WEBVTT 00:00:00.060 --> 00:00:02.500 The following content is provided under a Creative 00:00:02.500 --> 00:00:04.019 Commons license. 00:00:04.019 --> 00:00:06.360 Your support will help MIT OpenCourseWare 00:00:06.360 --> 00:00:10.730 continue to offer high quality educational resources for free. 00:00:10.730 --> 00:00:13.340 To make a donation or view additional materials 00:00:13.340 --> 00:00:17.229 from hundreds of MIT courses, visit MIT OpenCourseWare 00:00:17.229 --> 00:00:17.854 at ocw.mit.edu. 00:00:21.340 --> 00:00:23.080 PROFESSOR: Today we are introducing 00:00:23.080 --> 00:00:25.330 an exciting new pledge in 6034. 00:00:25.330 --> 00:00:29.280 Anyone who has already looked at any of the neural net problems 00:00:29.280 --> 00:00:31.860 will have easily been able to see that even though Patrick 00:00:31.860 --> 00:00:34.300 only has them back up to 2006 now, 00:00:34.300 --> 00:00:39.500 there's still-- well out of four tests, perhaps two or three 00:00:39.500 --> 00:00:42.140 different ways that the neural nets were drawn. 00:00:42.140 --> 00:00:44.960 Our exciting new pledge is we're going to draw them 00:00:44.960 --> 00:00:47.110 in a particular way this year. 00:00:47.110 --> 00:00:52.350 And I will show you which way, assuming that this works. 00:00:52.350 --> 00:00:53.820 Yes. 00:00:53.820 --> 00:00:57.580 We are going to draw them like the one on the right. 00:00:57.580 --> 00:01:01.050 The one on the left is the same as the one on the right. 00:01:01.050 --> 00:01:03.460 At first, not having had to explain 00:01:03.460 --> 00:01:05.209 the difference between the two of them, 00:01:05.209 --> 00:01:07.310 you might think you want the one on the left. 00:01:07.310 --> 00:01:09.590 But you really want the one on the right, 00:01:09.590 --> 00:01:11.590 and I'll explain why. 00:01:11.590 --> 00:01:15.810 The 2007 quiz was drawn, roughly similarly, to this. 00:01:15.810 --> 00:01:19.860 Although if you somehow wind up in tutorial or somewhere else 00:01:19.860 --> 00:01:21.930 doing one of the older quizzes, a lot of them 00:01:21.930 --> 00:01:24.040 were drawn exactly like this. 00:01:24.040 --> 00:01:27.650 In this representation, one thing I really don't like, 00:01:27.650 --> 00:01:30.900 is that the inputs are called x's, and the outputs 00:01:30.900 --> 00:01:37.330 are called y's, but there's two x's, so the inputs are not 00:01:37.330 --> 00:01:40.690 x and y, and then they often correspond to x's of a graph, 00:01:40.690 --> 00:01:43.720 and then people get confused. 00:01:43.720 --> 00:01:46.980 Additional issues that many people have 00:01:46.980 --> 00:01:50.880 are the fact that the summation and the multiplication 00:01:50.880 --> 00:01:52.190 with the weight is implied. 00:01:52.190 --> 00:01:54.780 The weights are written on the edges, where outputs and inputs 00:01:54.780 --> 00:01:58.390 go, and the summation of the two inputs into the node 00:01:58.390 --> 00:02:00.540 are also implied. 00:02:00.540 --> 00:02:02.970 But take a look here. 00:02:02.970 --> 00:02:05.560 This is the same net. 00:02:05.560 --> 00:02:17.500 These w's here would be the w's that are written 00:02:17.500 --> 00:02:20.610 onto these lines are here. 00:02:20.610 --> 00:02:22.450 Actually the better way to draw it 00:02:22.450 --> 00:02:32.380 would be like so, since each of these 00:02:32.380 --> 00:02:36.760 can have their own w, which is different. 00:02:40.730 --> 00:02:44.020 So each of the w's that are down here, 00:02:44.020 --> 00:02:46.250 are being explicitly set to a multiplier. 00:02:46.250 --> 00:02:48.470 Where as here, you just had to remember 00:02:48.470 --> 00:02:51.700 to multiply the weight by the input that was coming by. 00:02:51.700 --> 00:02:54.260 Here you see an input, comes to a multiplier, 00:02:54.260 --> 00:02:59.180 you multiply by the weight, then once you multiplied 00:02:59.180 --> 00:03:02.410 all the inputs by the weight, then you send them to a sum, 00:03:02.410 --> 00:03:04.870 so the sigma is just a sum, you sum them, add them 00:03:04.870 --> 00:03:09.910 all together, send the result of that into the sigmoid function, 00:03:09.910 --> 00:03:14.330 our old buddy, 1 over 1 plus e to the negative whatever 00:03:14.330 --> 00:03:18.900 our input was, with a weight for an offset, 00:03:18.900 --> 00:03:20.740 and then we send the result of that 00:03:20.740 --> 00:03:26.520 into more multipliers with more weights, more sums, more 00:03:26.520 --> 00:03:28.360 sigmoids. 00:03:28.360 --> 00:03:33.340 So this is how it's going to look like on the quiz. 00:03:33.340 --> 00:03:41.610 And this is a conversion guide from version 0.9 data 00:03:41.610 --> 00:03:42.940 into version 1.0. 00:03:42.940 --> 00:03:46.060 So if you see something that looks 00:03:46.060 --> 00:03:49.610 like this, on one of the old quizzes that you're doing, 00:03:49.610 --> 00:03:52.980 see if you can convert it, and then solve the problem. 00:03:52.980 --> 00:03:54.735 Chances are if you can convert it, 00:03:54.735 --> 00:03:56.110 you're probably going to do fine. 00:04:01.970 --> 00:04:04.550 We'll start off not only with this conversion guide, 00:04:04.550 --> 00:04:17.839 but also-- I'll leave that up here-- also 00:04:17.839 --> 00:04:20.310 I'm going to work out the formulas for you guys one more 00:04:20.310 --> 00:04:21.230 time. 00:04:21.230 --> 00:04:25.500 These are all the formulae that you're 00:04:25.500 --> 00:04:27.100 going to need on the quiz. 00:04:27.100 --> 00:04:29.700 And then we're going to decide what 00:04:29.700 --> 00:04:34.480 will change in the formulae, if, and this is a very 00:04:34.480 --> 00:04:38.230 likely if, there seems to be good amount of times 00:04:38.230 --> 00:04:41.820 that this happens, is that the sigmoid function in those 00:04:41.820 --> 00:04:44.530 neurons out there was ever changed 00:04:44.530 --> 00:04:46.050 into some other kind of function. 00:04:46.050 --> 00:04:46.550 Hint. 00:04:46.550 --> 00:04:49.460 It's changed into a plus already in the problem 00:04:49.460 --> 00:04:50.800 we're about to do. 00:04:50.800 --> 00:04:54.420 People change it all the time into some bizarro function. 00:04:54.420 --> 00:04:57.680 I've seen arc tangent, I think. 00:04:57.680 --> 00:04:59.910 So here we go. 00:04:59.910 --> 00:05:01.160 Let's look at the front of it. 00:05:01.160 --> 00:05:02.220 First of all, sigmoid. 00:05:02.220 --> 00:05:06.910 Well our old buddy, sigmoid, I just said it a moment ago, 00:05:06.910 --> 00:05:10.275 sigmoid is 1 over 1 plus e to the minus x. 00:05:18.330 --> 00:05:34.940 Also, fun fact about sigmoid, the derivative of sigmoid, 00:05:34.940 --> 00:05:41.210 is itself-- the derivative of sigmoid 00:05:41.210 --> 00:05:47.250 is-- let's say that the sigmoid-- we'll just 00:05:47.250 --> 00:05:53.001 turn sigmoid into like the letter say y. 00:05:53.001 --> 00:05:54.670 Y is the result, right? 00:05:54.670 --> 00:06:02.650 So if you say y equals 1 over 1 plus e to the negative x, 00:06:02.650 --> 00:06:09.480 then the derivative of sigmoid is y times 1 minus y. 00:06:13.330 --> 00:06:15.740 You can also write out the whole nasty thing, 00:06:15.740 --> 00:06:19.380 it's 1 over 1 plus e to the negative x times 1 minus 1 00:06:19.380 --> 00:06:21.780 over 1 plus e to negative x. 00:06:21.780 --> 00:06:23.820 So the nice property of sigmoid it's 00:06:23.820 --> 00:06:28.160 going to be important for us in the very near future, 00:06:28.160 --> 00:06:31.900 and that future begins now. 00:06:31.900 --> 00:06:33.790 So now the performance function. 00:06:33.790 --> 00:06:38.785 This is a function we used to tell neural nets when 00:06:38.785 --> 00:06:42.700 they inevitably act up and give us really crappy results. 00:06:42.700 --> 00:06:47.510 At first we tell them just how long they are, 00:06:47.510 --> 00:06:49.430 with our performance function. 00:06:49.430 --> 00:06:53.060 The first function can be any sane function 00:06:53.060 --> 00:07:01.980 that gives you a better score, where better can be decided 00:07:01.980 --> 00:07:05.991 as lower or higher, if you feel like, that gives you a better 00:07:05.991 --> 00:07:08.240 score, if your answers are closer to the answer you're 00:07:08.240 --> 00:07:09.920 looking for. 00:07:09.920 --> 00:07:17.360 However, in this case, we have, for a very sneaky reason, 00:07:17.360 --> 00:07:20.300 chosen the performance function to be 00:07:20.300 --> 00:07:27.530 1/2 d, which is the desired output, minus o, 00:07:27.530 --> 00:07:30.680 the actual output squared. 00:07:33.770 --> 00:07:38.900 So we want a small, well it's negative, 00:07:38.900 --> 00:07:43.450 So we want a small negative or 0. 