WEBVTT 00:00.840 --> 00:03.270 -: Hello and welcome back to the course on Deep Learning. 00:03.270 --> 00:05.430 Now that we've seen neural networks in action 00:05.430 --> 00:08.430 it's time for us to find out how they learn. 00:08.430 --> 00:10.470 So let's dive straight into it. 00:10.470 --> 00:13.800 There are two fundamentally different approaches 00:13.800 --> 00:16.230 to getting a program to do what you want it to do. 00:16.230 --> 00:19.920 One is hard coded coding where you actually 00:19.920 --> 00:24.920 tell the program specific rules and what outcomes you want 00:25.886 --> 00:28.592 and you just guide it throughout the whole way 00:28.592 --> 00:30.510 and you account for all the possible options 00:30.510 --> 00:33.300 that the program has to deal with. 00:33.300 --> 00:34.133 On the other hand 00:34.133 --> 00:38.020 you have neural networks where you create a facility 00:39.450 --> 00:43.170 for the program to be able to understand what it needs to do 00:43.170 --> 00:44.608 on its own. 00:44.608 --> 00:46.590 So you basically create this neural network where 00:46.590 --> 00:48.510 you provided inputs, 00:48.510 --> 00:50.100 you tell it what you want as outputs 00:50.100 --> 00:53.400 and then you let it figure everything out on its own. 00:53.400 --> 00:55.600 Two fundamentally different approaches 00:57.399 --> 00:58.770 and that is something to keep 00:58.770 --> 01:00.840 in mind as we go through these tutorials. 01:00.840 --> 01:04.200 Our goal is to create this network 01:04.200 --> 01:06.000 which then learns on its own. 01:06.000 --> 01:11.000 We, we are going to avoid trying to put in the rules. 01:11.010 --> 01:14.490 And a good example that I can give you right now is.... 01:14.490 --> 01:15.750 this will come further in the course 01:15.750 --> 01:18.120 but it's just a very visual example. 01:18.120 --> 01:20.340 For instance, how do you distinguish 01:20.340 --> 01:21.780 between a dog and a cat? 01:21.780 --> 01:25.260 For on the left side on the approach that's depicted 01:25.260 --> 01:28.590 on the left, you would program things in like the 01:28.590 --> 01:30.570 the cat's ears have to be like this, 01:30.570 --> 01:32.640 Look out for whiskers 01:32.640 --> 01:34.170 look out for this type of nose 01:34.170 --> 01:37.800 look out for this type of shape of face. 01:37.800 --> 01:38.880 Look out for these colors. 01:38.880 --> 01:40.650 You kind of, you'd describe all these things 01:40.650 --> 01:41.670 and you'd have conditions like 01:41.670 --> 01:44.670 if the ears are pointy, then cats 01:44.670 --> 01:49.560 if the ears are slopping down, then possibly dog and so on. 01:49.560 --> 01:50.940 On the other hand, for a neural network, 01:50.940 --> 01:53.100 you just code the neural network. 01:53.100 --> 01:54.730 So you code the architecture 01:55.610 --> 01:58.170 and then you point the neural network at a folder 01:58.170 --> 01:59.760 with all these cats and dogs 01:59.760 --> 02:02.670 with images of cats and dogs which are already categorized. 02:02.670 --> 02:04.244 And you tell it, 02:04.244 --> 02:06.870 okay I've got some images of cats and dogs. 02:06.870 --> 02:08.880 Go and learn what a cat is. 02:08.880 --> 02:10.560 Go and learn what a dog is 02:10.560 --> 02:11.850 and the neural network will 02:11.850 --> 02:15.270 on its own understand everything it needs to understand. 02:15.270 --> 02:17.520 And then further down, once it's trained up, 02:17.520 --> 02:19.860 when you give it a new image of a cat or a dog, 02:19.860 --> 02:21.600 it'll be able to understand what it was. 02:21.600 --> 02:23.160 So there they are, 02:23.160 --> 02:25.650 those are the two fundamentally different approaches 02:25.650 --> 02:28.090 and today we're going to slowly start getting 02:29.154 --> 02:30.993 into how that second approach works. 02:31.993 --> 02:33.360 All right, so let's get straight to it. 02:33.360 --> 02:37.200 Here we have a very basic neural network with a one layer. 02:37.200 --> 02:41.208 This is called a single layer feed forward neural network 02:41.208 --> 02:42.750 and it is also called a perceptron. 