh, minus that, yes.


[User] Please transcribe this text

[Assistant] Okay, the point of writing it this way is to show you that both these powers...


[User] Please transcribe this text

[Assistant] This is clearly a positive number, so it's e to the minus a negative number. I just wanted to show you that this object, that's all I wanted to emphasize.


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[Assistant] Inside the square brackets also possible, because this is gamma over 2. You can see this is a number smaller than gamma over 2 square.


[User] Please transcribe this text

[Assistant] If you take the square root of that number, it'll be smaller than γ over 2. So, this cannot overturn the sign of this. It'll still be positive, overall sign will be negative. So, if you draw the picture here, it's a sum of two exponentials. It'll just die down after a while.


[User] Please transcribe this text

[Assistant] To find a and b, what I have to do is to take extra data, one of them may be initial position, x of 0 is given to me.


[User] Please transcribe this text

[Assistant] If x and 0 is given to me as some number, I take the solution, I put t equal to 0, and have it match this. If I put t equal to 0,


[User] Please transcribe this text

[Assistant] Well, all this exponential vanish, and I just get a plus b, because e to the 0 is 1.


[User] Please transcribe this text

[Assistant] So I already have one condition on A and B. Their sum must be the initial position. How about the, uh, initial velocity?


[User] Please transcribe this text

[Assistant] Go back to this x and take dx dt. What do you get? dx dt is alpha plus a is the alpha plus t plus alpha minus b is the alpha minus t.


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[Assistant] The derivative of my answer is this, evaluated at t equal to 0. At t equal to 0,


[User] Please transcribe this text

[Assistant] You put t equal to 0 here, you find x dot of 0.


[User] Please transcribe this text

[Assistant] Equal to alpha plus a plus alpha minus b.


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[Assistant] So here are the two equations you need to find a and b. Solve these two simultaneous equations.


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[Assistant] In other words, I will tell you the initial position and I will tell you the initial velocity.


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[Assistant] You will take then this number, known, and that number, known. This is a linear simultaneous equation for A and B. You will fiddle around and solve for A and B.


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[Assistant] Ah, now we have to ask the following question. In this problem,


[User] Please transcribe this text

[Assistant] The conjugate turned into the other function, and the conjugate of that function turned back into this one. That's why A and B were related by complex conjugation. Here, if I take the complex conjugate of x,


[User] Please transcribe this text

[Assistant] e to the alpha plus t, if it's real, remains itself. So a just goes into a star, b goes into b star, and you want the answer to be unchanged. That requires a equal to a star and b equal to b star.


[User] Please transcribe this text

[Assistant] Thanks for pointing out that here we do want


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[Assistant] Conjugate it and equate it to itself. And remember that now this exponential remains real to begin with, so it doesn't go into anything. It remains itself.


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[Assistant] And I compare this exponential before and after its coefficient that went from a to a star. They have to be equal, so a is a star and b is b star. Yes?


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[Assistant] First I put gamma equal to zero, no friction, and I just re-derived the harmonic oscillator, cos omega t minus phi r plus phi. Then I took a problem with friction, then I got a solution that was just exponentially falling.


[User] Please transcribe this text

[Assistant] Because even though it looks like alpha plus, that's a negative number, that's a negative number, in the end both are falling. So they will, it says you pull the mass and let it go. It'll relax to its initial position and it'll stop. But all of you must know that there's got to be something in between. In the one case I have a mass that oscillates forever.


[User] Please transcribe this text

[Assistant] The other case, I have a mass, when I pull it and let it go, it goes back to equilibrium and reaches zero at infinite time.


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[Assistant] But we all know that the real situation you run into all the time when you pull something and let it go.


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[Assistant] It vibrates and it vibrates less and less and less and less and eventually comes to rest. Where is that solution?


[User] Please transcribe this text

[Assistant] That's correct. So you've got to go back to the roots I found for alpha. It's minus gamma over 2.


[User] Please transcribe this text

[Assistant] Plus or minus square root of, uh, γ over 2 squared minus ω0 squared. I had taken γ over 2 to be bigger than ω0.


[User] Please transcribe this text

[Assistant] I turned on a rather hefty amount of friction so that the friction term was bigger than the omega naught term.


[User] Please transcribe this text

[Assistant] But if you imagine the other limit, where you had no friction and you turned on a tiny amount of friction, then the tiny gamma over 2 will be smaller than this omega naught. Of course, then you got the square root of a negative number.


[User] Please transcribe this text

[Assistant] Right? So you should really write it as, so let's take gamma over 2 less than ω0, then you will write this as minus gamma over 2,


[User] Please transcribe this text

[Assistant] So now what do the solutions look like? They look like x equal to


[User] Please transcribe this text

[Assistant] Omega prime t, but I'm going to call this combination


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[Assistant] Now e to the minus gamma over, gamma t over 2 is common to both the factors. You can pull it out.


[User] Please transcribe this text

[Assistant] Imagine pulling this factor out common to the whole expression.


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[Assistant] Then you just got A at the I omega prime plus B at the minus I omega prime. That's a very familiar problem. If you want that to be real, you want A to be equal to the complex conjugate of B.


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[Assistant] Then you repeat everything I did before, so I don't want to do that one more time. You will get some numbers, see.


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[Assistant] That's e to the minus gamma over 2t times cosine omega prime t plus.


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[Assistant] So what does this look like? What does this graph look like? It looks like cos omega t, but it's got this thing in the front.


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[Assistant] If gamma vanishes, then forget the exponential completely, this is our oscillating math.


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[Assistant] If gamma is not zero, imagine it's one part in 10,000.


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[Assistant] Then for the first one second, this number will hardly change from 1. Meanwhile, this would have oscillated some number of times.


[User] Please transcribe this text

[Assistant] But if you wait long enough, this exponential will start coming into play. And the way to think about it is, it's an oscillation whose amplitude itself falls with time. And if you draw a picture of that, I think you will not be surprised.


[User] Please transcribe this text

[Assistant] So that's the method by which you describe the three cases. One is no friction, and one is small friction, or friction


[User] Please transcribe this text

[Assistant] Obeying this condition, when you have oscillatory motion whose amplitude is damped with time.


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[Assistant] Then you have the other case where γ has crossed some threshold, when ω0 is smaller than γ over 2, then you get two falling exponentials.


[User] Please transcribe this text

[Assistant] So what do you imagine the mass is doing? With no friction, if you pull it, let it go, vibrates forever. That's not very realistic. If you turn a tiny amount of friction,


[User] Please transcribe this text

[Assistant] It will do this, which is very ubiquitous. We see it all the time.


[User] Please transcribe this text

[Assistant] You pull a swing and you let it go, after a while it comes to rest.


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[Assistant] This tells you it never quite comes to rest, because as long as t is finite, this number is going to be non-zero, but it'll be very small. At some point, you just cannot see it. Third option is overdamped.


[User] Please transcribe this text

[Assistant] Overdamped is when gamma is bigger than omega naught over 2, then the answer is nothing that oscillates.


[User] Please transcribe this text

[Assistant] Nothing oscillates, everything falls exponentially with time. There you should imagine, you pull something, let it go, it comes slowly and stops.


[User] Please transcribe this text

[Assistant] When you buy your shocks in your car, the shock absorbers, they're supposed to damp the vibration of the car. It's got a spring, but it's suspending the tires, but it's immersed in some viscous medium, so that its vibrations are damped. So when you hit a bump,


[User] Please transcribe this text

[Assistant] If your sharks are dead, you vibrate a lot of time and slowly settle down. That's when your sharks are in this regime. When you bought them, they were in this regime.


[User] Please transcribe this text

[Assistant] When you bought them, they were doing this. Once you hit the bump and you overshoot from your normal position, you come down to zero and you stay there.


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[Assistant] Alright, so I'm going to the last topic in oscillation, but is there anything else, is there anything here that you need clarification?


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[Assistant] Ah, yes. So when gamma over 2 equals omega naught, this thing vanishes.


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[Assistant] And you seem to have only one solution, e to the minus gamma t over 2.


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[Assistant] You don't have the plus or minus, right? And we sort of know in every problem there must be two solutions, because we should be able to pick the initial position and velocity at will.


[User] Please transcribe this text

[Assistant] If a solution is only one free parameter, you cannot pick two numbers at will.


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[Assistant] Now that's a piece of mathematics I don't want to do now, but what you can show is in that case, the second solution looks like this.


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[Assistant] It's a new function, not an exponential, but t times an exponential. We'll solve the equation.


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[Assistant] Those who want to see that this is true can put that into the equation and check.


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[Assistant] In other words, pick your gamma carefully so that this square root vanishes.


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[Assistant] Only a gamma is left, but that gamma is not independent of omega. That gamma is equal to, uh, 2 omega naught.


[User] Please transcribe this text

[Assistant] For that problem, you can check that that's the solution, so is that.


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[Assistant] There are nice ways to motivate that, but I think I don't have time to do that. Yes?


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[Assistant] Why was a equal to a star here? You mean here? Okay, take this x. Demand that when you conjugate it, nothing should happen. Okay?


[User] Please transcribe this text

[Assistant] In this particular example, when alpha plus and alpha minus are real numbers, e to the alpha plus t remains e to the alpha plus t when you take conjugate. Therefore, a has to remain a star.


[User] Please transcribe this text

[Assistant] And B must also remain invariant when you take the conjugation.