00:07:43.450 --> 00:07:47.130 That would mean we performed well. 00:07:47.130 --> 00:07:47.915 So why this? 00:07:50.560 --> 00:08:05.090 Well the main reason is ddx of performance 00:08:05.090 --> 00:08:09.450 is, the 2 comes down, the o is the variable that we're 00:08:09.450 --> 00:08:16.930 actually, so maybe I should say ddo, that negative comes out, 00:08:16.930 --> 00:08:22.340 we get a simple d minus o. 00:08:25.980 --> 00:08:29.370 And yeah, we're using derivatives here. 00:08:29.370 --> 00:08:32.049 So those are fine. 00:08:32.049 --> 00:08:33.620 These are two assumptions. 00:08:33.620 --> 00:08:35.493 They could be changed on your test. 00:08:35.493 --> 00:08:37.909 We're going to figure out what happens, if we change them, 00:08:37.909 --> 00:08:41.440 if we change the performance, if we change the sigmoid, that 00:08:41.440 --> 00:08:44.927 is if we change the sigmoid to some other function, what's 00:08:44.927 --> 00:08:47.010 going to happen to the next three functions, which 00:08:47.010 --> 00:08:48.920 are basically the only things that you need 00:08:48.920 --> 00:08:51.410 to know to do backpropagation. 00:08:51.410 --> 00:08:52.880 So let's look at that. 00:08:52.880 --> 00:08:54.210 First, w prime. 00:08:54.210 --> 00:08:56.820 This is the formula for a new weight. 00:08:56.820 --> 00:08:59.520 After one step of backpropagation. 00:08:59.520 --> 00:09:01.490 A new weight in any of these positions 00:09:01.490 --> 00:09:07.370 that you can see up here on this beautiful neural net. 00:09:07.370 --> 00:09:11.670 That w-- each of the w's will have to change step by step. 00:09:11.670 --> 00:09:14.330 That's, in fact, how you do the hill climbing neural nets. 00:09:14.330 --> 00:09:16.635 You change the weights incrementally. 00:09:16.635 --> 00:09:19.000 You step a little bit in the direction 00:09:19.000 --> 00:09:23.170 towards giving you your desired results until eventually, you 00:09:23.170 --> 00:09:27.100 hope, you have an intelligent neural net. 00:09:27.100 --> 00:09:29.265 And maybe you have many different training examples 00:09:29.265 --> 00:09:32.140 that you run it on, in a cycle, hoping 00:09:32.140 --> 00:09:35.980 that you don't over fit to your one sample, on a computer. 00:09:35.980 --> 00:09:38.510 But on the test, we will probably will not do that. 00:09:38.510 --> 00:09:40.750 So let's take a look at how you calculate 00:09:40.750 --> 00:09:43.060 the weights for the next level. 00:09:43.060 --> 00:09:45.570 And then you have the weights for the current level. 00:09:45.570 --> 00:09:48.080 So first things first. 00:09:48.080 --> 00:09:49.810 New weight, weight prime equals-- 00:09:49.810 --> 00:09:51.500 starts with the old weight. 00:09:51.500 --> 00:09:54.110 That has to go there because otherwise we're 00:09:54.110 --> 00:09:56.910 just going to jump off somewhere at random. 00:09:56.910 --> 00:10:00.010 We want to make a little step in some direction, 00:10:00.010 --> 00:10:03.250 so we want to start where we are, with the weight. 00:10:03.250 --> 00:10:08.720 And then we're going to add three things. 00:10:08.720 --> 00:10:11.050 So if we're talking about the weight 00:10:11.050 --> 00:10:17.390 between some i and some j-- there's 00:10:17.390 --> 00:10:20.190 some examples of the names of weights. 00:10:20.190 --> 00:10:24.240 So this is w 1 i, that's the weight between 1 00:10:24.240 --> 00:10:29.332 and-- so this is w 1 a, it's the weight between 1 and a. 00:10:29.332 --> 00:10:34.920 This is w 2 b, which is the weight between 2 and b . 00:10:34.920 --> 00:10:36.170 Makes sense? 00:10:36.170 --> 00:10:38.270 Well makes sense so far, but what 00:10:38.270 --> 00:10:42.430 if it's just called w b, then it's 00:10:42.430 --> 00:10:46.279 the weight between-- these w's that only have one letter, 00:10:46.279 --> 00:10:47.070 we'll get to later. 00:10:47.070 --> 00:10:47.930 They're the bias. 00:10:47.930 --> 00:10:49.560 They're the offset. 00:10:49.560 --> 00:10:52.020 They are always attached to a negative 1. 00:10:52.020 --> 00:11:00.520 So you can pretty much treat them as being a negative 1 00:11:00.520 --> 00:11:04.840 here, that is then fed into a multiplier with this w b, 00:11:04.840 --> 00:11:05.673 if you like. 00:11:10.880 --> 00:11:12.370 This is implied to be that. 00:11:12.370 --> 00:11:15.920 All of the offsets are implied to be that. 00:11:15.920 --> 00:11:24.130 So w plus sum of alpha-- why is this Greek letter? 00:11:24.130 --> 00:11:25.240 Where does it come from? 00:11:25.240 --> 00:11:26.320 How do we calculate it? 00:11:26.320 --> 00:11:32.149 Well alpha is just some value told to you on the quiz. 00:11:32.149 --> 00:11:33.190 You'll find it somewhere. 00:11:33.190 --> 00:11:35.810 There's no way you're going to have to calculate alpha. 00:11:35.810 --> 00:11:38.090 You might be asked to try to give us an alpha, 00:11:38.090 --> 00:11:39.530 but probably not. 00:11:39.530 --> 00:11:42.660 Alpha is supposed to give the size of our little steps 00:11:42.660 --> 00:11:44.650 that we take when we're doing hill climbing. 00:11:44.650 --> 00:11:46.600 Very large alpha, take a huge step. 00:11:46.600 --> 00:11:49.410 Very small alpha, take tentative steps. 00:11:49.410 --> 00:11:53.250 So alpha is there, basically, to change this answer 00:11:53.250 --> 00:11:58.900 and to make the new value either very close to w, or far from w, 00:11:58.900 --> 00:12:00.770 depending on our taste. 00:12:00.770 --> 00:12:14.250 So plus alpha times i, so i is the value 00:12:14.250 --> 00:12:23.999 coming in into the node. 00:12:23.999 --> 00:12:25.290 We're changing the weight here. 00:12:25.290 --> 00:12:30.870 So i is the value, for instance, i sub 1 here, 00:12:30.870 --> 00:12:36.080 i would be the value of WAC, i would be the value coming 00:12:36.080 --> 00:12:40.170 output of node a. 00:12:40.170 --> 00:12:43.600 WBC, i would be the output of node b. 00:12:43.600 --> 00:12:47.630 i is sometimes as little as i is the input coming in 00:12:47.630 --> 00:12:51.140 to meet that weight at the multiplier. 00:12:51.140 --> 00:12:56.700 And then it's multiplied by delta j. 00:12:56.700 --> 00:12:59.560 Your delta is the delta that belongs 00:12:59.560 --> 00:13:02.200 to these neural net nodes. 00:13:02.200 --> 00:13:04.160 What is a delta, you said? 00:13:04.160 --> 00:13:05.420 Funny you may ask. 00:13:05.420 --> 00:13:07.222 It is a strange Greek letter. 00:13:07.222 --> 00:13:08.930 It sort of comes from the fact that we're 00:13:08.930 --> 00:13:10.638 doing some partial derivatives and stuff, 00:13:10.638 --> 00:13:13.335 but the main way you're going to figure out what the deltas are 00:13:13.335 --> 00:13:17.040 are these two formulae that I've not written in yet. 00:13:17.040 --> 00:13:20.970 So hold off on trying to figure out 00:13:20.970 --> 00:13:25.033 what the delta is until-- well right now, I'm 00:13:25.033 --> 00:13:26.710 about to tell you the delta is. 00:13:26.710 --> 00:13:30.670 So the delta is basically, think of the delta 00:13:30.670 --> 00:13:34.870 as using partial derivatives to figure out 00:13:34.870 --> 00:13:36.590 which way you're going to step, when 00:13:36.590 --> 00:13:37.940 you're doing hill climbing. 00:13:37.940 --> 00:13:39.981 Because you know when you're doing hill climbing, 00:13:39.981 --> 00:13:42.090 you look around, you figure out, OK, this 00:13:42.090 --> 00:13:44.320 is the direction of the highest increase, 00:13:44.320 --> 00:13:46.980 and then you step off in that direction. 00:13:46.980 --> 00:13:48.720 So the deltas are telling you which way 00:13:48.720 --> 00:13:51.270 to step, with the weights. 00:13:51.270 --> 00:13:55.480 And the way they do that is by taking the partial derivative 00:13:55.480 --> 00:13:58.460 of-- basically you try to figure out 00:13:58.460 --> 00:14:02.320 how the weight that you're currently looking at 00:14:02.320 --> 00:14:07.470 is contributing to the performance of the net. 00:14:07.470 --> 00:14:10.064 Contributing to, either the good performance 00:14:10.064 --> 00:14:11.980 of the net, or the bad performance of the net. 00:14:14.630 --> 00:14:21.330 So when you're dealing with the weights, like WBC, WAC, 00:14:21.330 --> 00:14:27.090 that pretty much directly feed into the end of the net. 00:14:27.090 --> 00:14:29.330 They feed into the last node, and it then comes out. 00:14:29.330 --> 00:14:31.990 It's the output. 00:14:31.990 --> 00:14:33.590 That's pretty easy. 00:14:33.590 --> 00:14:36.270 You can tell exactly how much those weights, 00:14:36.270 --> 00:14:39.440 and the values coming from them, are contributing to the end. 00:14:39.440 --> 00:14:46.950 And we do that by essentially, remember 00:14:46.950 --> 00:14:53.120 what the partial derivative, so partial derivative here 00:14:53.120 --> 00:14:59.240 is, in fact, the way that the final weights are contributing 00:14:59.240 --> 00:15:02.850 to the performance, is just the performance function. 