WEBVTT 00:00.760 --> 00:07.540 High in this session, we will discuss about neural networks, so let us, first of all, see what is 00:07.540 --> 00:14.800 neural network now, neural network is a technique for building a computer program that learns from 00:14.800 --> 00:15.370 the data. 00:15.970 --> 00:19.190 Well, this is exactly what machine learning is also doing. 00:19.210 --> 00:21.610 So what is different here in this? 00:21.790 --> 00:28.510 It is based on very loosely on how we think the human brain works. 00:28.810 --> 00:34.090 So just how the human brain works in the same way neural networks also work. 00:36.060 --> 00:43.710 In our brain, there are several neurons which are connected with each other and the first message from 00:43.710 --> 00:51.630 one to another, which are decrypted by these neurons, and then we are to think or feel something. 00:52.180 --> 00:55.620 Now, how is it related to neural networks? 00:55.860 --> 01:03.600 That is in neural networks, a collection of software neurons are created and connected together, which 01:03.600 --> 01:06.510 allow them to actually send a message to each other. 01:06.960 --> 01:10.290 Now the network is asked to solve this particular problem. 01:10.290 --> 01:15.780 So we will provide a particular problem to the network and the network will try to solve the problem 01:15.990 --> 01:19.470 and it will try to solve it again and again, again and again. 01:19.710 --> 01:26.760 Then that time it actually will affect the learning process, feel that it is actually able to perform 01:26.760 --> 01:28.100 that particular calculation. 01:28.110 --> 01:30.510 It will keep on doing it again and again. 01:31.530 --> 01:39.510 So every vibration when it is doing this or learning or sending the message again and again, it actually 01:40.590 --> 01:47.820 keeps connecting the dots and actually keeps learning from the data and improves the predictions which 01:47.820 --> 01:57.810 it is making so that it actually needs to success and diminishes the particular patterns which it has 01:57.810 --> 02:01.610 learned to reduce failure cases. 02:02.370 --> 02:04.770 So this is what neural networks are doing. 02:05.130 --> 02:10.750 So how are we actually creating this and what does this actually mean? 02:11.040 --> 02:14.680 So let us have a concentration on this particular image here. 02:15.120 --> 02:18.860 So here we have a lot of circles connected. 02:20.290 --> 02:28.420 Now, these are the inputs, not the ones in the Greens, the blue nodes or other connections which 02:28.420 --> 02:33.240 we know connected to and let us see the red is the decision point. 02:33.790 --> 02:41.500 So here all we want to do is we want to send our input values that is different X values or the features 02:41.500 --> 02:45.970 or attributes from this particular input nodes. 02:47.140 --> 02:53.170 And these green neurons will pass on the information to the blue note. 02:53.980 --> 03:01.930 Now these blue laws will actually try to decrypt these patterns between these green notes and say now 03:01.930 --> 03:10.060 they're listening to the red node, which will finally decide what the output should be, if the value 03:10.060 --> 03:10.720 should be. 03:10.840 --> 03:16.990 Let us see if we are looking out for continuous value, then what value should be predicted, what price 03:16.990 --> 03:18.030 should we predicted? 03:18.250 --> 03:22.450 And in case we are looking for a class, then if it should be yes or no. 03:22.480 --> 03:27.280 So these kind of decisions can be made using this kind of a structure. 03:28.840 --> 03:36.580 Now, it might look tricky on how this will actually be of the information, but this is a very simplistic 03:36.580 --> 03:38.050 neural network example. 03:38.410 --> 03:45.460 Here we have only one little prison and there is another neural network, which is even more simpler 03:45.460 --> 03:48.190 than this, which we are looking at right now. 03:48.820 --> 03:50.410 What is that neural net? 03:50.470 --> 03:53.260 Well, you remember logistic regression. 03:53.530 --> 04:00.580 Our very own logistic regression is the very smallest example of a neural network. 04:02.450 --> 04:10.070 How that is possible, we will have a look at it in a while, but let us try to connect the dots and 04:10.070 --> 04:11.360 create a picture. 04:12.950 --> 04:18.770 So if we look at this particular image, you can see there are several input values. 