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[Assistant] In other words, if this was an imaginary exponential, like in the other problem, when you take the conjugate, this exponential becomes this guy and that exponential becomes that guy, then by matching the solution you can, you will be able to show this must be the conjugate of that, that must be the conjugate of this.


[User] Please transcribe this text

[Assistant] But if no imaginary exponentials appear, each term must separately be real.


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[Assistant] Now this is something, uh, you will have to think about. I'm not saying my repeating it makes it any clearer. So what I want you to do is take the x, take the complex conjugate of x, equate the two sides.


[User] Please transcribe this text

[Assistant] That's the rule among functions that if you've got e to the plus alpha t, its coefficient should match on both sides, and e to the minus alpha t should have matching coefficients.


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[Assistant] It's like saying when two vectors are equal, the coefficient of i should match and the coefficient of j should match. There's a similar theorem that if you take a sum of two independent functions, equated to the sum of two other same independent functions, the coefficient must separately match. If you impose that, you will find what I told you.


[User] Please transcribe this text

[Assistant] Okay, now for the really interesting problem. The really interesting problem is this. I got the mass, I got the spring, I got the friction, but I'm going to apply an extra force, F naught cosine omega t. This is called a driven oscillator. So far the oscillator was not driven.


[User] Please transcribe this text

[Assistant] No one is pushing and pulling it. Of course, you pulled it in the beginning and you released it, but once you released it,


[User] Please transcribe this text

[Assistant] No one's touching the oscillator. The only forces on it are due to internal frictional forces or spring force.


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[Assistant] But now I want to imagine a case where I am actively driving the oscillator by my hand, exerting a cosine omega t force.


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[Assistant] So omega here is the frequency of the driving force. Okay? That's why there are so many omegas in this problem.


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[Assistant] The omega prime that you saw here is not going to appear too many times. It's a matter of convenience to call this omega prime. But this omega will appear all the time. When I write an omega with no subscript, it's the frequency of the driving force.


[User] Please transcribe this text

[Assistant] And the equation we want to solve is x double dot.


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[Assistant] Plus gamma x dot plus omega naught squared x equal to f over m because I divided everything by m cosine omega t.


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[Assistant] Now this is really difficult because you cannot guess the answer to this by word problem. Now you can do the following.


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[Assistant] If the right hand side had been e to the i omega t, instead of cos omega t,


[User] Please transcribe this text

[Assistant] You would be fine, because then you can pick an x that looks like e to the i omega t.


[User] Please transcribe this text

[Assistant] Then when you take two derivatives that look like e to the i omega t, one derivative looks like e to the i omega t, x itself will look like e to the i omega t, you can cancel it on both sides. But what you have is cos omega t. So here's what people do. It's a very clever trick.


[User] Please transcribe this text

[Assistant] People say, let me manufacture a second problem.


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[Assistant] Nobody gave me this problem, okay? This is the problem you gave me. I make up a new problem, the answer to which is called why.


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[Assistant] But y is the answer to the following problem. The driving force is sine omega t.


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[Assistant] This is my artifact. I introduced a new problem you did not give me, but I want to look at this problem.


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[Assistant] It's still going to satisfy the equation. Let me multiply by i. Put an i here, put an i here, put an i here, put an i here.


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[Assistant] Then I have got x plus iy double dot plus gamma times x dot plus iy dot plus ω0 squared times x plus iy. Let's introduce a number z, which is x plus iy. It varies with time.


[User] Please transcribe this text

[Assistant] Then this equation, by adding the three equations, looks like z double dot plus gamma z dot plus omega naught squared z is f over m e to the i omega squared.


[User] Please transcribe this text

[Assistant] This is a problem in which the thing that's vibrating is not a real number. The force driving it is also not a real number. It's the cosωt plus i sinωt. But, if I can solve this problem by some trick, at the end what do I have to do?


[User] Please transcribe this text

[Assistant] The real part of the answer, because the answer will look like a real part and an imaginary part. I'll have to dump the imaginary part. That'll be the answer to the question I posed.


[User] Please transcribe this text

[Assistant] Imaginary part of it will be the answer to the fictitious question I posed. Now why am I doing this?


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[Assistant] The reason is the following. If the driving force is e to the iωt, I can make the following ansatz at guess z is some constant times e to the iωt.


[User] Please transcribe this text

[Assistant] Because let me take that assumed form and put it into this equation.


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[Assistant] z naught e to the i omega t, because two derivatives of e to the i omega t give me i omega times i omega.


[User] Please transcribe this text

[Assistant] Then one derivative gives me i omega times gamma times z naught e to the i omega t, and no derivative just leaves it alone.


[User] Please transcribe this text

[Assistant] Well, e to the i omega t, whatever it is, can be cancelled on two sides, because it is not zero. Anything that's not zero, you can always cancel. And here is the interesting result you learn.


[User] Please transcribe this text

[Assistant] Easy part is to take the guess I made and stick it in the equation, cancel exponentials and get the answer. What you should understand is


[User] Please transcribe this text

[Assistant] x was what I was looking for, I brought in a partner y, and I solved for z, which is x plus i y, and z was assumed to take this form.


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[Assistant] So, I'm going to call it the Iωt divided by this number in the denominator. I'm going to call I for impedance.


[User] Please transcribe this text

[Assistant] And it's the following complex number, omega naught squared minus omega squared plus i omega gamma.


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[Assistant] E to the iωt divided by this complex number i. Imagine this complex number i. What does it look like? It's got a real part and an imaginary part.


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[Assistant] So we are told the answer to our problem is to find this number z and take the real part.


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[Assistant] It's everybody agree that every complex number i can be written as absolute value times e to the i phi, which is going to be here.


[User] Please transcribe this text

[Assistant] And I'm going to write it that way because now things become a lot simpler if you write it that way. f0 over m divided by absolute value of i, e to the iΦ, e to the iωt.


[User] Please transcribe this text

[Assistant] Now, this is the iΦ. I can delete it here and put it upstairs as minus iΦ.


[User] Please transcribe this text

[Assistant] So let me write it in that form, then it's very easy. f0 over m divided by the magnitude of this i times e to the i, ωt minus π.


[User] Please transcribe this text

[Assistant] The real part of this function, I hope you know by now, is cosωt minus phi.


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[Assistant] And that's the answer. The answer to the problem that was originally given to us is the following.


[User] Please transcribe this text

[Assistant] You know the magnitude of the applied force, the amplitude of the applied force. You know the mass of the particle.


[User] Please transcribe this text

[Assistant] You need to find this absolute value of i and phi. For that, you construct this complex number, whose real part is this, whose imaginary part is i omega gamma.


[User] Please transcribe this text

[Assistant] Then the absolute value of I is just, by Pythagoras' Theorem, ω0 squared minus ω squared squared plus ω squared γ squared.


[User] Please transcribe this text

[Assistant] And the phase Φ obeys the condition tan Φ is equal to ωγ divided by


[User] Please transcribe this text

[Assistant] So this is the answer to the problem that was given to us.


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[Assistant] But there's one subtle point you should notice, which is the following. Where are the free parameters in this problem?


[User] Please transcribe this text

[Assistant] Everything is determined in this problem. Phi, absolute i, all this is known, but we know every equation should have two free numbers. You know what they are?


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[Assistant] Okay, let me tell you what the answer to that question is. I'm saying I can add to this the solution I got earlier on without the driving force.


[User] Please transcribe this text

[Assistant] In this problem, when I had a right-hand side with a driving force, let me add a zero to that. That's harmless.


[User] Please transcribe this text

[Assistant] And by superposition principle, if that force will produce that displacement, 0 will produce what? Well, we have seen all morning that even when the right hand side is 0, there are the solutions they got for you. e to the gamma over 2, cos omega, prime t, etc.


[User] Please transcribe this text

[Assistant] So you can always add to this what's called a complementary function.


[User] Please transcribe this text

[Assistant] Which is the solution to the equation with no driving force, which is what we were studying earlier in the class. But usually people don't bother with this.


[User] Please transcribe this text

[Assistant] Because they all have in them e to the minus γt over 2. So if you wait long enough, this will die out. This is the only thing that will remain. So at early times, this is not the full answer. You should add to this the answer when there is no driving force. And together, they form the full answer.


[User] Please transcribe this text

[Assistant] And the numbers a and b that you have there will be chosen to match some initial conditions like initial position, initial velocity.


[User] Please transcribe this text

[Assistant] Okay, now, it's, time is up, I'm going to stop, so I have not been able to, uh, finish some parts of this.


[User] Please transcribe this text

[Assistant] So I'm trying to see what I can do. Uh, I had asked for you to give this problem set to me.


[User] Please transcribe this text

[Assistant] On our, what is this today? On Wednesday, right? So you don't have enough time.


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[Assistant] I mean, I haven't taught you a few other things you need about five minutes more of work, so I don't want to keep you back. Here's what I will do. I will post


[User] Please transcribe this text

[Assistant] On the website some notes on just the missing part here. So you can read it, and you can do one or two problems you may not be able to do without that. Then I will come on Wednesday, and I will teach that to you again, but you will be able to hand in your problems.


[User] Please transcribe this text

[Assistant] One Insect. Written by Catherine P. Burdick. Illustrated by Nora Voutis.


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[Assistant] Four legs.


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[Assistant] Welcome to Human-Centered Artificial Intelligence. The last couple of decades in the developments of deep learning have been exciting in the problems that we've been able to automate.