00:15:02.850 --> 00:15:05.160 Partial derivative-- I've already 00:15:05.160 --> 00:15:07.830 figured out the derivative here, it's just d minus o. 00:15:11.800 --> 00:15:15.490 This is for sort of final weights, 00:15:15.490 --> 00:15:17.670 the weights in the last level. 00:15:17.670 --> 00:15:19.790 D minus o, except we're not done yet, 00:15:19.790 --> 00:15:24.560 because when we do derivatives, remember the chain rule. 00:15:24.560 --> 00:15:29.330 To get from the end to these weights, we pass through, 00:15:29.330 --> 00:15:31.540 well it should be a sigmoid, here it's not, 00:15:31.540 --> 00:15:33.730 we're going to pretend it is for the moment, 00:15:33.730 --> 00:15:36.580 we pass through a sigmoid, and since we 00:15:36.580 --> 00:15:38.420 passed through the sigmoid, we had better 00:15:38.420 --> 00:15:41.050 take the derivative of the sigmoid function. 00:15:41.050 --> 00:15:46.700 That is, y times 1 minus y. 00:15:46.700 --> 00:15:47.510 Well what is y? 00:15:47.510 --> 00:15:50.150 What is the output of the sigmoid? 00:15:50.150 --> 00:15:51.970 It's up. 00:15:51.970 --> 00:15:56.520 So that's also multiplied by o times 1 minus o. 00:16:02.667 --> 00:16:05.480 However, there is a-- let me see, 00:16:05.480 --> 00:16:10.780 let me see, yes-- sorry, I'm carefully studying this sheet 00:16:10.780 --> 00:16:13.000 to make sure my nomenclature is exactly 00:16:13.000 --> 00:16:17.120 right for our new nomenclature, which so new and brave, 00:16:17.120 --> 00:16:19.510 that we're doing it, that we only knew for sure we're 00:16:19.510 --> 00:16:21.450 going to do it on Wednesday. 00:16:21.450 --> 00:16:26.160 So we have d minus o times o times 1 minus o. 00:16:29.100 --> 00:16:35.440 So you say, that's fine, that can get us these weights 00:16:35.440 --> 00:16:39.300 here, even this w c, how are we going 00:16:39.300 --> 00:16:48.070 to get the deltas for the new weights here? 00:16:51.330 --> 00:16:55.870 Oh, I realize-- yeah, I got it. 00:16:55.870 --> 00:16:58.860 So the delta-- by the way, this is a delta c, 00:16:58.860 --> 00:17:00.980 how is neuron c contributing to the output? 00:17:00.980 --> 00:17:03.020 Well it's directly contributing to the output , 00:17:03.020 --> 00:17:04.819 and it's got a sigmoid in it. 00:17:04.819 --> 00:17:07.290 It doesn't really, but we're pretending it does for now. 00:17:07.290 --> 00:17:10.440 d minus o times 1 minus o. 00:17:10.440 --> 00:17:12.329 What about inner node? 00:17:12.329 --> 00:17:15.780 Node d, node a, what are we going to have to do? 00:17:15.780 --> 00:17:18.329 Well the way they contribute to the output is 00:17:18.329 --> 00:17:20.819 that they contribute to node c. 00:17:20.819 --> 00:17:25.170 So we can do this problem recursively. 00:17:25.170 --> 00:17:27.680 So let's do this recursively. 00:17:27.680 --> 00:17:30.080 First of all, as you have probably figured out, 00:17:30.080 --> 00:17:32.880 all of them are going to have an o times 1 minus o factoring 00:17:32.880 --> 00:17:35.570 from the chain rule, because they're all sigmoid, pretending 00:17:35.570 --> 00:17:36.653 that they're all sigmoids. 00:17:39.430 --> 00:17:41.440 We also have a dearth of good problems 00:17:41.440 --> 00:17:44.800 that are actually sigmoid on the web right now. 00:17:44.800 --> 00:17:46.990 There's only 2007. 00:17:46.990 --> 00:17:50.800 But here's o times 1 minus o, what 00:17:50.800 --> 00:17:53.070 are we going to do for the rest of it? 00:17:53.070 --> 00:17:55.770 How does it contribute to our final result? 00:17:55.770 --> 00:18:00.460 Well it contributes to our final result recursively. 00:18:00.460 --> 00:18:01.920 So we're talking about delta i. 00:18:01.920 --> 00:18:04.930 I is an inner node. 00:18:04.930 --> 00:18:06.740 It's not a final node. 00:18:06.740 --> 00:18:08.390 It's somewhere along the way. 00:18:08.390 --> 00:18:24.500 So sum over j of w, going from i to j, times delta j. 00:18:24.500 --> 00:18:32.000 Now sum over all j, j such that i leads to j. 00:18:32.000 --> 00:18:34.860 I needs to have a direct path into j. 00:18:34.860 --> 00:18:38.830 So if i, in this instance, was j, 00:18:38.830 --> 00:18:45.240 everyone, the only possible j in this would be c. 00:18:45.240 --> 00:18:46.170 That's right. 00:18:46.170 --> 00:18:49.940 We would not sum over b as one of the j. 00:18:49.940 --> 00:18:54.620 i does not lead to b, or a does not lead to b, a only leads 00:18:54.620 --> 00:18:55.470 to c. 00:18:55.470 --> 00:18:57.820 Also note that c does not need to be here. 00:18:57.820 --> 00:18:59.860 That's going backwards. 00:18:59.860 --> 00:19:02.760 So you just-- to figure out which j you're looking at, 00:19:02.760 --> 00:19:07.430 look directly forwards at the next one. 00:19:07.430 --> 00:19:11.030 So if there was another d here, or that a does not go to d, 00:19:11.030 --> 00:19:14.262 a goes to c. 00:19:14.262 --> 00:19:15.970 You only look at the next level children, 00:19:15.970 --> 00:19:20.890 and you sum over all those children, 00:19:20.890 --> 00:19:23.050 the weight between them, multiplied 00:19:23.050 --> 00:19:25.040 by the child's delta. 00:19:25.040 --> 00:19:26.440 That makes sense, right? 00:19:26.440 --> 00:19:30.180 Because the way we affect, if the child's delta is the way 00:19:30.180 --> 00:19:33.850 the child affects the output, calling these children 00:19:33.850 --> 00:19:37.042 for a moment, and then if this one directly 00:19:37.042 --> 00:19:38.750 affects the output, then the way this one 00:19:38.750 --> 00:19:44.290 affects it is-- it affects it because it affects this, 00:19:44.290 --> 00:19:46.960 but it's also multiplied by it's weight. 00:19:46.960 --> 00:19:52.440 So in fact, for instance, if the weight between a and c were 0, 00:19:52.440 --> 00:19:55.690 then a doesn't affect the output at all, right? 00:19:55.690 --> 00:20:00.600 Because its weight is 0, and when we do this problem, 00:20:00.600 --> 00:20:05.010 we go this times 0, and then we try to add it in there, 00:20:05.010 --> 00:20:06.510 doesn't affect anything. 00:20:06.510 --> 00:20:08.620 It's weight is very high, it's going to really 00:20:08.620 --> 00:20:14.280 dominate c, and that is taken into account here, 00:20:14.280 --> 00:20:19.090 and then multiply by the delta for the right node. 00:20:19.090 --> 00:20:22.800 So the following question, and since I 00:20:22.800 --> 00:20:26.610 spent a lot of time with formulae and not that much time 00:20:26.610 --> 00:20:30.650 starting on the problem, I will not call on someone at random, 00:20:30.650 --> 00:20:32.152 but rather take a volunteer. 00:20:32.152 --> 00:20:33.910 If no one volunteers, I'll eventually 00:20:33.910 --> 00:20:37.530 tell you, which is, we've got some nice formulae 00:20:37.530 --> 00:20:39.970 on the bottom three. 00:20:39.970 --> 00:20:43.140 If we change the sigmoid function, what has to change? 00:20:50.770 --> 00:20:53.560 That's the only thing that changes 00:20:53.560 --> 00:20:56.000 in this crazy assed problem right here, which by the way, 00:20:56.000 --> 00:20:58.820 changes the sigmoid functions into adders, 00:20:58.820 --> 00:21:00.690 is that we take all of the o times 1 00:21:00.690 --> 00:21:04.440 minus o in delta f and the delta i, 00:21:04.440 --> 00:21:06.750 and we change it to a new derivative. 00:21:06.750 --> 00:21:09.850 We then do the exact same thing that we would've done. 00:21:09.850 --> 00:21:10.650 Correct. 00:21:10.650 --> 00:21:13.040 And on a similar note, if you change the performance 00:21:13.040 --> 00:21:15.090 function, how many of these equations 00:21:15.090 --> 00:21:18.770 at all have to change out of the bottom three. 00:21:21.360 --> 00:21:22.070 Yeah. 00:21:22.070 --> 00:21:24.430 That's right, just one, just delta f. 00:21:24.430 --> 00:21:26.480 Take the d minus o, make it the new derivative 00:21:26.480 --> 00:21:28.390 of the new performance function. 00:21:28.390 --> 00:21:31.920 And in fact, delta i doesn't change at all. 00:21:31.920 --> 00:21:33.220 Does everyone see that? 00:21:33.220 --> 00:21:37.530 Because it is very common for something to be replaced, 00:21:37.530 --> 00:21:39.670 I think three of the four the quizzes that we have, 00:21:39.670 --> 00:21:43.190 replaced in some-- changed something in some way. 00:21:43.190 --> 00:21:43.690 All right. 00:21:43.690 --> 00:21:44.620 Let's go. 00:21:44.620 --> 00:21:47.690 We're going to do 2008 quiz, because it 00:21:47.690 --> 00:21:49.710 has a part of the end that screwed up everyone, 00:21:49.710 --> 00:21:51.510 and so let's make sure we get to that part. 00:21:51.510 --> 00:21:53.593 That's going to be the part that you probably care 00:21:53.593 --> 00:21:54.920 about the most at this point. 00:21:54.920 --> 00:21:58.050 So these are all adders instead of sigmoids. 00:21:58.050 --> 00:22:03.180 That means that they simply add up everything as normal, 00:22:03.180 --> 00:22:04.960 for a normal neural net, and then there's 00:22:04.960 --> 00:22:06.070 no sigmoid threshold. 