02:42.750 --> 02:44.033 Now, before we proceed, one thing that we do need to 02:44.033 --> 02:47.370 adjust is that output value. 02:47.370 --> 02:48.480 Right now you can see that 02:48.480 --> 02:49.840 it's just a Y we need to 02:51.085 --> 02:51.918 put a Y hat in there. 02:51.918 --> 02:52.751 And the reason for that is 02:52.751 --> 02:55.470 usually Y stands for the actual value. 02:55.470 --> 02:56.490 And that's what we're going to be using. 02:56.490 --> 02:58.593 So Y is gonna be the actual value, 02:59.984 --> 03:01.184 which we see in reality, 03:02.043 --> 03:03.720 output value is the predicted value 03:03.720 --> 03:05.880 by the algorithm by the neural network. 03:05.880 --> 03:09.240 Y hat is the output value. 03:09.240 --> 03:11.990 Basically that's the denomination for the output value. 03:13.735 --> 03:15.330 And the perceptron was first invented in 1957 03:15.330 --> 03:17.430 by Frank Rosenblatt 03:17.430 --> 03:19.560 and his whole idea was to 03:19.560 --> 03:24.560 create something that can actually learn and adjust itself. 03:25.200 --> 03:27.933 And this is what we're going to be looking at now. 03:29.599 --> 03:30.432 So we've got our perceptron. 03:30.432 --> 03:32.040 let's see how our perceptron learns. 03:32.040 --> 03:34.980 So let's say we have some input values 03:34.980 --> 03:37.030 that have been supplied to the perceptron 03:39.101 --> 03:40.703 and or basically to our neural network. 03:42.286 --> 03:44.220 Then the activation functions applied, 03:44.220 --> 03:45.220 we have an output 03:46.409 --> 03:50.020 and now we're going to plot the output on a chart. 03:50.020 --> 03:51.780 So there it is our output Y hat. 03:51.780 --> 03:54.960 Now what we need to do is in order to be able to learn 03:54.960 --> 03:56.880 we need to compare the output value 03:56.880 --> 03:58.000 to the actual value 03:59.167 --> 04:01.560 that we want the neural network to get, right? 04:01.560 --> 04:04.330 And that is the value Y 04:05.666 --> 04:06.499 And so if we plot it here 04:06.499 --> 04:08.210 you'll see that there's a bit of a difference. 04:09.523 --> 04:10.356 Now we are going to calculate a function 04:10.356 --> 04:11.340 called the cost function 04:11.340 --> 04:13.530 is calculated as one half 04:13.530 --> 04:14.730 of the square difference 04:15.963 --> 04:17.483 between the actual value and output value. 04:19.148 --> 04:20.520 Now there are many ways you can come up with cost function. 04:20.520 --> 04:23.220 There are many different cost functions that you can use. 04:23.220 --> 04:25.870 This is probably the most commonly used cost function 04:27.940 --> 04:30.570 and why it is specifically this function we use 04:30.570 --> 04:33.534 We'll find out further down when we're talking 04:33.534 --> 04:36.010 about gradient descent, but for now 04:36.010 --> 04:37.740 we're just going to agree that this is the cost function. 04:37.740 --> 04:40.530 And basically what the cost function is telling us is, 04:40.530 --> 04:44.163 what is the error that you have in your prediction? 04:45.727 --> 04:47.670 And our goal is to minimize the cost function 04:49.175 --> 04:50.093 because the the lower the cost function, 04:50.942 --> 04:53.325 the closer the Y hat is to Y. Okay? 04:53.325 --> 04:55.725 So as long as we agree on that, let's proceed. 04:55.725 --> 04:57.240 So basically from here what happens is 04:57.240 --> 04:59.228 there's our cost function. 04:59.228 --> 05:01.830 And from here what happens is now we are going to, 05:01.830 --> 05:03.120 once we've compared, 05:03.120 --> 05:05.730 now we're going to feed this information 05:05.730 --> 05:08.970 back into the neural network. 05:08.970 --> 05:09.803 So there we go. 05:09.803 --> 05:12.730 There's the information going back into the neural network 05:13.993 --> 05:16.449 and it goes to the weights and the weights get updated. 