04:20.130 --> 04:26.180 And these input values will be giving a certain probability to us. 04:27.640 --> 04:34.400 And how are we getting this probability this is a simple logistic regression in logistic regression. 04:34.420 --> 04:36.950 What do we do in logistic regression? 04:36.970 --> 04:45.790 We have several input values and we apply a sigmoid function on top of it that we can avoid this particular 04:45.790 --> 04:49.120 of the input values into our equation. 04:50.310 --> 04:57.780 What will the equation be, the equation will be the one next one, plus we do X to plus B that three 04:57.990 --> 05:00.830 three plus B for export and so on. 05:01.680 --> 05:07.570 Right then we apply the sigmoid function, Lonard or the logit function on it. 05:08.010 --> 05:09.780 What is the logistic function? 05:09.780 --> 05:18.660 The logistic function is one upon one plus E to the power minus the equation which we just formally. 05:20.060 --> 05:24.380 That is logit function, so that is how this. 05:25.900 --> 05:32.650 Swan also will result in the probability to us this is how the logistic regression look. 05:33.190 --> 05:34.990 Now let us have a look at it for the. 05:36.800 --> 05:43.200 Now, the neural network is an algorithm inspired by the neurons in our brain. 05:44.180 --> 05:54.170 It is designed to recognize patterns in complex data and often performs the best when recognizing patterns 05:54.170 --> 05:56.810 in audio images and videos. 05:57.560 --> 06:04.550 Now, neural networks are not something which we will go towards at the very beginning or when we are 06:04.550 --> 06:06.770 striving to solve a particular problem. 06:08.470 --> 06:16.840 Whenever we are starting to solve a particular problem in that situation, we will first of all implement 06:16.840 --> 06:24.160 the Lenie models, then we will implement the decision tree and after that we will decide if we want 06:24.160 --> 06:27.310 to go towards bigging or boosting. 06:28.400 --> 06:37.640 In case we have less amount of data, then these algorithms, which we have learned earlier, like SBM, 06:37.970 --> 06:45.560 Ganon, Nijhuis, a random forest she used, all these algorithms will be more favorable. 06:47.050 --> 06:57.730 But in case they are trying to have more precision or a better model, then in that case we will be 06:57.730 --> 06:59.750 going towards neural networks. 07:00.670 --> 07:03.500 But why are going towards neural networks? 07:03.760 --> 07:08.200 The main challenge we face is the lack of data. 07:09.550 --> 07:18.910 Because neural networks required a lot of data to brain, that is the reason why we cannot implement 07:18.910 --> 07:26.020 neural networks for all types of problems, because we need a lot of data to get a good output from 07:26.020 --> 07:27.210 the neural networks. 07:28.300 --> 07:39.520 Hence, it is used immediately for problems like audio or video data where we can have exhaustive amount 07:39.520 --> 07:43.320 of examples and then we will apply neural networks on them. 07:45.520 --> 07:55.930 Now, neural networks simply consist of neurons, which are also called as nodes, so here these small 07:55.930 --> 08:00.910 blocks, these small soakers, these are called nodes. 08:03.280 --> 08:08.190 Each neuron holds a number and each connection holds big. 08:09.050 --> 08:15.250 So each and every node will hold some information in it. 08:16.080 --> 08:22.470 It will hold some information in there and each connecting line will actually hold a vote on. 08:23.800 --> 08:25.750 So what does this week? 08:27.300 --> 08:34.020 What is the weight, these weights are nothing but the be the values which we have been talking about 08:34.020 --> 08:35.680 in logistic regression. 08:36.000 --> 08:42.180 So in case of logistic regression, we had better values with which we multiply these input values. 08:42.180 --> 08:42.430 Right. 08:42.960 --> 08:48.710 The V created the equation using using the beta values. 08:49.050 --> 08:50.250 So be not. 08:51.170 --> 09:01.340 Plus one x one plus VW x2 plus bigotry to extreme plus veto voting to X four plus veto firing the ex-wife. 09:01.490 --> 09:06.130 So here's the different veto values that we have are the rates only. 09:06.350 --> 09:09.230 So in case of neural networks, we will be calling them. 09:10.040 --> 09:15.460 So this is how it will look like each node will hold certain. 09:16.910 --> 09:25.450 Value on it, certainly dynamic, and each connecting line will actually hold some great value. 