00:22:06.070 --> 00:22:07.710 They just give some kind of value. 00:22:07.710 --> 00:22:08.450 Question? 00:22:08.450 --> 00:22:11.354 STUDENT: So we talked about those multiplier things, 00:22:11.354 --> 00:22:14.750 we don't have those in nodes? 00:22:14.750 --> 00:22:16.940 PROFESSOR: They're not neural net nodes. 00:22:16.940 --> 00:22:22.020 That is one of the reasons why that other form that you 00:22:22.020 --> 00:22:23.940 can see over there is elegant. 00:22:23.940 --> 00:22:25.720 It only has the actual nodes on it. 00:22:25.720 --> 00:22:26.970 It is very compact. 00:22:26.970 --> 00:22:30.210 It's one of the front we've used in the previous tests. 00:22:30.210 --> 00:22:35.020 The question is, do those multipliers count as nodes? 00:22:35.020 --> 00:22:38.110 However by not putting in the multipliers, 00:22:38.110 --> 00:22:41.410 we feel it sometimes confuses people of explicitness. 00:22:41.410 --> 00:22:43.410 The ones that are nodes will always 00:22:43.410 --> 00:22:46.230 have a label, like a or here, you see 00:22:46.230 --> 00:22:49.240 there's a sigmoid and an L1. 00:22:49.240 --> 00:22:52.490 The multipliers are there for your convenience, 00:22:52.490 --> 00:22:54.310 to remind you to multiply, and also 00:22:54.310 --> 00:22:56.650 those, if you look those sigmoids that are over there, 00:22:56.650 --> 00:23:00.330 are there for your convenience to remind you to add. 00:23:00.330 --> 00:23:02.850 In fact, the only thing that counts 00:23:02.850 --> 00:23:04.636 as a node in the neural net-- and that's 00:23:04.636 --> 00:23:07.810 a very good question-- is usually the sigmoids, 00:23:07.810 --> 00:23:10.382 here it's the adders. 00:23:10.382 --> 00:23:12.090 We've essentially taken out the sigmoids. 00:23:12.090 --> 00:23:17.370 These adders are the-- oh, here's the way to tell. 00:23:17.370 --> 00:23:22.010 If it's got a threshold weight associated with it, 00:23:22.010 --> 00:23:25.200 then it's one of the actual nodes. 00:23:25.200 --> 00:23:26.220 A threshold weight. 00:23:26.220 --> 00:23:28.428 I guess the multipliers look like they have a weight, 00:23:28.428 --> 00:23:31.774 but this is just the weight that is being multiplied in. 00:23:31.774 --> 00:23:33.940 This is our witness be multiplied in with the input, 00:23:33.940 --> 00:23:35.973 but if it has a threshold weight, like wa, 00:23:35.973 --> 00:23:38.030 wb-- oh, I promised I would tell you guys 00:23:38.030 --> 00:23:39.760 the difference between the two weights. 00:23:39.760 --> 00:23:41.960 So let's do that very quickly. 00:23:41.960 --> 00:23:46.860 The kinds of weights that, say w2b or w1a, our weight the 00:23:46.860 --> 00:23:51.775 comes between input 1 and a or between a 00:23:51.775 --> 00:23:57.590 and c, then mentally multiplying the input by this weight, 00:23:57.590 --> 00:23:59.840 and then eventually that's added together. 00:23:59.840 --> 00:24:06.040 The threshold weights, they just have like wb, wa, wc. 00:24:06.040 --> 00:24:09.900 They are essentially to decide the threshold for a success 00:24:09.900 --> 00:24:14.715 or failure, for a 1 or a 0, or anything in between, 00:24:14.715 --> 00:24:17.150 at any of the given nodes. 00:24:17.150 --> 00:24:20.500 So the idea is maybe you at some node 00:24:20.500 --> 00:24:22.260 want to have a really high cut off, 00:24:22.260 --> 00:24:25.180 you have to very high value coming in, or else it's a 0. 00:24:25.180 --> 00:24:27.060 So you put a high threshold. 00:24:27.060 --> 00:24:29.200 The weight is multiplied by negative 1. 00:24:29.200 --> 00:24:37.880 And in fact, the threshold weight won't-- one could 00:24:37.880 --> 00:24:40.850 consider if you wanted to that the threshold weight times 00:24:40.850 --> 00:24:44.030 negative 1. was also added in it that sum, 00:24:44.030 --> 00:24:47.560 instead of putting at the same location as the node. 00:24:47.560 --> 00:24:50.140 If that works better for you, when you're converting it, 00:24:50.140 --> 00:24:52.010 you can also think of it that way. 00:24:52.010 --> 00:24:54.090 Because the threshold weight is essentially 00:24:54.090 --> 00:24:55.650 multiplied by negative 1 and added in 00:24:55.650 --> 00:24:58.130 at that same sum over there. 00:24:58.130 --> 00:25:02.062 So that's another way to do it. 00:25:02.062 --> 00:25:04.270 There's a lot of ways to visualize these neural nets. 00:25:04.270 --> 00:25:07.940 Just make sure you have a way that makes sense to you, 00:25:07.940 --> 00:25:09.690 and that you can tell pretty much whatever 00:25:09.690 --> 00:25:12.050 we write, as long as it looks vaguely like that, 00:25:12.050 --> 00:25:15.159 how to get it in your mind, into the representation 00:25:15.159 --> 00:25:15.950 that works for you. 00:25:15.950 --> 00:25:18.241 Because once you have the representation right for you, 00:25:18.241 --> 00:25:20.360 you're more than halfway to solving these guys. 00:25:20.360 --> 00:25:21.660 They aren't that bad. 00:25:21.660 --> 00:25:23.080 They just look nasty. 00:25:23.080 --> 00:25:24.310 They don't bite. 00:25:24.310 --> 00:25:24.900 OK. 00:25:24.900 --> 00:25:26.560 These are just adders. 00:25:26.560 --> 00:25:28.570 So if it's just an adder, then that 00:25:28.570 --> 00:25:34.410 means that, if we take all the x inputs coming in-- 00:25:34.410 --> 00:25:36.630 let's do x and y for the moment, so we can figure out 00:25:36.630 --> 00:25:39.980 the derivative-- then what comes out 00:25:39.980 --> 00:25:46.830 after we just add up the x, what comes out, y equals x, right? 00:25:46.830 --> 00:25:48.770 We're just adding it up. 00:25:48.770 --> 00:25:52.290 Adding up all the input, we're not doing anything to it. 00:25:52.290 --> 00:25:55.910 Y equals x is what this node does. 00:25:55.910 --> 00:25:56.790 You people see that? 00:25:56.790 --> 00:26:00.690 So the derivative is just one. 00:26:00.690 --> 00:26:04.590 So that's pretty easy, because the first problem says, 00:26:04.590 --> 00:26:10.850 what is the new formula, delta f. 00:26:10.850 --> 00:26:12.890 So I'll just tell you. 00:26:12.890 --> 00:26:14.810 You guys probably figured it out. 00:26:14.810 --> 00:26:17.538 o times 1 minus o. 00:26:17.538 --> 00:26:21.530 Because we replaced d minus o with 1. 00:26:21.530 --> 00:26:22.230 OK? 00:26:22.230 --> 00:26:23.172 Makes sense so far? 00:26:23.172 --> 00:26:24.630 Please ask questions along the way, 00:26:24.630 --> 00:26:26.660 because I'm not going to be asking you guys. 00:26:26.660 --> 00:26:27.805 I'll do it myself. 00:26:27.805 --> 00:26:28.305 Question? 00:26:28.305 --> 00:26:29.888 STUDENT: Why to we use d minus o of 1? 00:26:32.890 --> 00:26:34.600 PROFESSOR: That's a good question. 00:26:34.600 --> 00:26:37.510 The reason is because I did the wrong thing. 00:26:37.510 --> 00:26:42.230 So see, it's good that you guys are asking questions. 00:26:42.230 --> 00:26:44.850 It actually should be replaced with o times 1 minus o with 1. 00:26:44.850 --> 00:26:49.350 The answer is delta f equals d minus o. 00:26:49.350 --> 00:26:52.170 So yes, perhaps I did it to trick you. 00:26:52.170 --> 00:26:54.570 No, I actually messed up. 00:26:54.570 --> 00:26:56.820 But yes, please ask questions along the way. 00:26:56.820 --> 00:26:59.080 Again, I don't have time to call on you guys 00:26:59.080 --> 00:27:01.520 at random to figure out if you guys are following along. 00:27:01.520 --> 00:27:03.020 So I'll do it myself. 00:27:03.020 --> 00:27:06.180 We're placing the o times 1 minus o with 1 because 00:27:06.180 --> 00:27:07.860 of the fact that the sigmoid is gone, 00:27:07.860 --> 00:27:10.960 and we get just delta f equals d minus o. 00:27:10.960 --> 00:27:13.660 So great. 00:27:13.660 --> 00:27:18.320 We now want to know what the equation is for delta i, 00:27:18.320 --> 00:27:19.720 at the node a. 00:27:19.720 --> 00:27:21.740 So delta a. 00:27:21.740 --> 00:27:24.270 Well let's take a look. 00:27:24.270 --> 00:27:26.530 The o times 1 minus o is gone. 00:27:26.530 --> 00:27:30.210 Now we just have the sum over j, which you guys already 00:27:30.210 --> 00:27:36.120 told me is, only c of WAC times delta c. 00:27:36.120 --> 00:27:38.350 We know that delta c is d minus o. 00:27:38.350 --> 00:27:43.590 The answer is delta a is just WAC times d minus o. 00:27:43.590 --> 00:27:46.050 That time, I got it right. 00:27:46.050 --> 00:27:47.684 I see the answer here. 00:27:47.684 --> 00:27:49.600 Though it's written in a very different format 00:27:49.600 --> 00:27:52.290 from the old quiz. 00:27:52.290 --> 00:27:54.590 Any questions on that? 00:27:54.590 --> 00:27:58.070 Well that's part a that we finished out of c. 00:27:58.070 --> 00:27:59.300 Let's go to part b. 00:27:59.300 --> 00:28:01.625 Part b is doing one step backpropagation. 