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[Assistant] In the problems that we've been able to crack with learning based methods. One of the things underlying this lecture and the following lectures


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[Assistant] Is the idea that with purely the learning based approach that we have been using,


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[Assistant] There's certain aspects that are fundamental to our reality that we're going to hit a wall on.


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[Assistant] Underlying first prediction under the idea of human centered AI in this century is that the learning based approaches have been successful over the past two decades. Deep learning, machine learning approaches that learn from data are going to continue to become better.


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[Assistant] And dominate the real world applications. So as opposed to fine tuned


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[Assistant] Optimization based models that do not learn from data. More and more we're going to see learning based methods dominate real world applications.


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[Assistant] That's the underlying prediction that we're working with. Now, if that's the case, the corollary of that


[User] Please transcribe this text

[Assistant] If learning based methods is the solution to many of these real world problems, is the way we get smarter AI systems is by improving the machine learning and the machine teaching. Machine learning is the thing that


[User] Please transcribe this text

[Assistant] We've been talking about quite a bit, that's the deep learning, that's the algorithm, the optimization of neural network parameters, where you learn from data. That's the current focus of the community, current focus in the research, and the thing that's behind the success of, uh, much of the developments in deep learning. And then there's the machine teaching. That's the human center part.


[User] Please transcribe this text

[Assistant] It's optimization, it's optimizing not the models, not the algorithms, but optimizing how you select the data based on which the algorithms learn. It's to make better teachers. Just like when you yourself are learning as a student or as a child how to operate in this world, the world


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[Assistant] And the parents and the teachers around you.


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[Assistant] Are informing you with very sparse information.


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[Assistant] But providing the kind of information that is most useful for your learning process. The selection of data.


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[Assistant] Based on which to learn, I believe is the critical direction of research where we have to...


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[Assistant] Solve in order to create truly intelligent systems and ones that are able to work in the real world and I'll explain why in ways that I'm referring to.


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[Assistant] The implications of learning based systems. So when you have a learning system that, a system that learns from data.


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[Assistant] Neural networks, machine learning, learns from data.


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[Assistant] The fundamental reality of that is the model is trying to generalize


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[Assistant] Task with operating based on a very small subset.


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[Assistant] Of samples from that reality. And that generalization means that there's always going to be a degree of uncertainty. There's always going to be a degree of incomplete information. And so, no matter how much we want to, these systems will not be provably safe. So we can't put anything concrete down to how


[User] Please transcribe this text

[Assistant] It will not be explainable. Any step of the pipeline in which they made the decisions of AI systems will not be perfectly explainable to the satisfaction of, uh,


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[Assistant] Uh, uh, uh, us as human supervisors, uh, so there again, human supervision constantly will be required.


[User] Please transcribe this text

[Assistant] And the solution to this is a whole set of techniques, whole set of ideas, they're kind of, they were putting under the flag of human centered artificial intelligence, human centered AI. And the core ideas there,


[User] Please transcribe this text

[Assistant] Is that we need to integrate the human being deeply into the annotation process and deeply into the human supervision of the real world operation of the system. So both in the training phase and the testing phase, the execution, the operation of the system.


[User] Please transcribe this text

[Assistant] So this is what deep learning looks like with the human out of the loop.


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[Assistant] The human contributes to a learning model by helping annotate some data and that data is then used to train


[User] Please transcribe this text

[Assistant] To train a model that hopefully generalizes in the real world, in that model.


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[Assistant] Makes decisions and deep learning is really exciting because it's able to, in a greater and greater degree of autonomy, able to form high level representations of the raw data in a way that it's actually able to do quite well on certain kinds of tasks that were before very difficult.


[User] Please transcribe this text

[Assistant] Fundamentally the human is out of the loop both of the training and the operation. First you build the data set, annotate the data set, and then the systems run away with it.


[User] Please transcribe this text

[Assistant] They train on the data and the real world operation does not involve the human except as the recipient of the service the system provides.


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[Assistant] Now the human in the loop version of that, the human centered version of that means that annotation and operation of the system is both


[User] Please transcribe this text

[Assistant] Aided by human beings in a deep way. What does that mean?


[User] Please transcribe this text

[Assistant] So we can look at human experts or individuals and


[User] Please transcribe this text

[Assistant] At the, uh, at the training phase, the first part of that is the objective annotation. We need to significantly improve objective annotation, meaning annotation where


[User] Please transcribe this text

[Assistant] The human intelligence is sufficient to be able to look at a sample and annotate it. This is what we think about as an ImageNet and all the basic computer vision tasks where a single human is enough to do a pretty damn good job of determining what's in a particular sample. And then there's subjective annotation. Things that


[User] Please transcribe this text

[Assistant] At a low level of emotion, these things that are a little bit fuzzy, that require multiple people to annotate and at a high level are ethical questions.


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[Assistant] The supervision, again, of the system based and I'll give examples of this more concretely.


[User] Please transcribe this text

[Assistant] Guaranteed to be safe, that's not guaranteed to be explainable, and the subjective


[User] Please transcribe this text

[Assistant] Autonomous vehicles, the supervision of systems in the medical diagnosis, in medicine in general, and this is AI operating in the real world


[User] Please transcribe this text

[Assistant] Making ethical decisions that are fundamentally difficult decisions for humans to make and that's where the crowd intelligence needs to come in. And so we have to transform the machine learning problem by integrating the human being.


[User] Please transcribe this text

[Assistant] First up top in the training process, on the left, that's the usual machine learning formulation of a human being.


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[Assistant] Doing brute force annotation of some kind of data set, cats and dogs in ImageNet, segmentation data set in Cityscapes, video action recognition in the YouTube data set. Given the data set, humans put in a lot of expensive labor to annotate what's going on in that data, and then the machine learns.


[User] Please transcribe this text

[Assistant] The flip side of that, the machine teaching side, the human centered side of that, is the machine instead. The learning model, the learning algorithm, talking about most of the neural networks here.


[User] Please transcribe this text

[Assistant] Sparse subsets of the data that are most useful for the human to annotate. So instead of the human doing the brute force task first of the annotation, the machine queries the human. This is the field called machine teaching. The machine queries the human with questions and therefore the task is, and this is wide open research field, the task is to


[User] Please transcribe this text

[Assistant] Minimize in several orders of magnitude the amount of data that needs to be annotated. In the real world operation side,


[User] Please transcribe this text

[Assistant] The integration of the human looks like this. On the left, the machine, now trained with a learning model, makes decisions. And the human, living in this world,


[User] Please transcribe this text

[Assistant] But it's able to provide a degree of uncertainty is one of the big requirements to be able to specify a degree of uncertainty of that decision such that when uncertainty is below


[User] Please transcribe this text

[Assistant] A certain threshold human supervision is sought. And again, in that, in that decision,


[User] Please transcribe this text

[Assistant] Whether that's a costly decision financially or a costly decision in terms of human life, human supervision is sought.


[User] Please transcribe this text

[Assistant] And the service is received by the human, by the very same humans that are providing the supervision, or another, another set of humans. But ultimately, the decision is over, sought by human beings.


[User] Please transcribe this text

[Assistant] This is what I believe is going to be the defining mode of operation for AI systems in the 21st century, is we won't be able to, as much as we'd like to escape, to create perfect AI systems that escape the need to work together with human beings at every step.


[User] Please transcribe this text

[Assistant] Grand challenges here that define human centered AI. I'll focus on a few today. I'll focus on one very much so. And even with that degree of high pruning, we have 120 slides, so I'll skip around. Uh, but.


[User] Please transcribe this text

[Assistant] On the human centered AI during the learning phase.


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[Assistant] As opposed to needing 10,000, 100,000, a million examples, how do we reduce that where the algorithm query is only the essential elements and able to learn effectively from very little information, from very little samples. Just like we do when we're students, when we learn fundamental aspects of math,


[User] Please transcribe this text

[Assistant] Uh, language and so on. We just need a few examples, but those examples are critical to our understanding.


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[Assistant] And the second part of that is the reward engineering.


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[Assistant] That during the learning process injecting the human being into the definition of the loss function of what's good, what's bad. Systems that have to operate in the real world have to understand


[User] Please transcribe this text

[Assistant] What our society deems as good and bad, and we're not always good at injecting that in the very beginning. There has to be a continuous process of adjusting the rewards, of reward re-engineering by humans.


[User] Please transcribe this text

[Assistant] So that we can encode human values into the learning process. Now on the second part on the human centered AI during real world operation when the system is actually trained.


[User] Please transcribe this text

[Assistant] The, the, there is the interactive element of robots and humans working together. That means


[User] Please transcribe this text

[Assistant] The part I'll focus on quite a bit today because there's been quite a lot of development and progress on the deep learning side is human sensing.


[User] Please transcribe this text

[Assistant] Is algorithms that understand the human being.


[User] Please transcribe this text

[Assistant] Algorithms that, from taking raw information, whether it's video, audio, text, begin to get a context


[User] Please transcribe this text

[Assistant] A measure of the state of the human being in the short term and the long term over time, the temporal, the temporal understanding and the instantaneous understanding.


[User] Please transcribe this text

[Assistant] Then there is the interaction aspect.


[User] Please transcribe this text

[Assistant] So once you understand the human, the perception problem, you have to interact with them.


[User] Please transcribe this text

[Assistant] And interact in such a way that is continuous, collaborative, and a rich, meaningful experience. That's a, uh, we're in the very early days of creating anything like rich, meaningful experiences with AI systems. Especially learning-based AI systems. And the safety.