09:28.440 --> 09:35.820 Then they have activation functions which are usually non-linear, transforming functions which transform 09:35.820 --> 09:42.930 linear functions into a nonlinear form which is capable of capturing complex patterns now. 09:44.360 --> 09:52.220 Here we have the input data points that does X one, two, three and so on, here we have different 09:52.220 --> 09:56.670 values which are similar to the values which we had in the logistic regression. 09:57.140 --> 10:03.570 Then we have the net input function, which will basically, although some all of these things. 10:03.800 --> 10:06.650 So at this point, what will we have at this point? 10:06.660 --> 10:19.130 The equation will be w more or less because of the assumption W one X one plus W2 x2 plus W three extra 10:19.970 --> 10:21.160 W maksym. 10:21.950 --> 10:22.260 Right. 10:22.580 --> 10:23.870 This is what we will have. 10:24.260 --> 10:28.220 Then we have this activation function, which is nothing but. 10:29.540 --> 10:37.280 The logistic function or the logic, logic function or the sigmoid function, which we have been discussing 10:37.280 --> 10:42.560 about the equation, which was one upon one minus E to the power. 10:43.860 --> 10:51.360 B, where the B is the combination of this particular equation, a combination of these, so that this 10:51.570 --> 10:59.970 activation function now it's strictly says that the activation functions are usually nonlinear, transforming 10:59.970 --> 11:00.460 functions. 11:00.690 --> 11:09.050 So that means that this activation function could be any other function except other than the logic 11:09.060 --> 11:09.850 function also. 11:10.050 --> 11:14.040 But how will we decide what the value of the activation function should be? 11:15.600 --> 11:25.260 So consider this first thing is if we are applying this logistic function or the logic function or the 11:25.260 --> 11:27.090 sigmoid function, which we call it. 11:27.420 --> 11:31.320 So in that case, what does logistic regression give us? 11:32.690 --> 11:40.280 Because we are seeing this neural network, the very basic neural network, resembles the logistic regression. 11:40.490 --> 11:47.180 So and here we can clearly see that the equation which we are forming is similar to the logistic regression. 11:47.660 --> 11:53.450 So what does the output of the logistic regression, the output of the logistic regression is a probability. 11:55.590 --> 11:58.500 Which is usually ranging from zero to one. 11:59.920 --> 12:09.010 This means that in case we want to get probability as an output or we want to solve a classification 12:09.010 --> 12:16.080 problem, in that case, we can use this logic function based on the sigmoid function. 12:16.720 --> 12:23.740 But in case we want to find out the continuous value, then we should not use this function because 12:23.740 --> 12:26.450 this will convert the range of the data. 12:27.280 --> 12:33.520 You remember during discussion of the linear and logistic regression, we said that the equation of 12:33.520 --> 12:43.360 the line, the equation is converted to logistic equation into a global equation because of this activation 12:43.360 --> 12:43.810 function. 12:43.810 --> 12:50.680 Only if you want, you can go back to the theory of logistic regression, have a look at it and come 12:50.680 --> 12:52.170 back and see that. 12:52.330 --> 13:01.090 What I'm saying is exactly Guddi, that we have converted this linear equation into a nonlinear equation. 13:01.270 --> 13:07.330 That is something which is having a range from zero to one using this sigmoid function. 13:09.240 --> 13:17.670 Hence, in case we want to find out of continuous volume, that we want to make a prediction on a continuous 13:17.670 --> 13:24.210 value, that is, if we want to solve the immigration problem, then we don't need to have this sigmoid 13:24.210 --> 13:27.050 function at the end of the neural network. 13:28.190 --> 13:35.750 So this is one guideline that is if we are trying to solve an aggression problem, then by the end of 13:35.750 --> 13:40.910 the neural network, no matter how many layers we have here, no matter what we have on the left in 13:40.920 --> 13:47.510 sight, we will not have a sigmoid function here because the sigmoid function will change the output 13:47.780 --> 13:54.980 from a digression problem to a classification problem, that it will change the function from a linear 13:54.980 --> 13:57.550 function, the logistic function. 