00:28:01.625 --> 00:28:04.430 There's almost always going to be one of these in here. 00:28:04.430 --> 00:28:07.740 So the first thing it asks is to figure out 00:28:07.740 --> 00:28:11.510 what the output o is for this neural net 00:28:11.510 --> 00:28:15.670 if all weights are initially 1 except that this guy right here 00:28:15.670 --> 00:28:18.120 is negative 0.5. 00:28:18.120 --> 00:28:22.120 All the other ones start off as 1. 00:28:22.120 --> 00:28:25.560 Let's do a step-- oh, let's see what are the inputs. 00:28:25.560 --> 00:28:28.040 The inputs are also all 1. 00:28:28.040 --> 00:28:31.320 Desired output is also 1. 00:28:31.320 --> 00:28:37.980 And in fact, the rate constant alpha is also 1. 00:28:37.980 --> 00:28:40.490 This is the only thing that isn't 1, folks. 00:28:40.490 --> 00:28:42.070 So let's see what happens. 00:28:42.070 --> 00:28:48.210 1 times 1 is 1, then this is a negative 1 00:28:48.210 --> 00:28:50.870 times 1 is negative 1. 00:28:50.870 --> 00:28:53.062 That's 0. 00:28:53.062 --> 00:28:55.520 The exact same thing happens here because it's symmetrical. 00:28:55.520 --> 00:28:57.546 So these are both 0. 00:28:57.546 --> 00:29:03.150 0 times 1 is 0, 0 times 1 is 0. 00:29:03.150 --> 00:29:07.770 Then this is negative 1 times negative 0.5 is positive 0.5, 00:29:07.770 --> 00:29:14.740 so 0 plus 0 plus a positive 0.5, the output is positive 0.5. 00:29:14.740 --> 00:29:16.700 Does everyone see that? 00:29:16.700 --> 00:29:20.830 If not, you can convince yourself 00:29:20.830 --> 00:29:21.900 that it is positive 0.5. 00:29:21.900 --> 00:29:23.570 That would be a good exercise for you, 00:29:23.570 --> 00:29:25.470 run through one forward run. 00:29:25.470 --> 00:29:28.650 The output is definitely positive 0.5. 00:29:28.650 --> 00:29:30.000 First time around. 00:29:30.000 --> 00:29:31.130 OK? 00:29:31.130 --> 00:29:34.000 Now we have to do one step of backpropagation. 00:29:34.000 --> 00:29:35.900 To do that, let's calculate all the delta 00:29:35.900 --> 00:29:37.810 so that we can calculate all the new weights, 00:29:37.810 --> 00:29:39.560 the the new weight primes. 00:29:39.560 --> 00:29:42.660 So delta c. 00:29:42.660 --> 00:29:43.490 That's easy. 00:29:43.490 --> 00:29:45.060 You guys can tell me what delta c is. 00:29:45.060 --> 00:29:47.440 We figured out what the new delta c is going to be. 00:29:47.440 --> 00:29:50.500 So simple addition or subtraction problem? 00:29:50.500 --> 00:29:52.306 Everyone, delta c is? 00:29:52.306 --> 00:29:53.000 STUDENT: 0.5. 00:29:53.000 --> 00:29:58.086 PROFESSOR: 0.5, one half, yes. 00:29:58.086 --> 00:29:58.585 All right. 00:30:02.250 --> 00:30:07.690 We know that delta a and delta b are just WAC times delta c, 00:30:07.690 --> 00:30:09.150 and WBC times delta c. 00:30:09.150 --> 00:30:10.660 So they are? 00:30:10.660 --> 00:30:11.460 STUDENT: One half. 00:30:11.460 --> 00:30:14.440 PROFESSOR: Also one half, because all the weights were 1. 00:30:16.970 --> 00:30:17.750 Easy street. 00:30:17.750 --> 00:30:18.600 OK. 00:30:18.600 --> 00:30:20.980 We've got all of the deltas are one half. 00:30:20.980 --> 00:30:23.290 And all but a few of the weights are 1. 00:30:23.290 --> 00:30:25.190 So let's figure out what the new weights are. 00:30:29.910 --> 00:30:32.140 New WAC, OK. 00:30:37.520 --> 00:30:38.320 Yeah, so let's see. 00:30:38.320 --> 00:30:40.480 What's going to be the new WAC? 00:30:40.480 --> 00:30:45.080 So the new WAC is going to be old 00:30:45.080 --> 00:30:48.880 WAC, which is 1, because all of them are 1 except for wc, 00:30:48.880 --> 00:30:53.960 plus the rate constant which is 1, times the input coming 00:30:53.960 --> 00:30:57.270 in here, but remember that was 0, 00:30:57.270 --> 00:31:01.500 so actually it's just going to be the same as the old WAC. 00:31:01.500 --> 00:31:06.000 This is a metrical problem between b and a, at the moment, 00:31:06.000 --> 00:31:08.720 this is going to be the same. 00:31:08.720 --> 00:31:09.407 All right. 00:31:09.407 --> 00:31:10.990 Somethings are going to change though. 00:31:10.990 --> 00:31:14.960 What about wc, that was the one that was actually not 1? 00:31:14.960 --> 00:31:15.610 OK. 00:31:15.610 --> 00:31:25.120 So new wc, remember, the i for wc, 00:31:25.120 --> 00:31:26.720 the i that we use in this equation 00:31:26.720 --> 00:31:29.680 is always negative 1 because it's a threshold. 00:31:29.680 --> 00:31:37.700 So we have the old wc, which is negative 0.5, plus 1 times 00:31:37.700 --> 00:31:41.990 negative 1 times delta c, which is one half. 00:31:41.990 --> 00:31:49.330 So we have negative 0.5 plus negative 0.5 equals negative 1. 00:31:49.330 --> 00:31:57.260 w 1 a, well we've got w 1 a starts out as 1. 00:31:57.260 --> 00:32:04.180 Then we also know that w 1 a is going 00:32:04.180 --> 00:32:08.090 to be equal to 1 plus 1 times the input, which 00:32:08.090 --> 00:32:18.420 is 1, times delta of a, which is one half, so 1.5. 00:32:18.420 --> 00:32:25.000 And since it's symmetrical between a and b, then w 2 00:32:25.000 --> 00:32:29.400 b is also 1.5. 00:32:29.400 --> 00:32:35.730 And then finally, wa and wb, the offsets here, well they 00:32:35.730 --> 00:32:41.250 start at 1 plus 1 times negative 1 times 0.5. 00:32:41.250 --> 00:32:44.150 So they're both, everyone? 00:32:44.150 --> 00:32:44.947 STUDENT: One half. 00:32:44.947 --> 00:32:45.780 PROFESSOR: One half. 00:32:45.780 --> 00:32:46.321 That's right. 00:32:55.330 --> 00:32:56.080 That's right. 00:32:56.080 --> 00:33:00.780 Because negative 1 is their i. 00:33:00.780 --> 00:33:05.440 Negative 1 times one half plus positive 1 is just one half. 00:33:05.440 --> 00:33:07.690 That's one full step. 00:33:07.690 --> 00:33:10.180 Maybe a mite easier than you might be used to seeing, 00:33:10.180 --> 00:33:11.386 but there's a full step. 00:33:11.386 --> 00:33:13.510 And it asks what's going to be the output after one 00:33:13.510 --> 00:33:15.509 step of backpropagation? 00:33:15.509 --> 00:33:16.300 We can take a look. 00:33:19.860 --> 00:33:26.280 So we have 1 times the new wa, which is 1.5, you've got 1.5, 00:33:26.280 --> 00:33:29.130 then the new wa is just 0.5, now is 00:33:29.130 --> 00:33:31.920 0.5, that's a 1 coming into an adder. 00:33:31.920 --> 00:33:34.910 We've got another 1 coming in here because it's symmetrical. 00:33:34.910 --> 00:33:39.370 So 1 and a 1, 1 times WAC is 1. 00:33:39.370 --> 00:33:41.020 1 times WBC is 1. 00:33:41.020 --> 00:33:44.990 So we have two 1s coming in here, they're added, that's 2. 00:33:44.990 --> 00:33:50.860 Then this has become negative 1, in fact, at this point. 00:33:50.860 --> 00:33:55.970 So negative 1 times negative 1, that's 3, and the output is 3. 00:33:58.540 --> 00:33:59.070 All right. 00:33:59.070 --> 00:33:59.590 Cool. 00:33:59.590 --> 00:34:03.880 We've now finished part b, which is over half of everything. 00:34:03.880 --> 00:34:05.186 Oh no, we've not. 00:34:05.186 --> 00:34:05.810 One more thing. 00:34:10.929 --> 00:34:11.690 These are adders. 00:34:11.690 --> 00:34:12.565 They're not sigmoids. 00:34:16.210 --> 00:34:19.095 What if we train this entire neural net 00:34:19.095 --> 00:34:21.389 to try to learn this data, so that it 00:34:21.389 --> 00:34:25.520 can draw a line on a graph, or draw some lines, 00:34:25.520 --> 00:34:29.199 or do some kind of learning, to separate off the minuses 00:34:29.199 --> 00:34:31.070 from all the pluses. 00:34:31.070 --> 00:34:33.280 You've seen, maybe, and if not, you 00:34:33.280 --> 00:34:34.780 are about to in a second, because it 00:34:34.780 --> 00:34:37.600 asks you to do this in detail, than neural nets can usually 00:34:37.600 --> 00:34:40.830 draw one line on the graph for each of these, 00:34:40.830 --> 00:34:43.120 sort of, nodes in the net, because each of the nodes 00:34:43.120 --> 00:34:44.449 has some kind of threshold. 00:34:44.449 --> 00:34:49.480 And you can do some logic between them like ands or ors. 00:34:49.480 --> 00:34:52.830 What do you guys think this net is going to draw? 00:34:52.830 --> 00:34:55.389 Anyone could volunteer, I'm not going to ask anyone 00:34:55.389 --> 00:34:58.260 to give this answer. 00:34:58.260 --> 00:35:01.510 That's a little bit tricky, because usually 00:35:01.510 --> 00:35:03.890 if you had this many nodes, you could easily 00:35:03.890 --> 00:35:07.750 draw a box and box off the minuses from the pluses. 00:35:07.750 --> 00:35:11.680 However, it draws this. 00:35:11.680 --> 00:35:13.350 And it asks what is the error? 00:35:13.350 --> 00:35:16.570 The error is-- oh yeah, it even tells you the error is 1/8, 00:35:16.570 --> 00:35:19.260 because why? 00:35:19.260 --> 00:35:20.660 These are all adders. 00:35:20.660 --> 00:35:23.460 You can't actually do anything logical. 00:35:23.460 --> 00:35:25.760 This entire net boils down to just one node, 00:35:25.760 --> 00:35:27.530 because it just adds up every time. 00:35:27.530 --> 00:35:30.330 It never takes a threshold at any point. 