[User] Please transcribe this text

[Assistant] Real world operation, safety, ethics, unrolling the results of the reward, the engineered rewards that were in place during the learning process now come to fruition. And we need to make sure that the, the trained model


[User] Please transcribe this text

[Assistant] Does not result in things that are highly detrimental, catastrophic to our safety.


[User] Please transcribe this text

[Assistant] Bounds on AI systems and there's an entire group of work and I'll mention what we're doing in that area. So first on the machine teaching side.


[User] Please transcribe this text

[Assistant] And the efficient supervised learning. I'd like to sort of do one slide on each of these to kind of give you an idea, uh, near term and, and do two things for, for each area that we will elaborate in future lectures on and some of it I'll elaborate today.


[User] Please transcribe this text

[Assistant] And a sort of thought experiment, a grand challenge, that when, if we can do it.


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[Assistant] That would be damn impressive. That would be a definition of real progress in this area.


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[Assistant] So near term directions of research for machine teaching for improved supervised learning integrating the human into the annotation process is instead of annotating brute force is annotate by asking the human questions.


[User] Please transcribe this text

[Assistant] Transform the way we do annotations where the process of annotation is not defining the data set and then you go through the entire data set. It's a machine teaching system that queries the user for questions to annotate.


[User] Please transcribe this text

[Assistant] And on the algorithm side, active learning, these are all sort of areas of work where we can be more clever about the way we use data. Select data on which to train. So active learning is actively selecting during the training process which part of the data to train on.


[User] Please transcribe this text

[Assistant] Uh, data augmentation is taking, uh, things that have been supervised by a human and expanding them, modifying the data, uh, warping the data in interesting ways such that it expands, it multiplies the human effort that was injected into helping understand what's in the data.


[User] Please transcribe this text

[Assistant] The one-shot learning, zero-shot learning and transfer learning are all in that category and self-play is in the reinforcement learning area where the system


[User] Please transcribe this text

[Assistant] That would define serious progress in the field, as if we take ImageNet or Coco, uh, the ImageNet challenge or Coco object detection challenge, and training only on a totally different kind of data.


[User] Please transcribe this text

[Assistant] Be able to achieve steady results. So training only on Wikipedia.


[User] Please transcribe this text

[Assistant] With the text and images that are there on Wikipedia, be able to perform object detection on the state of the art benchmark of Cocoa.


[User] Please transcribe this text

[Assistant] Cocoa is the dataset of different objects with rich annotation of the localization of the objects. That I believe is exactly the kind of thing that all the problems in the transfer learning and efficient data annotation machine teaching have to be solved to achieve that.


[User] Please transcribe this text

[Assistant] Another way to, another challenge you can think of, if you can even just simplify it more, is achieve 3 percent, 0.3 percent error on MNIST. That's the handwritten recognition task that everybody always provides as an example. So achieve a very good, uh, accuracy.


[User] Please transcribe this text

[Assistant] State-of-the-art accuracy by training only on a single example of a digit.


[User] Please transcribe this text

[Assistant] As opposed to training on thousands, training on one example. That's something that most us humans can do, uh, given


[User] Please transcribe this text

[Assistant] One example of a new language you haven't seen before, for each character, after studying them for a little bit, be able to now classify future characters at high accuracy.


[User] Please transcribe this text

[Assistant] Of the learning process where the human needs to be injected and the near term directions of research there is the reward engineering.


[User] Please transcribe this text

[Assistant] And the tuning of those, continuous tuning of those rewards by human beings.


[User] Please transcribe this text

[Assistant] So OpenAI is doing quite a bit of work here. Here's a game played by Human and AI.


[User] Please transcribe this text

[Assistant] It's really my favorite example of this. Uh, on the left, human is controlling a boat that's finishing a race. On the right is a RL agent, reinforcement learning agent that's controlling a boat that's trying to, uh, not finish a race, trying to maximize the reward.


[User] Please transcribe this text

[Assistant] Defined prior to, uh, by, by, initially by a human being. And what it finds is that you can get much more.


[User] Please transcribe this text

[Assistant] Uh, reward by collecting green turbos that appear as opposed to finishing the race.


[User] Please transcribe this text

[Assistant] It realizes that finishing the race actually gets in the way of maximizing the reward. And so that's the unintended consequences of, uh, a reward function that was, uh, that was specified


[User] Please transcribe this text

[Assistant] Uh, AI system to operate in a context where there's a lot of fuzziness for us humans.


[User] Please transcribe this text

[Assistant] There's a lot of uncertainty. There's a lot of gray area. There's a lot of challenging aspects in terms of, uh, what is right and what is wrong.


[User] Please transcribe this text

[Assistant] That we continually need to improve on. An example I provide here is one of the least popular things, uh, in, in the world, is, uh, the U.S. Congress.


[User] Please transcribe this text

[Assistant] It makes perfect sense that an AI system should be able to take on this challenge.


[User] Please transcribe this text

[Assistant] And that would, I see that as a grand challenge is replacing some of the fundamental representation of large crowds of people that make ethical decisions, uh, replaced by, uh, by a human-centered AI system.


[User] Please transcribe this text

[Assistant] Okay, in real world operation, the first thing we have to do


[User] Please transcribe this text

[Assistant] Before we have a robot and a human work together, the first thing is the robot has to perceive perceive the human. Question?


[User] Please transcribe this text

[Assistant] The question was, do you want to, so there's currently, there's Congress, do you want to change the way Congress works? Make it better? Or do you want to just take the system that currently is and automate it? So,


[User] Please transcribe this text

[Assistant] The idea is take the system as it currently is supposed to be and automate that.


[User] Please transcribe this text

[Assistant] So an AI system can provide a lot more transparency of the inputs.


[User] Please transcribe this text

[Assistant] The idea of Congress is supposed, the only inputs is supposed to be the people. And the beliefs of the people.


[User] Please transcribe this text

[Assistant] And there's also, you know, and there's rich information there.


[User] Please transcribe this text

[Assistant] So, for example, I mean, the, the input, there's a, you know, for me,


[User] Please transcribe this text

[Assistant] Not saying anything about politics, but there's certain issues I care a lot about and certain issues I don't care much about, uh, in this.


[User] Please transcribe this text

[Assistant] Put that aside and then there's certain issues that I know a lot about and certain issues I know very little about.


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[Assistant] And those don't actually intersect, uh, well, I'm very opinionated about things I don't know anything about. It's very common. All of us are. So, being able to put that representation of me into a system.


[User] Please transcribe this text

[Assistant] That would take a lot of our entire nation together and be able to, uh, make bills that represent the people.


[User] Please transcribe this text

[Assistant] Now the challenge there can't be just the training set and then the system now operates. AI is running the country. No, there has to be that human-centered element where we're constantly supervising, just like we're in theory supposed to be supervising our congressmen and congresswomen.


[User] Please transcribe this text

[Assistant] Human sensing. The first part, in order to have an AI system that works with a human being, the AI system has to perceive, understand the state of the human being at the very simplest level and the more complex, temporal, contextual, over time level.


[User] Please transcribe this text

[Assistant] So the near-term directions of research is purely the perception problem, the deep, where deep learning shines of taking data, whether that comes in the...


[User] Please transcribe this text

[Assistant] Uh, visual, audio, text, and so on, and being able to classify.


[User] Please transcribe this text

[Assistant] The physical, mental, social state, social context of the person. Be able to everything, this is what I'll cover a little bit of today. Everything from


[User] Please transcribe this text

[Assistant] Face detection, face recognition, emotion recognition, natural language processing, body pose estimation.


[User] Please transcribe this text

[Assistant] Uh, those same recommender systems, speech recognition, all of those conversions of raw data that captures something about the human being into actually meaningful, actionable information. The grand challenge there is emotional recognition.


[User] Please transcribe this text

[Assistant] You know, there's been a lot of companies and ideas that we've somehow cracked emotion recognition.


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[Assistant] That we are able to determine the mood of a person. But really, that's, uh, for those who were here last year with, uh, Lisa Feldman Barrett, but just, if you're sort of very honest and you study, uh, emotional intelligence and emotion and the expression of emotion,


[User] Please transcribe this text

[Assistant] It's a fascinating area and we're not even close to being able to build perceptual systems that detect emotion. What we're more so doing is detecting very simple facial expressions that correspond to our storybook versions of emotions. Smiling, crying, like frowning in a caricatured way.


[User] Please transcribe this text

[Assistant] Uh, real emotional recognition, you can think of it as...


[User] Please transcribe this text

[Assistant] Some, exactly the kind of human understanding we need to be able to build in, uh, in our learning models. And we're very far away from that. Especially the long temporal aspect of that. Of being able to integrate data over a long period of time.


[User] Please transcribe this text

[Assistant] Then the second part of human robot interaction in the real world operation is the experience. This is where we're now just beginning to consider that interactive experience of how do we have a rich fulfilling experience.


[User] Please transcribe this text

[Assistant] Uh, autonomous vehicles, for example, semi-autonomous vehicles, whether that's Tesla, Volvo, Super Cruise with the Cadillac, there's a bunch of systems that have now greater and greater degrees of automation in the car, and we get to have the human interact with that AI system, and trying to figure out how do we have, uh, a rich, fulfilling experience in the, uh,


[User] Please transcribe this text

[Assistant] The, currently the Volvo system, that's, that experience is more limited. There's a little icon. It's more kind of traditional driving situation.