13:57.830 --> 13:59.550 So we don't want to do that. 13:59.570 --> 14:00.590 That is why we will. 14:01.710 --> 14:07.650 Remove this, but in case you want to have a class overclassification problem, then we will keep this 14:07.650 --> 14:08.550 logic function. 14:10.230 --> 14:18.480 Another thing to keep in mind, this, in case we are solving a problem where we are deciding if all 14:18.480 --> 14:21.870 animal is a gag or a dog. 14:23.430 --> 14:31.320 OK, this is the problem that we have, if a type of animal is a cat or dog, then how we will be solving 14:31.320 --> 14:31.440 it. 14:31.800 --> 14:39.240 So this one logic will be able to give us an answer at all if the animal is a cat or not, OK? 14:40.120 --> 14:48.820 So for solving if all animal is a cat or dog, then we need to have two lords instead of one. 14:49.630 --> 14:55.540 So in that case, what we will be having is in that case, we will have something like this. 14:56.290 --> 14:58.710 So we will have another function here. 14:59.680 --> 15:03.250 This is one node here and we have another node here. 15:06.360 --> 15:09.440 And these will be connected to this one also. 15:09.450 --> 15:12.780 So one would be connected to this and another would be. 15:14.020 --> 15:15.910 Connected to this one also. 15:17.470 --> 15:19.930 So these will also be connected to this one. 15:30.110 --> 15:32.220 And this will again be a logic function. 15:32.690 --> 15:34.130 So now what will happen? 15:35.230 --> 15:40.600 This one will give answer if it is a cat or not a get. 15:41.420 --> 15:45.560 And here, this one, Valenciennes, if something is up, doc. 15:46.900 --> 15:47.960 Or not all. 15:49.930 --> 15:55.050 OK, so this Wilhelmsen, if this is a or not, again, and this will answer. 15:55.210 --> 15:55.870 This is a guy. 15:56.290 --> 15:57.120 Well, not at all. 15:57.310 --> 16:02.560 So in case the animal is a cat, then the output will be. 16:03.660 --> 16:04.590 One here. 16:05.680 --> 16:12.810 And something near to zero here, and if the animal is a dog, then the output will be zero here. 16:13.660 --> 16:14.380 And one. 16:16.150 --> 16:18.330 OK, so this is what we will be doing. 16:20.020 --> 16:27.400 So always remember that seeing the logic function will give you one set of only X or not the X that 16:27.400 --> 16:34.840 this guy or not look at, if you're trying to find out if there is another class present or not, then 16:34.840 --> 16:40.300 it will have to be dog or not or dog, which will be a part of the class here. 16:42.150 --> 16:49.050 Now, let us have a look at this, so how this logistic regression looks like so this was the equation 16:49.050 --> 16:56.310 of logistic regression, physical to one upon one plus, one minus be done on plus with our next one, 16:56.310 --> 16:57.390 plus that we do. 16:57.810 --> 17:06.540 So this comes out of the blue note, plus the blue one makes one so the blue can be replaced with Vitara. 17:06.660 --> 17:08.700 Rita has can be replaced with the W. 17:09.180 --> 17:13.800 So here we have the blue note plus W one X1 plus WBAY x2. 17:14.700 --> 17:18.000 So this is the equation which we have got from this. 17:18.510 --> 17:24.420 The combination and this combination is when fed into this sigmoid function. 17:27.050 --> 17:28.540 At this point of time. 17:31.350 --> 17:32.580 This is the equation. 17:33.790 --> 17:39.880 And after it is the dysfunction, the equation changes to sigmoid of. 17:41.080 --> 17:48.170 W w an example of this is nothing but distinguished. 17:50.220 --> 17:57.890 So this is actually one on one plus one minus W W one X one does W do it. 17:58.410 --> 18:03.030 So this is how neural network is similar to logistic regression. 18:04.180 --> 18:11.470 But how does it actually help us, because this is a very simple logistic regression and this will be 18:11.470 --> 18:18.360 able to solve only a few problems and it will be solving only immediate problems. 18:18.730 --> 18:22.150 So how can we actually use it for complex problems? 18:22.570 --> 18:28.030 So for using it for complex problems, we will be adding several layers to this structure. 18:28.570 --> 18:35.470 So now, instead of having just this kind of a simple structure, we will be having the framework for 18:35.470 --> 18:41.740 those structures so we can have a more complex structure in comparison to this one. 18:44.580 --> 18:49.270 So the activation function, which is being used here, which is the sigmoid function. 