00:35:30.330 --> 00:35:33.160 So you can't turn into logical ones and zeroes, 00:35:33.160 --> 00:35:37.440 because it's basically not digital at all, its analog. 00:35:37.440 --> 00:35:39.500 It's giving us some very high number. 00:35:39.500 --> 00:35:41.840 So it all boils down to one cut off. 00:35:41.840 --> 00:35:43.850 And that's the best one. 00:35:43.850 --> 00:35:46.700 The one that I drew right here. 00:35:46.700 --> 00:35:47.929 OK. 00:35:47.929 --> 00:35:49.220 Did that not make sense to you? 00:35:49.220 --> 00:35:50.280 That's OK. 00:35:50.280 --> 00:35:52.080 This problem is much harder. 00:35:52.080 --> 00:35:56.040 And putting them both on the same quiz, was a bit brutal, 00:35:56.040 --> 00:35:57.880 but by the time you're done with this, 00:35:57.880 --> 00:36:00.380 you'll understand what a neural net can do or not. 00:36:00.380 --> 00:36:02.840 I put these in simplified form because of the fact 00:36:02.840 --> 00:36:06.350 that we don't care about their values or anything like that. 00:36:06.350 --> 00:36:09.570 But inside of these little circles is a sigmoid, 00:36:09.570 --> 00:36:13.860 the multipliers and the summers are implied. 00:36:13.860 --> 00:36:16.380 I think in the simplified form when we're not actually 00:36:16.380 --> 00:36:18.590 doing backpropagation is easier to view it, and see 00:36:18.590 --> 00:36:19.950 how many nodes there are. 00:36:19.950 --> 00:36:21.741 For the same reason you asked your question 00:36:21.741 --> 00:36:22.850 about how many there are. 00:36:22.850 --> 00:36:26.130 So all of those big circles are node. 00:36:26.130 --> 00:36:30.080 And in those nodes is a sigmoid now, not those crazy adders. 00:36:30.080 --> 00:36:31.680 We have the following problem. 00:36:31.680 --> 00:36:33.590 We have to try to match each of a, 00:36:33.590 --> 00:36:37.690 b, c, d, e, f to 1, 2, 3, 4, 5, 6, using each of them 00:36:37.690 --> 00:36:39.100 only once. 00:36:39.100 --> 00:36:43.140 That's important, because some of the more powerful networks 00:36:43.140 --> 00:36:45.730 in here can do a lot of these. 00:36:45.730 --> 00:36:49.050 So it's like yes, the powerful networks could 00:36:49.050 --> 00:36:50.620 do some of the easier problems here, 00:36:50.620 --> 00:36:53.940 but we want to match each net to a problem it can do, 00:36:53.940 --> 00:36:57.720 and there is exactly one mapping that will map-- that 00:36:57.720 --> 00:37:02.290 is one to one, and maps exactly, uses all six of the nets 00:37:02.290 --> 00:37:04.700 to solve all six of these problems here. 00:37:04.700 --> 00:37:07.030 So some of you may be going like, what? 00:37:07.030 --> 00:37:08.870 How am I going to solve these problems? 00:37:08.870 --> 00:37:11.490 I gave away a hint before, which is 00:37:11.490 --> 00:37:16.940 that each node in the neural net, each sigmoid node 00:37:16.940 --> 00:37:21.070 can usually draw one line on the-- it 00:37:21.070 --> 00:37:23.290 can draw one line into the picture. 00:37:23.290 --> 00:37:25.225 The line can be diagonal if that nodes 00:37:25.225 --> 00:37:28.320 receives both of the inputs, which is here, i 1 and i 2. 00:37:28.320 --> 00:37:30.470 See there is an i 1 and an i 2 axis. 00:37:30.470 --> 00:37:32.330 Like x- and a y-axis. 00:37:32.330 --> 00:37:36.420 The node has to be horizontal, or vertical, if-- sorry, 00:37:36.420 --> 00:37:38.920 the line has to be horizontal or vertical if the node only 00:37:38.920 --> 00:37:41.810 receives one of the inputs. 00:37:41.810 --> 00:37:46.560 And then, if you have a deeper level, 00:37:46.560 --> 00:37:51.090 these secondary level nodes can sort of do a logical, 00:37:51.090 --> 00:37:53.810 can do some kind of brilliant thing like and or or of 00:37:53.810 --> 00:37:58.020 the first two, which can help you out. 00:37:58.020 --> 00:37:58.770 All right. 00:37:58.770 --> 00:38:01.530 And so let's try to figure it out. 00:38:01.530 --> 00:38:05.030 So right off the bat, and I hope that people will help and call 00:38:05.030 --> 00:38:06.930 this out, because I know we don't 00:38:06.930 --> 00:38:09.305 have enough time that I can force you guys to all get it. 00:38:09.305 --> 00:38:11.013 But right off the bat, which one of these 00:38:11.013 --> 00:38:12.699 looks like it's the easiest one? 00:38:12.699 --> 00:38:13.240 STUDENT: Six. 00:38:13.240 --> 00:38:13.865 PROFESSOR: Six. 00:38:13.865 --> 00:38:14.530 That's great. 00:38:14.530 --> 00:38:15.946 Six is definitely the easiest one. 00:38:15.946 --> 00:38:17.220 It's a single line. 00:38:17.220 --> 00:38:19.430 So this is just how I would have solved this problem, 00:38:19.430 --> 00:38:20.530 is find the easiest one. 00:38:20.530 --> 00:38:23.010 Which of these is the crappiest net? 00:38:23.010 --> 00:38:23.510 STUDENT: A. 00:38:23.510 --> 00:38:25.500 PROFESSOR: A is the crappiest net. 00:38:25.500 --> 00:38:27.440 But there's no way in hell that A 00:38:27.440 --> 00:38:30.510 is going to be able to get any of these except for six. 00:38:30.510 --> 00:38:39.240 So let's, right off the bat, say that six is A. All right. 00:38:39.240 --> 00:38:44.550 Six is A. That's A. We don't have to worry about A. OK. 00:38:44.550 --> 00:38:45.560 Cool. 00:38:45.560 --> 00:38:49.400 Now let's look at some other ones that are very interesting. 00:38:49.400 --> 00:38:52.430 All the rest of these draw two lines, 00:38:52.430 --> 00:38:53.835 well these three draw two lines. 00:38:53.835 --> 00:38:55.380 These three draw three lines. 00:38:55.380 --> 00:38:58.800 They draw a triangle. 00:38:58.800 --> 00:39:02.740 So despite the fact that this c is a very powerful node, 00:39:02.740 --> 00:39:09.470 that indeed, with three whole levels here of sigmoids, 00:39:09.470 --> 00:39:12.400 it looks like there's only two that's 00:39:12.400 --> 00:39:14.490 in our little stable of nets that are equipped 00:39:14.490 --> 00:39:16.460 to handle number one and two. 00:39:16.460 --> 00:39:18.530 And those are? 00:39:18.530 --> 00:39:23.335 E and F, because E and F have three nodes at the first level. 00:39:23.335 --> 00:39:25.276 They can draw three lines. 00:39:25.276 --> 00:39:27.650 And then they can do something logical about those lines, 00:39:27.650 --> 00:39:31.690 like for instance, maybe, if it's inside all of those lines. 00:39:31.690 --> 00:39:32.960 There's a way to do that. 00:39:32.960 --> 00:39:36.260 You just-- basically you can give negative and positive 00:39:36.260 --> 00:39:38.120 weights as you so choose to make sure 00:39:38.120 --> 00:39:40.264 that it's under certain ones, above other ones, 00:39:40.264 --> 00:39:42.930 and then make the threshold such that it has to follow all three 00:39:42.930 --> 00:39:45.160 of your rules. 00:39:45.160 --> 00:39:49.725 So between E and F, which one should be two 00:39:49.725 --> 00:39:52.050 and which one should be one. 00:39:52.050 --> 00:39:53.160 Anyone see? 00:39:53.160 --> 00:39:55.140 Well let's look at two and one. 00:39:55.140 --> 00:39:56.790 Which one is easier to do? 00:39:56.790 --> 00:39:57.880 Between two and one. 00:39:57.880 --> 00:39:59.120 Two. 00:39:59.120 --> 00:40:00.820 It's got a horizontal and a vertical. 00:40:00.820 --> 00:40:03.350 One has all three diagonal. 00:40:03.350 --> 00:40:08.262 And which one of these is a weaker net, between E and F. 00:40:08.262 --> 00:40:10.620 F. F has one node that can only do a horizontal, 00:40:10.620 --> 00:40:13.630 and one node that can only do a vertical line. 00:40:13.630 --> 00:40:16.370 So which one is F going to have to do? 00:40:16.370 --> 00:40:17.850 Two. 00:40:17.850 --> 00:40:19.210 And E does what? 00:40:19.210 --> 00:40:20.530 Good job, guys. 00:40:20.530 --> 00:40:22.470 Good job, you got this. 00:40:22.470 --> 00:40:24.940 So now let's look at the last three. 00:40:31.070 --> 00:40:32.790 Number three is definitely the hardest. 00:40:32.790 --> 00:40:35.470 It's an exceller. 00:40:35.470 --> 00:40:37.260 Those of you who've played around 00:40:37.260 --> 00:40:41.750 with double o 2 kind of stuff, or even just logic, 00:40:41.750 --> 00:40:45.560 probably know that there is no way 00:40:45.560 --> 00:40:52.490 to make a sort of simple linear combination in one 00:40:52.490 --> 00:40:55.610 level of logic to create an x or. 00:40:55.610 --> 00:40:58.660 x or is very difficult to create. 