05:16.449 --> 05:18.844 Basically, the only thing that we have control of 05:18.844 --> 05:20.190 in this very simple neural network 05:20.190 --> 05:21.023 are the weights, 05:21.023 --> 05:22.268 W one 05:22.268 --> 05:23.101 W two, 05:23.101 --> 05:23.934 all the way to WM 05:25.406 --> 05:26.760 And our goal is to minimize the cost function. 05:26.760 --> 05:29.460 So all we can do is update the weight. 05:29.460 --> 05:30.813 So we update the weights, 05:32.220 --> 05:33.550 tweak them a little bit 05:35.213 --> 05:36.995 and how exactly we'll find out further down. 05:36.995 --> 05:39.863 But for now, we, we agree that we update the weights 05:39.863 --> 05:40.696 and then we continue. 05:40.696 --> 05:44.820 So, but here I've put up this screenshot of the data 05:44.820 --> 05:48.594 just to make one point very clear that right now 05:48.594 --> 05:50.460 throughout this whole experiment, 05:50.460 --> 05:51.990 everything we're doing right now, 05:51.990 --> 05:54.000 we're dealing with just the one row. 05:54.000 --> 05:55.170 So we're dealing with, 05:55.170 --> 05:57.150 we have a data set of one row 05:57.150 --> 05:58.980 where we have, for instance 05:58.980 --> 06:02.010 we're dealing with how long you study 06:02.010 --> 06:04.950 like the variable that we're predicting is 06:04.950 --> 06:08.400 what results you're gonna get on an exam. 06:08.400 --> 06:10.770 And the independent variables that we have is, 06:10.770 --> 06:12.720 how many hours did you study for? 06:12.720 --> 06:14.170 How many hours did you sleep? 06:15.550 --> 06:18.095 and what did you get on the quiz in the mid-semester? 06:18.095 --> 06:19.876 So in the middle of the semester, there's a quiz 06:19.876 --> 06:20.950 what percentage did you get there? 06:20.950 --> 06:22.202 So based on those variables 06:22.202 --> 06:24.690 we're trying to predict what score you'll get for the exam. 06:24.690 --> 06:28.020 And in exam, the 93%, that's the actual value. 06:28.020 --> 06:28.953 So that's Y. 06:30.690 --> 06:32.280 So we feed these three values 06:32.280 --> 06:34.080 into our neural network again 06:34.080 --> 06:35.320 for the second time now 06:37.010 --> 06:39.120 and then going to be comparing the result to Y. 06:39.120 --> 06:40.770 So let's see how this works. 06:40.770 --> 06:43.800 We feed these values into the neural network 06:43.800 --> 06:46.740 everything gets adjusted and weights get adjusted. 06:46.740 --> 06:49.873 So as you can see, let's do this again. 06:49.873 --> 06:51.372 We're going to feed the values again. 06:51.372 --> 06:53.220 The point here is that we're feeding in these same values. 06:53.220 --> 06:54.510 So we only have one row 06:54.510 --> 06:56.370 We're trying to, we're training on one row 06:56.370 --> 06:59.610 This is because this is just a very simple basic example. 06:59.610 --> 07:01.770 Then we'll see what happens when there's more rows. 07:01.770 --> 07:03.460 So again, we feed these rows in 07:05.152 --> 07:06.995 our cost functions get adjusted. 07:06.995 --> 07:10.530 As you can see, everything happens along those lines again. 07:10.530 --> 07:13.710 So as you can see, every time our Y hat is changing 07:13.710 --> 07:15.030 because we've tweaked the weights, 07:15.030 --> 07:16.470 our Y hat is changing 07:16.470 --> 07:17.580 our cost function's changing 07:17.580 --> 07:18.780 let's have a look again. 07:19.656 --> 07:20.490 So we feed those in. 07:20.490 --> 07:21.480 Y hat is changing 07:21.480 --> 07:22.890 cost function is changing. 07:22.890 --> 07:24.060 We get information back, 07:24.060 --> 07:25.410 feed back to the weights 07:25.410 --> 07:27.060 so that the weights get adjusted again. 07:27.060 --> 07:29.760 We feed in the same values every time. 07:29.760 --> 07:30.960 Everything gets adjusted, 07:30.960 --> 07:31.860 goes back to the weights 07:31.860 --> 07:33.661 and one more time, 07:33.661 --> 07:34.494 we feed in. 07:34.494 --> 07:35.700 Okay? 07:35.700 --> 07:36.690 And another time. 07:36.690 --> 07:38.520 So we've adjusted the weights 07:38.520 --> 07:39.820 we feed in the information 07:40.800 --> 07:42.125 and there we go. 07:42.125 --> 07:44.430 So now this time the Y hat is equal 07:44.430 --> 07:45.990 to Y cost functional zero. 07:45.990 --> 07:48.450 Usually you won't get cost function equal to zero. 07:48.450 --> 07:50.223 But this is a very simple example. 