[User] Please transcribe this text

[Assistant] In the Tesla, you have a much bigger display about what's going on. In the Super Cruise, there's a camera looking at your eyes in the Cadillac.


[User] Please transcribe this text

[Assistant] Super crew system, there's a camera looking at your eyes determining if you're awake or not.


[User] Please transcribe this text

[Assistant] And uh, in the Tesla case, you know, the miles are racking up. We have real data.


[User] Please transcribe this text

[Assistant] Here at MIT we're studying this exact interaction. There's now over a billion miles driven in the Tesla. And the same in the fully autonomous side with Waymo. They've now reached 10 plus million miles driven autonomously. And there's a lot of people experimenting with this.


[User] Please transcribe this text

[Assistant] That's the, that collaborative interaction of going back and forth, of being able to, for the AI system to express the degree of uncertainty it has about the environment. The AI system being able to express


[User] Please transcribe this text

[Assistant] The deep to deep learning into the pure robotics HRHRI human robotic interaction aspects. One grand challenge would be, you know, Tesla's driven one billion miles now under autopilot under the semi-autonomous mode. The grand challenge here is when we start getting


[User] Please transcribe this text

[Assistant] To the kind of mileage that we see in the United States every year. You start getting into the hundreds of billions of miles driven semi-autonomously. We get to see teenagers.


[User] Please transcribe this text

[Assistant] 16, 17, 18 using these systems for the first time. You get to see older folks, folks who don't necessarily, uh, drive, uh, or use any kind of AI in their lives get to use these systems. Start to explore that aspect. That's the real challenge.


[User] Please transcribe this text

[Assistant] And of course the, the touring, the old touring test.


[User] Please transcribe this text

[Assistant] Now reimagined by Alexa with the Alexa Prize Challenge.


[User] Please transcribe this text

[Assistant] A social bot is creating a natural language is such a beautiful thing to explore human robot interaction with is both on the audio side and in just the text side is


[User] Please transcribe this text

[Assistant] Passing the touring test, that's, that's the true grand challenge in a real way, where you want to have a conversation with a robot, uh, for prolonged periods of times, maybe more than even some of your other friends. And, on the other side of friends, is the risk.


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[Assistant] The catastrophic risk that's potential when you have an AI system that's learning from data.


[User] Please transcribe this text

[Assistant] The near-term directions of research is purely the human supervision of AI decisions.


[User] Please transcribe this text

[Assistant] In terms of safety and ethics, there's a lot of systems like with cars.


[User] Please transcribe this text

[Assistant] or, uh, medical diagnosis and so on where there's some life-critical, safety-critical aspect that we want to be able to supervise the safety of that. And there's ethical decisions.


[User] Please transcribe this text

[Assistant] In terms of who gets a loan and not, uh, who gets a certain, uh, criminal penalty or not. Any degree to which AI systems are incorporated into that, you have to consider ethical questions. And even just the crude, uh, the low level,


[User] Please transcribe this text

[Assistant] Perception systems like face recognition, you want to make sure that your face recognition systems are not discriminating based on color or gender or age and so on. You want to make sure that


[User] Please transcribe this text

[Assistant] At that basic fundamental level of ethics, the systems are trained in a way they maintain our human values. Or the better angels of our nature, the better sides of our values, some of the brighter aspects of our values.


[User] Please transcribe this text

[Assistant] And the other thing is, in terms of just maintaining values, that's the, the normal that's looking at the mean of the distribution. But we also want to do, control the outliers from the AI system not to do anything catastrophic.


[User] Please transcribe this text

[Assistant] So the unintended consequences, when something happens that you didn't anticipate, you want to be able to put boundaries on that. And, uh, the grand challenge there...


[User] Please transcribe this text

[Assistant] Really, it all boils down to the ability of an AI system to say that it's uncertain about something.


[User] Please transcribe this text

[Assistant] And that measure of uncertainty has to be good. It has to be able to make a prediction always accompanied with uncertainty.


[User] Please transcribe this text

[Assistant] Even on things he hasn't seen before, that's the real challenge. To be able to be trained on cats and dogs and then seeing a giraffe and saying, I'm not sure what that is. We're quite far away from that because right now it would probably confidently say it's a dog, depending on the giraffe.


[User] Please transcribe this text

[Assistant] But we want to be able to have an extremely high accuracy in the ability of AI systems to determine their own uncertainty, to know what they don't know. Because from that comes the supervision. From that comes the ability to stop


[User] Please transcribe this text

[Assistant] Under things that it's uncertain about catastrophic events.


[User] Please transcribe this text

[Assistant] The first aspect of real world operation is understanding the human. One of the places where deep learning has really sh-shined is the perception problem.


[User] Please transcribe this text

[Assistant] And all begins at the ability to look at raw data and convert that into meaningful information. That's really the understanding the human comes in. Not the kind of understanding that when you're in a relationship with somebody, when you're friends with somebody over a long period of time, you gain an understanding.


[User] Please transcribe this text

[Assistant] Of their quirks, limitations, capabilities, so on. That's really fascinating.


[User] Please transcribe this text

[Assistant] But the first step is just to be able to, when you see them, recognize who they are, what's on their mind.


[User] Please transcribe this text

[Assistant] What's there are the, the body language, the, what are they saying with their mouth, uh, all those basic raw perception tasks. That's where deep learning really shines. I'd like to cover the state of the art in, in, uh,


[User] Please transcribe this text

[Assistant] In those various perception tasks. So first face recognition.


[User] Please transcribe this text

[Assistant] Now there's a full slide presentation with this and I'm skipping around. The full slide presentation has the following structure for each of these topics. It has the motivation description, the excitement,


[User] Please transcribe this text

[Assistant] Paper three is the recent breakthrough, often associated with deep learning. Paper four is the current state of the art.


[User] Please transcribe this text

[Assistant] And paper five is the thing that defines the future direction.


[User] Please transcribe this text

[Assistant] Face recognition, so what is it? It's the first thing, you know, the face contains so much rich...


[User] Please transcribe this text

[Assistant] Information about the state of the human being. So understanding the human being really starts at the face.


[User] Please transcribe this text

[Assistant] And, uh, detecting the face is the first step. Detecting the body and then that there's a head on top of that body, that's the first step.


[User] Please transcribe this text

[Assistant] And then there is the task of face recognition being an ex, exceptionally active area of research because it has a lot of applications and through that research we're able to now study, study a lot of aspects how we perform perception on the face.


[User] Please transcribe this text

[Assistant] So, recognition, purely stated, is the recognizing the identity of a human face. Who is this?


[User] Please transcribe this text

[Assistant] Detection is just detecting a face. Now, recognition means there's a database of identities. What is it? Seven billion of them on earth. And you're trying to determine which of them it is.


[User] Please transcribe this text

[Assistant] Which of the 7 billion it is, or whatever the database is. The face verification problem is something that your phone uses when you unlock it with your face. Is it saying, is it you or not? Is it Lex or somebody else? It's a database of two. One person.


[User] Please transcribe this text

[Assistant] There's a lot of applications here, obviously, uh, from identification to all the security aspects of using the, using the face as a sort of fingerprint of your identity in all the interactive elements of AI systems, software based systems in this world.


[User] Please transcribe this text

[Assistant] So why is it hard? So all the usual computer vision problems come in. Lighting variation, pose variation. It's just computer vision is really hard. It's just you get these raw numbers and you have to infer so many things that are


[User] Please transcribe this text

[Assistant] We're trying to, it's like cats versus dogs. There's thousands of breeds of dog and thousands of breeds of cats. In that same way, there's, faces can look very similar to each other.


[User] Please transcribe this text

[Assistant] So these two classes that you're trying to separate can be very, very, very close together and intermingle.


[User] Please transcribe this text

[Assistant] Now there's a lot of face data available now because of the application, because of the


[User] Please transcribe this text

[Assistant] So you have to, in making the face recognition task, you have to be invariant to all the hairstyles, all the, that you change yourself over time, the weight gain, the weight loss, the beard you decided to, uh, to grow.


[User] Please transcribe this text

[Assistant] The glasses you wear sometimes and not others, the different styles of glasses and so on, makeup or no makeups, all of these things is still you, still the same identity. You have to be able to classify that. And the kind of accuracy, especially for security applications, is extremely high that's required.


[User] Please transcribe this text

[Assistant] The reason it's an exciting area is there's a lot of possibility, but, and there's also a lot of concern, right? So the future impact


[User] Please transcribe this text

[Assistant] Utopia, dystopia, and the more reasonable middle path here is


[User] Please transcribe this text

[Assistant] Face provides a very user-friendly way of letting your devices recognize you and say hello.


[User] Please transcribe this text

[Assistant] Your voice is certainly one, but one of the most powerful ones to really classify at a distance is face.


[User] Please transcribe this text

[Assistant] So what does that mean, the utopian view, the possibility of the future?


[User] Please transcribe this text

[Assistant] The, the best possible, brightest possible future is you can use your face to, uh, as a passport, you know, you replace the license, replace all the security measures we put from the passwords in our devices to the credit card and so on. All of that, uh, you know, Apple pays, it'll be face pay. You show up,


[User] Please transcribe this text

[Assistant] It will automatically connect to all your devices, all your banking information and so on. Obviously the flip side of that, just rephrasing that sentence is also can be dystopian. Because, you know, complete violations of privacy, being watched at any time, being able to


[User] Please transcribe this text

[Assistant] Your Facebook and social media and all your devices being able to identify you, making it impossible for you to sort of hide from society.