00:40:58.660 --> 00:41:00.830 There are some interesting problems 00:41:00.830 --> 00:41:04.560 involving trying to teach an exceller to a neural net. 00:41:04.560 --> 00:41:06.280 Because a neural net is not to be 00:41:06.280 --> 00:41:09.720 able to get the x or, because of the fact that you can tell it, 00:41:09.720 --> 00:41:14.120 OK, I want this one to be high, and this one to be low. 00:41:14.120 --> 00:41:14.930 That's fine. 00:41:14.930 --> 00:41:16.610 You say these both have to be high. 00:41:16.610 --> 00:41:17.620 That's fine. 00:41:17.620 --> 00:41:21.110 It's hard to say, it's pretty much impossible to say, 00:41:21.110 --> 00:41:24.860 this one or this one, but not the other, because need 00:41:24.860 --> 00:41:27.460 to be high in a single node, because of the fact that if you 00:41:27.460 --> 00:41:29.460 just play with it, you'll see. 00:41:29.460 --> 00:41:31.470 You need to set a threshold somewhere, 00:41:31.470 --> 00:41:33.680 and it's not going to be able to distinguish 00:41:33.680 --> 00:41:36.325 between, if the threshold is set such that the 00:41:36.325 --> 00:41:38.450 or is going to work, the whole or is going to work. 00:41:38.450 --> 00:41:42.060 It's going to accept when both of them are positive as well. 00:41:42.060 --> 00:41:43.360 So how we can do x or? 00:41:43.360 --> 00:41:44.730 We need more logic. 00:41:44.730 --> 00:41:46.990 We need to use some combinations of ands and ors 00:41:46.990 --> 00:41:48.480 in a two level way. 00:41:48.480 --> 00:41:51.520 To do that we need the deepest neural net that we have. 00:41:51.520 --> 00:41:53.390 There's only one that's capable of that. 00:41:53.390 --> 00:41:54.680 And that is? 00:41:54.680 --> 00:41:55.785 It's C. 00:41:55.785 --> 00:41:57.410 There are many different ways to do it. 00:41:57.410 --> 00:41:59.510 Let's think of a possibility. 00:41:59.510 --> 00:42:04.230 i 1 and i 2 draw these two lines. 00:42:04.230 --> 00:42:08.450 Let's call these one, two, three, four, five, 00:42:08.450 --> 00:42:12.010 node 1 and node 2 draw these two lines. 00:42:12.010 --> 00:42:14.680 And I'll just sort of draw it here for you guys. 00:42:14.680 --> 00:42:20.050 Then maybe node 3 gives value to-- yeah, 00:42:20.050 --> 00:42:29.810 let me see-- node three can give value to perhaps-- let's 00:42:29.810 --> 00:42:36.924 see-- node 3 can give value to everything that is-- there are 00:42:36.924 --> 00:42:38.090 a lot of possibilities here. 00:42:38.090 --> 00:42:48.410 Node 3 can give value to everything that is up here. 00:42:48.410 --> 00:42:50.650 Actually node 3 can give value to everything 00:42:50.650 --> 00:42:56.630 except for this bottom part, and then 00:42:56.630 --> 00:43:05.510 node 4 could give value to say-- doesn't do it yet, 00:43:05.510 --> 00:43:07.700 but there's a few-- there's a few different ways 00:43:07.700 --> 00:43:09.130 to do it if you played around. 00:43:09.130 --> 00:43:12.470 The key idea is that node 3 and node 4 00:43:12.470 --> 00:43:17.350 can give value to some combination and or or not, 00:43:17.350 --> 00:43:23.490 and then node 5 can give value based on being above or below 00:43:23.490 --> 00:43:26.280 a certain threshold, combination of 3 and 4. 00:43:26.280 --> 00:43:29.200 You can build an exceller out of the logic gates. 00:43:29.200 --> 00:43:32.820 I will ponder on that in the back burner for a moment, 00:43:32.820 --> 00:43:35.200 as we continue onward, but clearly C 00:43:35.200 --> 00:43:38.010 has to do number three. 00:43:38.010 --> 00:43:38.620 OK. 00:43:38.620 --> 00:43:40.490 Now we're left with four and five. 00:43:40.490 --> 00:43:42.447 I think, interestingly, five looks 00:43:42.447 --> 00:43:45.030 like it may be more complicated than four, because of the fact 00:43:45.030 --> 00:43:48.297 that it needs to do both different directions instead 00:43:48.297 --> 00:43:49.570 of two of the same direction. 00:43:52.930 --> 00:43:55.720 So however, just the idea of the one with the fewer lines, 00:43:55.720 --> 00:43:58.720 being a simpler one, may not get us through here. 00:43:58.720 --> 00:43:59.860 And there's a reason why. 00:43:59.860 --> 00:44:01.180 Look what we have left to use. 00:44:01.180 --> 00:44:06.610 We have to use D or B. What is the property of the two lines 00:44:06.610 --> 00:44:08.740 that D can draw? 00:44:08.740 --> 00:44:11.930 D being the simpler one. 00:44:11.930 --> 00:44:14.760 One horizontal, one vertical, that's right. 00:44:14.760 --> 00:44:16.260 So even though it may look simpler 00:44:16.260 --> 00:44:17.740 to just have two horizontal lines, 00:44:17.740 --> 00:44:20.860 it actually requires B. B is the only one that 00:44:20.860 --> 00:44:24.030 can draw two horizontal lines because D has to draw one 00:44:24.030 --> 00:44:25.660 horizontal and one vertical. 00:44:25.660 --> 00:44:33.160 So that leaves us with, B on this, D on this. 00:44:33.160 --> 00:44:34.410 Excellent, we have a question. 00:44:34.410 --> 00:44:36.327 I would've thought it would have been possible 00:44:36.327 --> 00:44:37.743 that we had no questions, or maybe 00:44:37.743 --> 00:44:39.471 I just explained it the best I ever have. 00:44:39.471 --> 00:44:39.970 Question. 00:44:39.970 --> 00:44:43.825 STUDENT: I didn't get why B has to be two horizontal lines. 00:44:43.825 --> 00:44:44.700 PROFESSOR: All right. 00:44:44.700 --> 00:44:46.450 So the question is, I don't understand why 00:44:46.450 --> 00:44:48.200 B to be two horizontal lines. 00:44:48.200 --> 00:44:52.340 The answer is, it doesn't. 00:44:52.340 --> 00:44:56.510 B can be anything, but D can't be two horizontal lines. 00:44:56.510 --> 00:44:58.180 And so by process of elimination, 00:44:58.180 --> 00:45:03.680 it's B. Well take a look at D, right. 00:45:03.680 --> 00:45:09.530 So D has three nodes, one, two, three. 00:45:09.530 --> 00:45:12.660 Node 1 and node 2 can just draw a line anywhere 00:45:12.660 --> 00:45:15.140 they want, involving the inputs they receive. 00:45:15.140 --> 00:45:18.470 What input does node 1 receive? 00:45:18.470 --> 00:45:19.280 Let's go to node 1. 00:45:21.910 --> 00:45:26.550 So it can only make a cut off based on i 1. 00:45:26.550 --> 00:45:30.800 So therefore, it can only draw by making the cut off 00:45:30.800 --> 00:45:32.200 above and below a certain point. 00:45:32.200 --> 00:45:34.990 Node 1 can only draw vertical lines. 00:45:34.990 --> 00:45:37.174 Node 2 can only draw a horizontal line, 00:45:37.174 --> 00:45:38.590 because it can only make a cut off 00:45:38.590 --> 00:45:41.780 based on where it is an i 2. 00:45:41.780 --> 00:45:44.390 Therefore they can't both draw a horizontal. 00:45:44.390 --> 00:45:46.640 That's why this is the trickiest part. 00:45:46.640 --> 00:45:49.160 This last part, because B is more powerful. 00:45:49.160 --> 00:45:51.340 B does not only have to do two horizontal lines. 00:45:51.340 --> 00:45:54.280 It can do two diagonal lines. 00:45:54.280 --> 00:45:55.490 It can do anything it wants. 00:45:55.490 --> 00:45:58.222 It just happens that it's stuck doing this somewhat easier 00:45:58.222 --> 00:46:00.680 problem, because the fact that it is the only one left that 00:46:00.680 --> 00:46:02.490 has the power to do it. 00:46:02.490 --> 00:46:05.760 So let's see, we're done, and we'd 00:46:05.760 --> 00:46:09.490 have aced this part of the quiz that like no one got, 00:46:09.490 --> 00:46:11.240 well not no one, but very few people got, 00:46:11.240 --> 00:46:13.660 when we put it on in 2008. 00:46:13.660 --> 00:46:17.140 The only thing we have left to ask 00:46:17.140 --> 00:46:22.430 is-- let me see-- yeah, the only thing we have left to ask 00:46:22.430 --> 00:46:29.931 is what are we going to do here for this? 00:46:29.931 --> 00:46:30.430 All right. 00:46:30.430 --> 00:46:31.070 Let's see. 00:46:33.860 --> 00:46:38.360 For the x or, let's see if I can do this x or. 00:46:41.360 --> 00:46:43.240 OK. 00:46:43.240 --> 00:46:44.970 How about this one. 00:46:44.970 --> 00:46:45.510 Right. 00:46:45.510 --> 00:46:46.180 I'm an idiot. 00:46:46.180 --> 00:46:47.910 This is the easiest way. 00:46:47.910 --> 00:46:49.926 Number one draws this line. 00:46:49.926 --> 00:46:51.050 Number two draws this line. 00:46:51.050 --> 00:46:55.307 Number three ends the line, the two lines. 00:46:55.307 --> 00:46:56.890 Number three says only if both of them 00:46:56.890 --> 00:46:58.360 are true, will I accept. 00:46:58.360 --> 00:47:02.510 Number four maps the two lines. 00:47:02.510 --> 00:47:05.550 And number five ors between three and four. 00:47:08.430 --> 00:47:09.740 Thank you. 00:47:09.740 --> 00:47:11.840 No, it's not that hard. 00:47:11.840 --> 00:47:13.902 I just completely blanked, because there's 00:47:13.902 --> 00:47:15.860 another way that a lot of people like to do it. 00:47:15.860 --> 00:47:17.300 It involves drawing in a lot of lines, 00:47:17.300 --> 00:47:18.570 and then making the clef b 2. 00:47:18.570 --> 00:47:20.280 But I can't remember it at the moment. 00:47:20.280 --> 00:47:21.610 Or there any other questions? 00:47:21.610 --> 00:47:26.958 Because I think if you have a question now, 00:47:26.958 --> 00:47:28.582 like four other people have it and just 00:47:28.582 --> 00:47:29.630 aren't raising their hand. 00:47:29.630 --> 00:47:31.470 So ask any questions about this drawing thing. 