07:51.533 --> 07:52.830 So hopefully all that made sense. 07:52.830 --> 07:56.250 Every time we feed in exactly that same row 07:56.250 --> 07:58.170 because just in this case we're just dealing 07:58.170 --> 07:59.790 with that one row, 07:59.790 --> 08:01.360 into our neural network 08:03.497 --> 08:05.610 where then the values get supplied by the weights, 08:05.610 --> 08:06.990 the activation functions applied. 08:06.990 --> 08:08.130 We get Y hat 08:08.130 --> 08:10.290 Y hat is compared to Y. 08:10.290 --> 08:12.360 Then we see how the cost function has changed. 08:12.360 --> 08:13.860 Feed back that information back 08:13.860 --> 08:14.910 into the neural network 08:14.910 --> 08:17.850 and adjust the weights again. 08:17.850 --> 08:19.560 And then we repeat the same process again 08:19.560 --> 08:21.600 with the same exact row. 08:21.600 --> 08:23.783 We're trying to minimize that cost function. 08:24.650 --> 08:27.000 So up until now we've been dealing with just that one row. 08:27.000 --> 08:29.460 Let's see what happens when you have multiple rows. 08:29.460 --> 08:31.350 So here's the full data set. 08:31.350 --> 08:33.810 We have eight rows of 08:33.810 --> 08:35.340 how many hours you slept? 08:35.340 --> 08:37.630 or maybe these are different students 08:38.470 --> 08:40.218 in taking the same exam, 08:40.218 --> 08:41.280 how many others hours they studied? 08:41.280 --> 08:44.191 how many hours they slept before the exam? 08:44.191 --> 08:47.313 what to get on the quiz and their final result on the test. 08:48.336 --> 08:50.333 And as you can see here on the left 08:50.333 --> 08:51.900 I've got eight of these perceptrons. 08:51.900 --> 08:54.750 Actually they are all the same perceptron. 08:54.750 --> 08:57.478 So this is also important to understand. 08:57.478 --> 08:59.140 I just multiplied it 08:59.140 --> 09:00.240 or like duplicated eight times just 09:00.240 --> 09:01.330 so that we can 09:03.360 --> 09:04.320 conceptually understand. 09:04.320 --> 09:05.430 But the important thing here, 09:05.430 --> 09:06.933 it's the same neural network. 09:08.417 --> 09:09.300 We're going to be feeding these 09:10.414 --> 09:11.257 into one same neural network. 09:11.257 --> 09:12.090 So let's go. 09:12.090 --> 09:12.923 Let's get started. 09:12.923 --> 09:14.880 So one epoch 09:14.880 --> 09:17.250 as you'll hear (indistinct) mentioning, 09:17.250 --> 09:19.290 one epoch is when we go 09:19.290 --> 09:20.610 through a whole data set 09:20.610 --> 09:25.610 and we train our neural network on all of these rows 09:26.310 --> 09:28.415 So let's go, let's get started. 09:28.415 --> 09:30.226 So there's our first row 09:30.226 --> 09:32.550 and there's Y hat for the first row. 09:32.550 --> 09:33.720 There's the second row 09:33.720 --> 09:36.088 there's Y hat for the second row. 09:36.088 --> 09:36.921 So again, it's being fed 09:36.921 --> 09:39.360 into the same neural network every time. 09:39.360 --> 09:41.220 I've just copied them several times 09:41.220 --> 09:44.043 so we can visually see how this is happening. 09:45.906 --> 09:47.880 Then again, it's happening again. 09:47.880 --> 09:50.670 That's third row, fourth row 09:50.670 --> 09:53.040 there's our Y hat for the fourth row and so on. 09:53.040 --> 09:55.110 Basically then we get the same values 09:55.110 --> 09:56.610 for the remaining four rows as well. 09:56.610 --> 09:57.960 So every time we just feed 09:57.960 --> 10:01.528 in a row into our neural network, 10:01.528 --> 10:02.673 we get a value. 10:04.502 --> 10:06.990 Then we compare to the actual values. 10:06.990 --> 10:08.540 So there are the actual values. 10:09.487 --> 10:11.813 So for every single row we have an actual value. 10:12.816 --> 10:14.730 And now based on all of these differences 10:14.730 --> 10:16.200 between Y hat and Y 10:16.200 --> 10:18.300 we can calculate the cost function 10:18.300 --> 10:23.300 which is the sum of all of those squared differences 10:24.210 --> 10:25.510 between Y hat and Y 10:26.460 --> 10:28.200 and all of that is halved. 