18:49.620 --> 18:56.940 This could be replaced by several other activation functions like that is of this unique step function, 18:57.300 --> 19:02.540 which is used in Perceptron, which looks like this. 19:02.940 --> 19:04.710 Then there is a fine function. 19:06.460 --> 19:07.660 It looks like this. 19:09.260 --> 19:15.290 Then there is a linear function which looks like this office wisely function, which looks like this 19:15.650 --> 19:22.470 logistic function, which looks like this hyperbolic engine which looks like this, then we have rectifier 19:22.550 --> 19:28.700 below, which looks like this, and then we have rectifiers of plus which looks like this. 19:29.100 --> 19:30.980 Now these. 19:34.670 --> 19:40.500 Equations which we have, these equations can be used in different places. 19:40.700 --> 19:43.990 So the most frequently used is the logistics. 19:44.750 --> 19:50.870 And the second most recently used is the venue function, which is used very highly. 19:51.350 --> 19:58.960 And all of these functions, we have a linear function which may or may not be used. 19:59.330 --> 20:03.380 Why do we prefer using linear function is because. 20:03.530 --> 20:04.700 Let's have a look. 20:06.410 --> 20:07.370 Now let's us see. 20:07.640 --> 20:15.500 I am the beauty of linear regression or logistic regression, and instead of using the sigmoid function, 20:15.500 --> 20:20.960 if I apply a linear function, then the output of this will be linear equation. 20:21.230 --> 20:27.860 So after this I will get something like a human plus WOMEX one plus the mutilates do so. 20:28.100 --> 20:35.050 All the same equation will be that if I apply a linear function on the only difference of the population 20:35.100 --> 20:35.660 with this. 20:36.410 --> 20:43.100 Now again, if I might apply something to it and add something to it again, the equation which I will 20:43.100 --> 20:45.960 be getting would be another linear equation. 20:46.850 --> 20:55.580 So if I keep on applying linear equations on this on this collection of the detail on this function, 20:55.760 --> 21:02.240 then the output which I will be getting will be a linear function only, which is not ideal model. 21:03.760 --> 21:09.340 If you want it, you'll have a linear function, then there is nothing better than applying a linear 21:09.340 --> 21:09.940 regression. 21:10.960 --> 21:16.340 We could have simply applied regardless of English and I would have loved the way work now. 21:16.810 --> 21:18.910 So we don't want to do that. 21:19.540 --> 21:26.520 The thing is, we should always use a nonlinear, transforming function so that we can capture different 21:26.890 --> 21:28.840 complex for the patterns. 21:29.080 --> 21:36.940 If we will not have a complex function created, then it will not be able to capture complex patterns 21:36.940 --> 21:38.000 present in the data. 21:38.440 --> 21:41.560 It will only be able to capture linear functions in the data. 21:41.860 --> 21:45.820 That is why we use the nonlinear functions. 21:47.550 --> 21:51.530 So now let us have a look at this particular unilingual. 21:51.780 --> 21:55.320 So in this particular neural network, we have two hidden lives. 21:55.680 --> 21:56.560 Olian what? 21:56.560 --> 22:00.330 Kihei did not have any hidden here. 22:00.330 --> 22:02.140 We did not have any the levees. 22:02.370 --> 22:05.210 We had the input and the output here. 22:06.250 --> 22:10.250 So here we have the booklet and the booklet. 22:10.480 --> 22:13.360 Apart from that, I have done this. 22:14.400 --> 22:23.340 Now, notice that each point of the input layer is connected to both the points and then led one and 22:23.340 --> 22:31.470 both the points in the hidden layer one up and with all the value of nodes and then layer. 22:32.600 --> 22:39.980 Now, for the then, these will be connected with the output again, they will be connected with all 22:39.980 --> 22:43.070 the less so. 22:46.000 --> 22:51.550 So it will look something like this, so all of these will be connected to each of. 22:55.340 --> 22:57.740 So after that, the output will be given. 23:05.410 --> 23:13.690 Now, let's look further now to solve this, what will happen is, first of all, then we will be working 23:13.690 --> 23:14.230 on this. 23:14.390 --> 23:22.390 What will happen is that the input values have we have certain values and those values will be multiplied 23:22.390 --> 23:28.480 with their corresponding weight and added together, I pushed into this sigmoid function. 