1 00:00:01,720 --> 00:00:14,820 We're 50 samples, I will call it X, one equals minus pays from zero to two PI and then 50. 2 00:00:15,430 --> 00:00:17,760 Don't forget to put the semicolon here. 3 00:00:17,770 --> 00:00:30,550 Ricki's and for Y let's call it real live one equals two signers of X one semicolon and then plot X 4 00:00:30,550 --> 00:00:32,710 and Y, X and Y one. 5 00:00:34,860 --> 00:00:35,310 That's it. 6 00:00:36,600 --> 00:00:41,710 Now, we don't need this one, let's back to the waiting to hear. 7 00:00:42,390 --> 00:00:49,980 We can simply click back and then choose your samples again this time X one and why one? 8 00:00:51,570 --> 00:00:58,370 Click on Next the same, I'm just going to choose five layers like a previous one and click on train. 9 00:01:00,030 --> 00:01:04,340 So here it is, you can see some information to mean square error. 10 00:01:04,350 --> 00:01:06,750 And let me open this window. 11 00:01:06,750 --> 00:01:14,970 It's order this time the gradient stop of our training, which means the gradient just went to zero 12 00:01:14,970 --> 00:01:16,400 and then that was good enough. 13 00:01:16,400 --> 00:01:17,970 We just stopped the training. 14 00:01:18,510 --> 00:01:20,100 Let's check the performance. 15 00:01:20,370 --> 00:01:21,010 OK. 16 00:01:21,690 --> 00:01:23,160 Actually, this is very great. 17 00:01:23,160 --> 00:01:29,420 Now that we have more samples over network was able to train itself better. 18 00:01:29,430 --> 00:01:35,880 We see more examples, just like when you are teaching math, if you give your students more samples, 19 00:01:36,150 --> 00:01:41,880 then they will have a better understanding and the chance that they can pass the test or the quizzes 20 00:01:42,210 --> 00:01:42,810 is more. 21 00:01:43,020 --> 00:01:45,170 Now we can see the result. 22 00:01:45,180 --> 00:01:47,400 It's definitely a better training. 23 00:01:48,090 --> 00:01:50,820 And let's check the training state. 24 00:01:51,780 --> 00:01:59,970 Here is our gradient, which went to Z towards zero and we had the number of Époque actually. 25 00:01:59,970 --> 00:02:00,880 It's very interesting. 26 00:02:00,990 --> 00:02:05,640 Two hundred sixty four, it means two hundred sixty four times. 27 00:02:05,880 --> 00:02:13,000 The network train itself adjusts the weights until it finds the best result. 28 00:02:13,000 --> 00:02:14,940 Then it just stopped the training. 29 00:02:16,350 --> 00:02:18,570 Let's see the error histogram. 30 00:02:19,110 --> 00:02:19,920 Here it is. 31 00:02:20,190 --> 00:02:29,510 It's all around zero except these two, the rest are just around zero and that's a very good error histogram. 32 00:02:30,240 --> 00:02:32,060 Next one is our regression. 33 00:02:32,100 --> 00:02:33,060 Let's check it here. 34 00:02:33,810 --> 00:02:36,570 Just compare it to the previous one with twenty samples. 35 00:02:36,570 --> 00:02:39,630 We can obviously see the improvement even for testing. 36 00:02:39,870 --> 00:02:44,970 It's just closer to our goal, which is one Y equal to T. 37 00:02:45,570 --> 00:02:46,200 That's good. 38 00:02:46,530 --> 00:02:49,300 And finally, let's see, how was Overfitting? 39 00:02:49,710 --> 00:02:50,470 Very well. 40 00:02:50,470 --> 00:02:53,310 Defeating is just like a sinus wave. 41 00:02:53,640 --> 00:02:59,610 This is what we expected from our neural network to give us a sinus wave. 42 00:02:59,610 --> 00:03:00,420 And that's it. 43 00:03:00,420 --> 00:03:06,300 We can see already the sinus way you train of our network with five measuring, this time with fifty 44 00:03:06,300 --> 00:03:07,050 samples. 45 00:03:07,380 --> 00:03:11,910 And as the result, we can see a better result than we can see a better training. 46 00:03:12,060 --> 00:03:13,950 And here are other errors. 47 00:03:14,370 --> 00:03:19,440 You can analyze it later if you need, but that's a very good outfit. 48 00:03:20,340 --> 00:03:27,300 The other thing is, let's see what will happen if we give it more data, more samples like what will 49 00:03:27,300 --> 00:03:29,310 happen if we have 1000 samples. 50 00:03:29,760 --> 00:03:35,370 If you click on next here, you can choose different inputs and targets. 51 00:03:35,640 --> 00:03:38,400 Let me go back to the command window. 52 00:03:38,400 --> 00:03:40,830 So I'm going to define different samples. 53 00:03:40,830 --> 00:03:41,550 This time. 54 00:03:43,080 --> 00:03:52,500 X two equals two space from zero to two PI just same with previous one. 55 00:03:53,400 --> 00:03:59,070 And let's go for one thousand data and see what will happen with one thousand samples. 56 00:03:59,070 --> 00:04:02,640 And one two would be equal to sign this of course. 57 00:04:02,640 --> 00:04:03,240 X to. 58 00:04:04,870 --> 00:04:11,320 Plots and let's see the result, plot X to Y to. 59 00:04:15,450 --> 00:04:24,060 Just go back to normal fitting to this time, choose X one, y two here, you can also see some information, 60 00:04:24,060 --> 00:04:26,400 like one thousand samples of one element. 61 00:04:26,400 --> 00:04:29,640 And here we have 1000 samples of one element, four y two. 62 00:04:29,850 --> 00:04:32,760 Now I'm going to click and test network. 63 00:04:33,420 --> 00:04:36,780 Here is my mistake or in the regression. 64 00:04:36,790 --> 00:04:38,180 You can also see the plot. 65 00:04:38,450 --> 00:04:40,950 Let's see if we can have some improvement. 66 00:04:41,460 --> 00:04:45,000 However, the previous 450 sample, that was enough already. 67 00:04:45,270 --> 00:04:50,010 We saw the sine wave, which we were expecting from all of our network. 68 00:04:50,310 --> 00:04:51,990 Here it is in a separate window. 69 00:04:52,350 --> 00:04:55,560 OK, that's that's also a better fit. 70 00:04:55,920 --> 00:05:01,710 The reason that you can see it like a tick line is because you have 1000 samples. 71 00:05:01,710 --> 00:05:05,760 So fitting all of them just gave us this result. 72 00:05:06,030 --> 00:05:13,320 We can see some error histogram that's around zero and that's a very better training. 73 00:05:14,610 --> 00:05:18,120 And for the past regression, it's almost actually one. 74 00:05:18,790 --> 00:05:25,970 Now, the next team that we are going to learn is the effect of different layers on our network. 75 00:05:26,250 --> 00:05:34,200 Let's see how the behavior off of our neural network will change if we set the different number of neurons 76 00:05:34,200 --> 00:05:35,100 like one neuron. 77 00:05:35,100 --> 00:05:40,860 If you tried with one neuron to number one five neuron and finally one hundred neurons, let's see what 78 00:05:40,860 --> 00:05:41,370 will happen.