[User] Please transcribe this text

[Assistant] The fundamental aspects of privacy, uh, maintaining privacy that many of us value greatly. The middle path is really just a useful way to unlock your phone.


[User] Please transcribe this text

[Assistant] The recent breakthroughs here, it started with the, uh,


[User] Please transcribe this text

[Assistant] With deep face, the essential idea there is applying deep neural networks to the task of face recognition. I mean, with a lot of the breakthroughs here on the perception side, we're not covering the old school papers and so on, uh, and the


[User] Please transcribe this text

[Assistant] The historical context here, biggest breakthroughs came in with deep learning. 2006, 7, 8, last, uh,


[User] Please transcribe this text

[Assistant] Last 10 years. So that's, the same is true with face recognition. Uh, DeepFace was the big first application that achieved, uh, near human performance on the, one of the big benchmarks at the time on the labeled faces in the wild.


[User] Please transcribe this text

[Assistant] So using a very large data set being able to form a good representation. The state of the art, or at least close to the state of the art, is FaceNet. The key idea there is using those same deep architectures to now optimize for the representation itself directly.


[User] Please transcribe this text

[Assistant] The notebook we're putting out was shared with some of you for the assignment.


[User] Please transcribe this text

[Assistant] Describes face recognition. The challenge there. That it's not like the traditional classification problem. You have to...


[User] Please transcribe this text

[Assistant] Into a small vector, compressed vector, such that in that embedding, faces that are similar to each other, so identities that are close together.


[User] Please transcribe this text

[Assistant] In a way that directly optimizes for the Euclidean distance between non-matching identities.


[User] Please transcribe this text

[Assistant] So there's still a lot of excitement about Facebook condition. There's a lot of benchmark competitions and a lot of people working in this and really bigger, better networks and more data is really one of the ways to crack this problem.


[User] Please transcribe this text

[Assistant] So public large dataset with 672,000 identities, 4.7 million photos, that's in 2017, and that just keeps scaling up and up and up and up.


[User] Please transcribe this text

[Assistant] Now we have to also be honest here on the, on the, uh, the possible future directions of work in that, you know, even though the benchmarks are growing, that's still a tiny subset of the people in the world. We're still not quite there to be able to


[User] Please transcribe this text

[Assistant] Have the general face recognition applicable to the entirety of the population or a large swath of the population of the world.


[User] Please transcribe this text

[Assistant] So in this topic here, brief coverage. We're not covering all the aspects of the face, especially temporal, that are useful in face recognition or useful saying a lot of things about the face, which is the FACES, FACS.


[User] Please transcribe this text

[Assistant] You know, uh, raise the eyebrows and all those kinds of things and can provide rich information for recognizing and interpreting the face and the different other modalities including 3D face recognition we're not covering. There's a lot of exciting areas there where we're just looking at the pure formulation of the face recognition problem


[User] Please transcribe this text

[Assistant] Not often stated and misinterpreted by people, uh, is that most of these methods of face recognition start with assuming that you have a bounding box around the face.


[User] Please transcribe this text

[Assistant] The, often times recognition can happen, so they're assuming a frontal or near frontal view of the face. But you can do recognition in all kinds of poses.


[User] Please transcribe this text

[Assistant] And it's very interesting to think, you know, that recognition, the way we recognize our friends and colleagues, parents and children is often using a lot of cue context information that's beyond just the pure frontal view of the face. It can do pretty well on profile views, it can from body language and so on.


[User] Please transcribe this text

[Assistant] So all those things that's open in the field, how we incorporate that into face recognition. Then the black box side is problematic for both bias and just being able to understand why incorrect decisions are made is the making those face recognition systems more interpretable.


[User] Please transcribe this text

[Assistant] The ability to collect the kind of data where the face recognition


[User] Please transcribe this text

[Assistant] It would be performing extremely well and yet not violating the fundamental aspects of privacy that we value.


[User] Please transcribe this text

[Assistant] into the richer temporal context of what people do. Again, the same structure from recent breakthroughs to the future direction of work. What is it?


[User] Please transcribe this text

[Assistant] It's class, it's classifying human activity from images or from video. And why is it important?


[User] Please transcribe this text

[Assistant] Is it provides a cont- depending on the...


[User] Please transcribe this text

[Assistant] The kind of data we're dealing with is just much larger. The kind of video, the richness of possibilities that define what activity is is much larger, so the complexity is much larger. It's often


[User] Please transcribe this text

[Assistant] Difficult to quantify motion because the fundamental aspect of activity is the change in the world, is the motion of things, and then it's difficult to determine


[User] Please transcribe this text

[Assistant] How the dynamics of the physics of the world, especially from a 2D view of what's background information, what's noise and what's essential to the, uh, to understanding the activity. And, uh,


[User] Please transcribe this text

[Assistant] The subjective ambiguous elements of activity. When does, uh,


[User] Please transcribe this text

[Assistant] When does a particular activity begin? When does it end?


[User] Please transcribe this text

[Assistant] When you start to annotate these things, when you start to try to do the detection, it becomes clear that sometimes the activity, uh,


[User] Please transcribe this text

[Assistant] Is partially undertaken, and the beginning and the end is fuzzy.


[User] Please transcribe this text

[Assistant] Future impact, utopia, dystopia, middle path. So, the impact here comes from being able to understand the world in time. And be able to predict.


[User] Please transcribe this text

[Assistant] The utopian possibilities is that


[User] Please transcribe this text

[Assistant] Being able to understand sort of human activities can let the robots, uh, sever the relationship. So it can damage the, the human robot interaction to where they just do their own thing.


[User] Please transcribe this text

[Assistant] The middle path is just finding useful information, massive amounts of data like YouTube. Now there's a YouTube video data set, being able to identify what's going on in this video, being able to infer rich, useful semantic information. And so what do we do with video? How do we do perception in video? Now the recent breakthrough came with deep learning.


[User] Please transcribe this text

[Assistant] Coming from a slightly, well, from a different architecture that takes in two streams. One is the image RGB data. The other is optical flow data that's really focusing on the motion in the image. Those are the two that's open the wave of two stream networks here from that paper showing the different architectures.


[User] Please transcribe this text

[Assistant] The on the far right is the two stream architecture and the C3D on the


[User] Please transcribe this text

[Assistant] Showing under B here, taking a sequence of images, but all these are just different architectures. And then first one is LSTMs. There's different architectures of how do you represent, how do you allow a network? How do you allow a learning model to be able to capture the dynamics in the data?


[User] Please transcribe this text

[Assistant] The future possibilities has to do literally with the future, being able to take single images or sequences of images and predicting the future. It's very interesting to think about.


[User] Please transcribe this text

[Assistant] In our ability to hallucinate the future and generate the future from images, you start to think about what are the defining qualities of activities and in this way augment data and be able to train much, much more accurate action recognition systems.


[User] Please transcribe this text

[Assistant] Topics not covered is the localization of activity in video, so action recognition purely defined is I give you a clip and you tell me what's going on in this clip.


[User] Please transcribe this text

[Assistant] Uh, now if you take actually a full YouTube video, you want to be able to localize, find all the, all the times when a particular activity is going on. It could be multi-label, multiple activities going on at the same time, beginning and ending in, uh, asynchronously.


[User] Please transcribe this text

[Assistant] And then there is more richly, uh, three-dimensional or 2D, uh, classification of activity based on human movement. So looking at, like from a Kinect, from 3D sensors, looking at skeleton-based action recognition from sensors that are not, that provide you more than just, uh, the 2D image data. The open problems is that


[User] Please transcribe this text

[Assistant] It's activity recognition is more than just the way we move our body or if it's baseball, like a ball in your hand and hitting it with a baseball bat.


[User] Please transcribe this text

[Assistant] It also has to do with context. There's, you know, sitting down or working or


[User] Please transcribe this text

[Assistant] Looking at something, picking up an item, those sometimes can change profoundly based on the other objects in the scene and the activity of other people in the scene. And so, being able to work with that kind of context is a totally open problem.


[User] Please transcribe this text

[Assistant] It's having to reduce a very complex real world context into something where you can clearly identify an activity.


[User] Please transcribe this text

[Assistant] Body pose estimation is the task of...


[User] Please transcribe this text

[Assistant] Localizing the joints that form the uh, the skeleton of the human body. So infer from visual information the positions of the different joints.


[User] Please transcribe this text

[Assistant] Along the line of complexity, it's important to be able to understand the body language, the rich, uh,


[User] Please transcribe this text

[Assistant] So that's from reading body language to animation to acting.


[User] Please transcribe this text

[Assistant] Aiding activity recognition and it's just a useful representation of the human body. If you're analyzing pedestrians or in an interactive environment, human-robot interaction, being able to understand what the heck it is the human is trying to do. A body pose is really, is really useful. It's hard because


[User] Please transcribe this text

[Assistant] The body, when you look at a 2D image projection of the body, there's a lot of, it's a highly dimensional optimization problem figuring out how the raw pixels match to the, to the actual three dimensional orientation of the human joints.


[User] Please transcribe this text

[Assistant] And the usual computer vision challenges of pose, lighting and so on.