10:28.200 --> 10:30.330 And there's our cost function. 10:30.330 --> 10:31.680 And basically now what we do 10:31.680 --> 10:34.320 after we have the full cost function 10:34.320 --> 10:36.963 we go back and we update the weights. 10:38.011 --> 10:39.510 We update W one, W two, W three. 10:39.510 --> 10:41.857 And the important thing to remember here is 10:41.857 --> 10:44.790 that all of these perceptrons, 10:44.790 --> 10:45.810 all of these neural networks 10:45.810 --> 10:48.223 is actually one neural network. 10:48.223 --> 10:49.793 So there's not eight of them, there's just one. 10:50.899 --> 10:51.732 And when we update the weights, 10:51.732 --> 10:53.220 we're going to update the weights 10:53.220 --> 10:54.480 in that one neural network. 10:54.480 --> 10:56.370 So basically the weights are gonna be the same 10:56.370 --> 10:57.723 for all of the rows. 10:59.184 --> 11:00.510 So it's not the case that every row has its own weights. 11:00.510 --> 11:02.880 Now all the rows share the weights. 11:02.880 --> 11:06.360 And so that's why we looked at the cost function 11:06.360 --> 11:10.203 which is the sum of the square differences. 11:11.368 --> 11:12.201 And then we updated the weights. 11:12.201 --> 11:15.300 And now from here, that was just one iteration. 11:15.300 --> 11:19.020 Next, we're going to run this whole thing again. 11:19.020 --> 11:22.320 We're going to feed every single row 11:22.320 --> 11:23.730 into the neural network, 11:23.730 --> 11:25.050 find out our cost function 11:25.050 --> 11:26.400 and do this whole process again. 11:26.400 --> 11:28.270 So just as we saw previously 11:29.394 --> 11:30.630 where we had just one row 11:30.630 --> 11:31.500 and we were doing everything 11:31.500 --> 11:32.880 again and again, again, again 11:32.880 --> 11:33.713 same thing here. 11:33.713 --> 11:35.534 But now we're gonna be doing it for 11:35.534 --> 11:37.620 eight rows or 800 rows or 8,000 rows, 11:37.620 --> 11:40.800 however many rows you have in your data set. 11:40.800 --> 11:41.940 You do this process 11:41.940 --> 11:44.190 and then you calculate the cost function. 11:44.190 --> 11:48.420 And the goal here is to minimize the cost function 11:48.420 --> 11:49.980 and to get, 11:49.980 --> 11:52.050 as soon as you found the minimum of the cost function, 11:52.050 --> 11:54.360 that is your final neural network. 11:54.360 --> 11:56.470 That means your weights have been adjusted 11:57.740 --> 12:02.483 and you have found the optimal weights 12:03.330 --> 12:07.200 for this data set that you're training on a 12:07.200 --> 12:09.102 and you're ready to proceed 12:09.102 --> 12:11.550 to the testing phase or to the application phase. 12:11.550 --> 12:14.970 And this whole process is called backpropagation. 12:14.970 --> 12:18.550 So some additional reading that you might want to do 12:20.450 --> 12:21.559 for the cost function, 12:21.559 --> 12:23.220 and I know we we just talked about one 12:24.100 --> 12:24.933 and they are many different ones. 12:24.933 --> 12:28.650 A good article is located on Cross Validated. 12:28.650 --> 12:29.483 It's called, 12:29.483 --> 12:31.500 A list of cost functions used in neural networks 12:31.500 --> 12:32.883 alongside applications. 12:33.914 --> 12:34.823 So the URL's there, 12:35.708 --> 12:38.100 but you can just Google for that exact search term 12:38.100 --> 12:39.100 or search phrase 12:40.951 --> 12:42.120 and you'll that this one will be the first one that pops up. 12:42.120 --> 12:44.110 It's actually got some good examples 12:45.096 --> 12:48.420 and application or use cases for different cost functions. 12:48.420 --> 12:50.310 So if you're interested to learn more about cost functions 12:50.310 --> 12:51.603 check out this article. 12:52.917 --> 12:54.390 And on that note, I hope you enjoy today's tutorial. 12:54.390 --> 12:56.040 I look forward to seeing you next time. 12:56.040 --> 12:58.203 Until then, enjoy Deep Learning.