00:47:31.470 --> 00:47:31.970 Question? 00:47:31.970 --> 00:47:33.569 STUDENT: Why do we do this? 00:47:33.569 --> 00:47:35.360 PROFESSOR: Why do we do this drawing thing? 00:47:35.360 --> 00:47:37.680 That's a very good question. 00:47:37.680 --> 00:47:40.990 The answer is so that you can see what kinds of nets 00:47:40.990 --> 00:47:43.680 you might need to use in these simple problems, 00:47:43.680 --> 00:47:45.590 to answer these simple problems. 00:47:45.590 --> 00:47:51.320 So that if Athena forbid that you 00:47:51.320 --> 00:47:54.340 have to use a neural net in a job 00:47:54.340 --> 00:47:56.640 somewhere to do some actual learning, 00:47:56.640 --> 00:48:00.260 and you see some sort of quality about the problem, 00:48:00.260 --> 00:48:02.910 you know not to make a net that's too simple, 00:48:02.910 --> 00:48:03.720 for instance. 00:48:03.720 --> 00:48:05.178 And you wouldn't want a net that is 00:48:05.178 --> 00:48:06.660 more complex than it has to be. 00:48:06.660 --> 00:48:10.840 So you can sort of see what the net's do at each level, 00:48:10.840 --> 00:48:13.140 and more visibly understand. 00:48:13.140 --> 00:48:15.970 I think a lot of people who drew problems like this just 00:48:15.970 --> 00:48:17.595 want to make sure people know, oh yeah, 00:48:17.595 --> 00:48:19.636 it's not just these numbers that we're mindlessly 00:48:19.636 --> 00:48:21.760 backpropagating from the other part of the problem 00:48:21.760 --> 00:48:23.720 to make them higher or lower. 00:48:23.720 --> 00:48:25.760 This is what we're doing at each level. 00:48:25.760 --> 00:48:29.280 This is the space that we're looking at. 00:48:29.280 --> 00:48:32.780 Each node is performing logic on the steps before. 00:48:32.780 --> 00:48:36.680 So that if you actually have to use a neural net later on, down 00:48:36.680 --> 00:48:41.409 the road, then you'll be able to figure out 00:48:41.409 --> 00:48:43.200 what your net's going to need to look like. 00:48:43.200 --> 00:48:45.530 You'll be able to figure out what it's doing. 00:48:45.530 --> 00:48:47.174 At least as well as you can figure out 00:48:47.174 --> 00:48:48.590 what it's doing, for a neural net, 00:48:48.590 --> 00:48:50.950 since it often will start getting up 00:48:50.950 --> 00:48:54.070 these really crazy numbers, will have all sorts of nodes in it, 00:48:54.070 --> 00:48:56.981 and like a real neural net that's being used nowadays, 00:48:56.981 --> 00:48:58.730 there'll be tons of nodes, and you'll just 00:48:58.730 --> 00:49:00.104 see the numbers fluctuate wildly, 00:49:00.104 --> 00:49:04.402 and then suddenly it's going to start working or not. 00:49:04.402 --> 00:49:05.360 That's a good question. 00:49:05.360 --> 00:49:06.193 Any other questions? 00:49:06.193 --> 00:49:08.220 We still have a few minutes. 00:49:08.220 --> 00:49:09.340 Not many, but a few. 00:49:09.340 --> 00:49:11.564 Any other questions about any of this stuff? 00:49:11.564 --> 00:49:12.064 Sorry. 00:49:12.064 --> 00:49:12.556 STUDENT: Talk about what you just asked. 00:49:12.556 --> 00:49:15.016 Just because we draw it, does the machine need to learn-- 00:49:20.929 --> 00:49:23.220 PROFESSOR: You're confused why the machine is run what, 00:49:23.220 --> 00:49:26.140 by the pictures on the right? 00:49:26.140 --> 00:49:27.137 Oh OK. 00:49:27.137 --> 00:49:29.720 Machine does not have to learn by drawing pictures and calling 00:49:29.720 --> 00:49:30.676 them in. 00:49:30.676 --> 00:49:32.300 Let me give you some real applications. 00:49:32.300 --> 00:49:35.110 My friend at the University of Maryland 00:49:35.110 --> 00:49:38.300 recently actually used neural nets 00:49:38.300 --> 00:49:41.640 because, yeah, he actually did, because of the fact that he 00:49:41.640 --> 00:49:45.410 was doing an game plan competition, where 00:49:45.410 --> 00:49:48.795 the game was not known when you were designing your AI. 00:49:48.795 --> 00:49:52.490 It had to be able to-- there was some very elegant, general game 00:49:52.490 --> 00:49:54.950 solver thing that you had be able to hook up into, 00:49:54.950 --> 00:49:58.140 and then they made up the rules, and you had a little bit 00:49:58.140 --> 00:49:59.570 of time, and then it started. 00:49:59.570 --> 00:50:03.320 Some of the AI's, what they did was, they trained, 00:50:03.320 --> 00:50:05.780 once they found out what the rules were on their own, 00:50:05.780 --> 00:50:08.450 with the rules, in his case he had a neural net, because it 00:50:08.450 --> 00:50:11.660 was so generic, you just have a web of random gook. 00:50:11.660 --> 00:50:13.970 He thought it could learn anything, 00:50:13.970 --> 00:50:16.910 and then-- he never did tell me how it went, probably 00:50:16.910 --> 00:50:18.090 didn't go well. 00:50:18.090 --> 00:50:20.700 But maybe it did. 00:50:20.700 --> 00:50:25.119 It basically tried to learn some things about the rules. 00:50:25.119 --> 00:50:26.660 Some of the other people who are more 00:50:26.660 --> 00:50:29.930 principled game players actually tried to find out 00:50:29.930 --> 00:50:32.950 fundamental properties of the space of the rules 00:50:32.950 --> 00:50:34.820 by testing a few different things, 00:50:34.820 --> 00:50:36.640 so they could view more knowledge 00:50:36.640 --> 00:50:39.110 is less search so they could do less search 00:50:39.110 --> 00:50:41.180 when the actual game playing came on. 00:50:41.180 --> 00:50:43.390 And then when the actual game playing came on, 00:50:43.390 --> 00:50:48.680 pretty much everyone did some kind of game tree based stuff. 00:50:48.680 --> 00:50:51.640 He's telling me that a lot of Monte Carlo 00:50:51.640 --> 00:50:55.340 based game tree stuff that is this very non deterministic 00:50:55.340 --> 00:50:57.349 as what they're doing nowadays, rather than 00:50:57.349 --> 00:50:59.140 what determines the alpha beta, although he 00:50:59.140 --> 00:51:02.380 said it converges to alpha beta, if you've given enough time. 00:51:02.380 --> 00:51:05.050 That's what he told me, But that someone I 00:51:05.050 --> 00:51:06.570 know who is using neural nets. 00:51:06.570 --> 00:51:08.800 I've also in a cognitive science class I took, 00:51:08.800 --> 00:51:11.720 saw neural nets that tried to attach like qualities 00:51:11.720 --> 00:51:15.620 to objects, by having just this huge, huge number of nodes 00:51:15.620 --> 00:51:18.160 in levels in between, and then eventually it was like, 00:51:18.160 --> 00:51:20.780 a duck flies, and you're like, how's it doing this again? 00:51:20.780 --> 00:51:22.640 I'm not sure, but it is. 00:51:22.640 --> 00:51:25.890 So the basic idea is that when-- one 00:51:25.890 --> 00:51:28.140 of the main reasons that neural nets were used so much 00:51:28.140 --> 00:51:31.340 back in the day is that people on many different sides 00:51:31.340 --> 00:51:33.450 of this problem, cognitive science, AI, 00:51:33.450 --> 00:51:35.620 whatever, were all saying, wait a minute, 00:51:35.620 --> 00:51:38.610 there's networks of neurons, and they can do stuff, 00:51:38.610 --> 00:51:40.360 and we're seeing it in different places. 00:51:40.360 --> 00:51:42.860 And when you've seen it in so many different places at once, 00:51:42.860 --> 00:51:44.490 must be a genius idea that's going 00:51:44.490 --> 00:51:46.140 to revolutionize everything. 00:51:46.140 --> 00:51:47.780 And so then everyone started using 00:51:47.780 --> 00:51:50.860 them to try to connect all these things together, which I think 00:51:50.860 --> 00:51:53.340 is a noble endeavor, but unfortunately people 00:51:53.340 --> 00:51:54.300 just stopped using it. 00:51:54.300 --> 00:51:56.180 It didn't work as they wanted. 00:51:56.180 --> 00:51:58.950 It turned out that figuring out our neurons worked in our head 00:51:58.950 --> 00:52:03.860 was not the way to solve all AI hard problems at once. 00:52:03.860 --> 00:52:06.360 And they fall into disfavor, although are still 00:52:06.360 --> 00:52:09.510 used for some reasons, like the sum is like that. 00:52:09.510 --> 00:52:11.610 So we wouldn't use it just to draw these pictures. 00:52:11.610 --> 00:52:13.492 The reason why we have these pictures 00:52:13.492 --> 00:52:15.950 is because we give you simple nets that you can work it out 00:52:15.950 --> 00:52:17.720 by hand on the quiz. 00:52:17.720 --> 00:52:20.340 Any net that is really used nowadays 00:52:20.340 --> 00:52:23.700 would make your head explode, if we 00:52:23.700 --> 00:52:26.140 tried to make you do something with it on the quiz. 00:52:26.140 --> 00:52:27.660 It would just be horrible. 00:52:27.660 --> 00:52:29.315 So I think that's a good question. 00:52:29.315 --> 00:52:31.440 If there's no other questions, or even if they are, 00:52:31.440 --> 00:52:34.390 because we have to head out, if there's any other questions, 00:52:34.390 --> 00:52:37.360 you can see me as I'm walking out.