[User] Please transcribe this text

[Assistant] Future Impact is, it's really exciting for interactive environments for a robot to be able to know the position of the human body which is trying to interact. Whether he's trying, whether it's a robot that's trying to


[User] Please transcribe this text

[Assistant] You have to be able to find where their hand is so you can do the trade off. Same thing in the car. You have to determine if, uh, the person's hands are on the steering wheel, if their head and orientation is such that they're able to physically take control of the vehicle. That's a really exciting set of possibilities there.


[User] Please transcribe this text

[Assistant] And, you know, there's applications and sports and CGI and video games and all aspects when a robot and human have to work together. Uh, the dystopian view you can imagine is, uh,


[User] Please transcribe this text

[Assistant] Of course, being able to localize all those joints means...


[User] Please transcribe this text

[Assistant] Uh, robots that are able to more effectively hurt humans and so that's always, that's always a huge concern and always


[User] Please transcribe this text

[Assistant] Uh, a dark dystopian view of the world, uh, with so much AI in it. Of course, the reality is, it's just more rich, fulfilling HCI that, uh, takes advantage of not just the face, stuff coming from the face, but also stuff, uh, about the body of the human that the robot is interacting with.


[User] Please transcribe this text

[Assistant] So it started with, uh, deep learning being applied to the body pose estimation problem 2014 with deep pose.


[User] Please transcribe this text

[Assistant] The key idea is there is looking at the holistic human pose estimation problem of detecting all the different joints of a single person in an image.


[User] Please transcribe this text

[Assistant] Power of deep learning is that you no longer have to do handcrafted expert engineered features that it automatically determines a set of features. All the parts are being detected for you. So this highly complex problem is all solved with data.


[User] Please transcribe this text

[Assistant] This is, uh, the, the state of the art. The 2017 and beyond has been a few papers, uh, from CMU along this line. It's doing real-time multi-person 2D pose estimation, but in a bottom-up way, where you're detecting individual joints first.


[User] Please transcribe this text

[Assistant] So all the knees in the picture, all the elbows, all the shoulders, all the wrists and so on, and then stitching them together using parts affinity fields. What is the most likely, so if you find 17 elbows in a picture, you then have to try to see which elbow belongs to which person.


[User] Please transcribe this text

[Assistant] So that actually turns out to be an extremely powerful way to detect, especially multipose, especially to deal with occlusions, a way of detecting body pose.


[User] Please transcribe this text

[Assistant] It's really interesting and uh, also is able to, because of that, because of the separation,


[User] Please transcribe this text

[Assistant] of the detections is able to run in real time, which is also really exciting.


[User] Please transcribe this text

[Assistant] Possible future direction is the, using much more information.


[User] Please transcribe this text

[Assistant] Uh, deformable models of the human body, so not just a skeleton, eh, uh, rich volumetric information to do the, uh, to do the detection and then optimizing for what's the most likely orientation of the body.


[User] Please transcribe this text

[Assistant] The open problems in the field is the fact that, uh,


[User] Please transcribe this text

[Assistant] You know, pose is not a thing that happens in a single image. Pose that happens...


[User] Please transcribe this text

[Assistant] Is part of human behavior and part of movement through time. So here, Monty Python, Ministry of Silly Walks, people walking funny ways, but, uh, so we collect a lot of data on pedestrians. I can tell you that people walk in different ways and people position their body in different ways. And so the temporal aspects of human motion are


[User] Please transcribe this text

[Assistant] Are, for the most part, not incorporated in the body pose estimation problem than they should be. There's a lot of exciting possibilities of capturing the, the, the temporal dynamics.


[User] Please transcribe this text

[Assistant] That I'm just skipping through speech recognition.


[User] Please transcribe this text

[Assistant] That was, 2018 was really big for recommender systems, for Netflix, OkCupid.


[User] Please transcribe this text

[Assistant] Each one of the things I mentioned briefly today will have a separate mini lecture. I taught an entire course on this at CHI last year. So deep learning for understanding the human is a topic I'm really excited about because it's really the first step for a machine


[User] Please transcribe this text

[Assistant] To be able to interact in a rich way with a human being is to understand it. And it's also area where the most near term impact can happen. A system to be able to effectively detect what a human being is up to, what they're thinking about, uh, how to best, uh, serve them and enrich the experience, uh, of interacting with that human. Let me jump to AI safety.


[User] Please transcribe this text

[Assistant] And then the interactive experience with humans and robots to just give examples of some work in that direction, some research in that direction I'm really excited about. So AI safety at the very basic level.


[User] Please transcribe this text

[Assistant] There's an AI system that's making decisions where we want human beings to supervise those decisions. We've done quite a bit of work here at MIT on that aspect of supervising machines, arguing machines, and OpenAI has done work with safety,


[User] Please transcribe this text

[Assistant] Uh, by having machines debate each other. So this kind of idea that you can achieve


[User] Please transcribe this text

[Assistant] Having to, uh, make decisions and agree with each other.


[User] Please transcribe this text

[Assistant] It allows us to then produce a signal of uncertainty based on which the human supervision can be sought. Without that, when we have a state of the art


[User] Please transcribe this text

[Assistant] Black box AI system that does something like drive a car. All we have is a system that just runs and we're supposed to have faith that it's always going to be right. We don't have any uncertainty signal coming from the system. So the idea of arguing machines,


[User] Please transcribe this text

[Assistant] Uh, the, we've developed and been working on is to have multiple AI systems and an ensemble of AI systems where the disagreement


[User] Please transcribe this text

[Assistant] When there's a disagreement detected, human supervision is sought. And the idea there is that when you have a system like Tesla Autopilot, here we've instrumented a Tesla vehicle.


[User] Please transcribe this text

[Assistant] It is about the decision it's making. It just knows, you know, the system, once the system is on, it's now steering the car for you. And in very rare cases, this is just disengage.


[User] Please transcribe this text

[Assistant] But no matter what, it's not showing to you the degree of uncertainty it has about the world around it. And so the way we create that signal of uncertainty is by adding another


[User] Please transcribe this text

[Assistant] Uh, shown in the plot there is we can predict with high accuracy.


[User] Please transcribe this text

[Assistant] The times when the driver chose to disengage the system because they were uncomfortable. So you're detecting, you're using this mechanism to detect risky, challenging situations.


[User] Please transcribe this text

[Assistant] It's an idea about how we supervise AI by having multiple AI systems that are independent and through their disagreement emerges the uncertainty signal.


[User] Please transcribe this text

[Assistant] And we can apply this like the AI folks in natural language with debate. We can apply this in computer vision as well, taking two independently trained, but on the same training set.


[User] Please transcribe this text

[Assistant] Networks, ResNet and VGGNet train on ImageNet, and we can have them argue.


[User] Please transcribe this text

[Assistant] And in the process, improve significantly the accuracy. So when, uh, in the case of ResNet is an architecture, the EugeneNet is an architecture trained on the ImageNet training data set. They separately have a certain error.


[User] Please transcribe this text

[Assistant] ResNet has an error of 8%, VGG16 has an error of 10%. When we apply the argue machines framework, when the disagreement is brought to the human, that error rate decreases at 2.8%. Now if that, this is just


[User] Please transcribe this text

[Assistant] ImageNet challenge, but if that error meant the loss of human life, this kind of framework is really powerful for, uh, overseeing the operation of the AI system.


[User] Please transcribe this text

[Assistant] That is just examples here where they disagree. So taking this image that's from ImageNet.


[User] Please transcribe this text

[Assistant] The ground truth is a wine bottle and resonant prediction is that it's definitely .93, 93% confidence that it's a paper towel and VGG net, uh, 25% confidence that it's a seatbelt. So these disagreements are then brought in and then we, uh, the fact that they disagree arises, uh,


[User] Please transcribe this text

[Assistant] The uncertainty and then human supervision is brought and then humans are able to annotate correctly what's going on in this picture. Same thing here, mailbox. The ground truth is a mailbox. The, again, the two architectures disagree. One says traffic light, the other one says garbage truck.


[User] Please transcribe this text

[Assistant] And for an autonomous vehicle, you can imagine this being problematic. If, if there's a traffic light, you might stop for this mailbox, that kind of thing. That's, uh, early research in the field of how do we have AI systems that are more and more powerful? We can also


[User] Please transcribe this text

[Assistant] Inject human effort to supervise when it's needed. The when it's needed part, the uncertainty signal is the critical thing. So we have to figure out ways to create that uncertainty signal.


[User] Please transcribe this text

[Assistant] The sub area of just creating a rich human interaction.


[User] Please transcribe this text

[Assistant] So we have a human centered autonomous vehicle here at MIT that's taking control back and forth from the human based on the activity.


[User] Please transcribe this text

[Assistant] That the driving experience, the human-robot interaction experience should be fun and uh, awesome and enriching to life. And that's why you would want to use these kinds of systems.


[User] Please transcribe this text

[Assistant] We have a bunch of videos online, you can check them out, including the ridiculous one of me playing guitar, and there's a paper along with this describing different principles of how we have humans and robots work together in this, in this kind of way. There's a lot of totally untouched problems in that space.


[User] Please transcribe this text

[Assistant] Most of the robotics community and the machine learning community approaches AI as a system that we want to make perfect.


[User] Please transcribe this text

[Assistant] And once it's perfect, we want to then put it in the real world where us humans get to interact with it. Uh, just like...


[User] Please transcribe this text

[Assistant] What is it? Robin Williams in Good Will Hunting.


[User] Please transcribe this text

[Assistant] Talking about relationships, that nobody's perfect. Uh, I think the way I foresee it, AI systems will not be perfect for the next hundred years. And so we have to have humans and AI systems work together and optimize that problem, solve that problem.


[User] Please transcribe this text

[Assistant] That both of us are flawed, but together there's something enriching to both.


[User] Please transcribe this text

[Assistant] As I mentioned, the videos here will be available online, the lectures underlying all the deep learning for understanding the human and underlying the five principles here of human centered AI. And it's, it's an area of active research here at MIT.


[User] Please transcribe this text

[Assistant] And globally, and it's one that I'm extremely passionate about. And one of the, uh, analogies I think about when I think about the success of artificial intelligence systems as an analogy of, of, uh, parasitism and symbiosis, a lot of the ways we're training machine learning algorithms now is


[User] Please transcribe this text

[Assistant] We inject a lot of human labor, a lot of really costly human labor, separately, offline, out of the loop, in order to improve the learning models through brute force annotation.


[User] Please transcribe this text

[Assistant] Success in the future requires that the learning is done, the models improve.


[User] Please transcribe this text

[Assistant] In a symbiotic way, as a side effect of interacting with humans. This is done a lot now in reinforcement learning through game playing and so on.


[User] Please transcribe this text

[Assistant] The human computation, the human effort of annotation is something that happens naturally through interaction, not a costly thing you have to pay for because


[User] Please transcribe this text

[Assistant] When it happens naturally, in a symbiotic way, we can increase scale. We can scale learning to a degree that's required to solve some of the, some of the real world problems. That also requires solving a lot of aspects of human-robot interaction.


[User] Please transcribe this text

[Assistant] From understanding our own brain, from the biological to the electrical and neuroscience, to the behavioral aspects captured by cognitive science, psychology, sociology, to the mathematical formulations of behavior and game theory, to


[User] Please transcribe this text

[Assistant] The, when you take that human behavior and put it in the real world with engineering systems, human factors and design, these are all giant subfields with conferences and papers that all of them need to work together. And then on the computer science side with natural language processing, understanding language,


[User] Please transcribe this text

[Assistant] The human-robot interaction, human-computer interaction, just the interfaces.


[User] Please transcribe this text

[Assistant] The, what does, how does and what does the computer, the robot show to you?


[User] Please transcribe this text

[Assistant] Again, entire conferences. And then the exciting aspects of learning from data and deep learning and learning to act from data and reinforcement learning, deep reinforcement learning. And then the robotics is actually building these things, the building the hardware, the


[User] Please transcribe this text

[Assistant] Again, an entire, entire area exciting field of research. All of them have to work together to create systems here that integrate the human during the learning process and integrate the human during the operation process. So.


[User] Please transcribe this text

[Assistant] The videos on deeplearning.mit.edu, videos and slides available there, code is available there. With that, I'd like to thank you very much.


[User] Please transcribe this text

[Assistant] Oh, hello. I'd like to ask about insurance for my car.


[User] Please transcribe this text

[Assistant] Oh, hello. I'd like to ask about insurance for my car.


[User] Please transcribe this text

[Assistant] Well, uhm, mainly for social use.


[User] Please transcribe this text

[Assistant] That seems okay. It's quite a bit lower than I've been paying up to now.


[User] Please transcribe this text

[Assistant] It's interesting because yeaah, they wanna have the Devourer for later for Varus to save him, but that means they're gonna have Tahm Kench in lane as well. And RNG could very well go for another ranged support matchup. That's why Kingzone are starting to ban them out.


[User] Please transcribe this text

[Assistant] Yep, definitely still multiple ones. Karma, as you said, and uh, Morgana is an option for them as well. Black Shield would definitely make it a little bit more mobile.


[User] Please transcribe this text

[Assistant] Transfer from the AD carry to the Tahm Kench because your opponents are just going to focus the


[User] Please transcribe this text

[Assistant] Yeah, and remember, the Glent is good against all these follow-up CCs. Won't be useful against the Suppression, but Morghanna bindings, the taunts from the Galio, and the rest of the stuns coming in, even from Skarner himself.


[User] Please transcribe this text

[Assistant] Yeah, probably the next thing I'm looking for is what Kingzone are gonna do when the first Galio ultimate actually...


[User] Please transcribe this text

[Assistant] It adds a tremendous amount of damage here to the combinations that Irelia can pull off on the bottom side end. With Uzi and Ming constantly under pressure down here at King's Zone, we'll probably keep up the similar strategy.


[User] Please transcribe this text

[Assistant] Yeaah, they're even in gold, and Uzi is getting very close to his trinity force on Ezreal. Once you get that, once you get the Muramana transformation, then RNG get to bring him to the fights, rather than having him be struggling down here in the bottom side, constantly under threat of this Rangeblade Ferris.


[User] Please transcribe this text

[Assistant] Well, speaking of those builds, those AD carries in the bottom lane, the dragon is about to come up in two seconds and that might be the site that actually draws them back into another confrontation. Galio ultimate is ready. Teleport from Letme is also ready and these are going to be level two ultimates that they bring to the fight this time.


[User] Please transcribe this text

[Assistant] Yeah, that was an abysmal voyage actually, last time around for Gorilla towards the mid lane. Cost him his death that he's sporting there. He does now have a Quicksilver in addition to, uh, changing his cleanse to Exhaust for the teamfights though. He's been able to supplement his Summoner spells with Ida build.


[User] Please transcribe this text

[Assistant] Now it's time. Let's just go for the engage. If I was this team, I would say it's time when Ezreal completes his Trinity Force. As soon as Uzi is able to get that Trinity Force and get up those damage numbers you're talking about, Trevor, then we have the Ornhorn. You just blow that sucker, get Skarner to run in, and Galio to jump down.


[User] Please transcribe this text

[Assistant] This show's got some big talk, but a good friend of mine, Captain Flowers, once told me, when Ornn blows the horn, you better run!


[User] Please transcribe this text

[Assistant] Now the reward would be another dragon. Now seven seconds and Kingzone are doing the homework first. Scuttle crab down, establishing vision. Such a smart move from Kaathe, knowing.


[User] Please transcribe this text

[Assistant] Something else we have learned over this tournament is that Kingzone do not look good playing from behind. After that last teamfight, it's gonna be, it's gonna have to be a different story for them because so far, they have not been able to come back very well.


[User] Please transcribe this text

[Assistant] It's so hard when you are the slow moving Goliath that is Galio.


[User] Please transcribe this text

[Assistant] Alright, but that brings us to the fight that strikes back for Kingzone in their own jungle. As Kobe said, there's always room for outplay and that's exactly what they do.


[User] Please transcribe this text

[Assistant] We won't know now, but we may soon enough whether or not that was the fight that turned the tides of it all. I do want to push forward one more time to the final fight of the game, this one inside RNG's base.


[User] Please transcribe this text

[Assistant] Yeah, we asked which was more likely a 3-0 for RNG, a 3-0 for Kingzone. I think it was starting to trend in the favor of an RNG 3-0, but as you mentioned, serious saving play there for Kingzone.


[User] Please transcribe this text

[Assistant] In that game too, they're gonna push us to a third game and at least a fourth and that's where I want to start talking about what's the response here for RNG. I mean, if you're coming out of that game knowing that hey, just maybe one or two mechanically different, you know, different plays made in that team fight, we've got it. I almost feel like you don't do anything.


[User] Please transcribe this text

[Assistant] Right, I was gonna say, so do we think RNG should be comfortable sticking to their guns with what they had here in game 2?


[User] Please transcribe this text

[Assistant] Alright, well Kings don't have shown they're not going down without a fight. Meet us here for game three to see who can bring this series to match point. We'll see you here after the break.


[User] Please transcribe this text

[Assistant] Okay, so what problem were we trying to solve?


[User] Please transcribe this text

[Assistant] Various forces and equations that we need.


[User] Please transcribe this text

[Assistant] So that's the problem we looked at. This is F sub 0. I may have just called it F last time. It doesn't matter. It's a matter of just symbols, okay?


[User] Please transcribe this text

[Assistant] But now I'm calling it ω0, and you should understand why I'm doing that, because there are now two ω's in the problem.


[User] Please transcribe this text

[Assistant] That is the ω of the driving force. So, you should imagine an oscillatory force grabbing this mass and moving it back and forth.


[User] Please transcribe this text

[Assistant] Omega 0 is the natural frequency of the math. If you pull the spring and let it go, that's the frequency that it will vibrate. There are really natural frequencies which are fixed by k and m, and omega is for you to decide. You can decide to apply to it any force you like of any frequency.


[User] Please transcribe this text

[Assistant] So first take the easy case in which the right-hand side is zero. No driving force.


[User] Please transcribe this text

[Assistant] So I'm saying let's consider a simple case F, 0, or F, the applied force vanishes.


[User] Please transcribe this text

[Assistant] That's the problem I spent considerable amount of time on yesterday. You can say, well, if there's no driving force, why does anything move?


[User] Please transcribe this text

[Assistant] That's actually correct. If you took a mass and a spring and you didn't do anything to it, the solution to this equation is x equal to 0, and that's just fine.


[User] Please transcribe this text

[Assistant] But it also has interesting non-trivial solutions because you can pull the mass and then let it go.


[User] Please transcribe this text

[Assistant] There are no forces on the system except the force of friction and the force of the spring. And that is this problem.


[User] Please transcribe this text

[Assistant] How do you solve this problem? I told you the way you solve this problem is you make a guess. x of t is some number a times e to the alpha t. See if it'll work.