23:29.590 --> 23:34.290 Similarly, the same thing will be pushed in to the other side of. 23:37.810 --> 23:43.190 So what comes inside this will be somewhat similar like here. 23:43.330 --> 23:47.850 Initially, we could have seen this or we can have random beats also. 23:48.010 --> 23:53.950 So based on the value of the weights, we will have different things coming in to these microchips than 23:53.950 --> 24:00.950 from the sigmoid functions, which will be multiplied from all the lines of juggling connected with 24:00.970 --> 24:01.650 each of these. 24:02.350 --> 24:05.800 I will push into this another sigmoid. 24:08.800 --> 24:11.890 So from this point, the values will go up. 24:12.610 --> 24:14.650 Now let us have a look at this. 24:14.920 --> 24:21.580 So this is the team we would like to be following for the what of the value of the loot? 24:21.860 --> 24:30.730 Because in this entire time, this entire neural network, the more the input values we know of the 24:30.730 --> 24:35.250 output values, we also know what function we will be applying. 24:35.470 --> 24:38.700 But the only thing that we don't know is the value of the beads. 24:38.710 --> 24:39.890 But in these lines. 24:40.420 --> 24:43.210 So we need to find the values of the. 24:43.930 --> 24:49.120 So how we can find out the values of the game is actually designed by Jean. 24:50.630 --> 24:54.320 So let us have a look at this now, this looks like a new rolnick. 24:55.720 --> 25:00.770 So you really would imagine that this is the first move which has value? 25:01.090 --> 25:01.370 It is. 25:01.450 --> 25:04.390 And then there is another input more. 25:05.890 --> 25:12.070 Now, this function, this is one of the sigmoid functions, just imagine this, this is a sigmoid function 25:12.070 --> 25:16.340 and in it we get the biopsy, which is equal to a cross. 25:17.170 --> 25:20.470 Here we have video your which is equal to the last one. 25:21.160 --> 25:28.590 Now, both of these are coming together at the end, which are given by this small, multiplied by the 25:28.600 --> 25:28.990 lower. 25:31.200 --> 25:39.150 So what will happen is that we will be able to calculate these values by we will be able to calculate 25:39.150 --> 25:47.880 the value of C by month by multiplying, and so we can easily find the value of C then the value of 25:47.880 --> 25:48.750 the envy's. 25:48.750 --> 25:55.290 We can buy the plus one, then value E can be easily calculated by C and to be. 25:55.500 --> 25:57.250 So this will be easy for us to get. 25:58.140 --> 25:59.610 But the thing is. 26:01.350 --> 26:09.330 We have to find out the values of the backlights, we want to find out the values of the backbone, 26:09.330 --> 26:15.650 if we want to find out if the only know the value of in will be the only know the value of it. 26:15.960 --> 26:20.760 And then we want to find out the value and then how can we do that? 26:21.120 --> 26:21.620 What then? 26:21.640 --> 26:30.630 We can have to avoid the bad word that so maybe away from it and B the words E that this word for word. 26:32.490 --> 26:38.590 And when we are going from E the West and it is for the back for us. 26:39.150 --> 26:47.860 So what happens in the back for us to find out the value of we can be competitive so that day will feed 26:47.880 --> 26:49.980 with respect to even be equal to one. 26:50.760 --> 26:56.840 Now that they feed, the respect you see will be equal then by then. 26:56.850 --> 27:01.770 See, I'm very critical of it with respect to the will be equal. 27:01.770 --> 27:03.450 Do then evade the. 27:05.240 --> 27:13.970 Now, if we want to find out that initiative of E now, we still don't know the value of so to calculate 27:13.970 --> 27:17.620 the value of the again, we will have to find out the value of the. 27:17.960 --> 27:19.220 So how will we do that? 27:19.670 --> 27:22.170 So they by identity is already there. 27:22.670 --> 27:30.200 Now, before I know the value of Baldie, the info you can give that these people will then be Oborne 27:30.200 --> 27:30.710 baby. 27:32.420 --> 27:43.280 So the value of then E with respect to Dalbavie will be valued by the including the Vivendi. 27:44.480 --> 27:49.640 Similarly, the value of E with respect to E will be. 27:50.940 --> 27:56.760 They eat by the sea into the sea by baby. 27:58.440 --> 28:09.030 Similarly, they eat by the sea in the Bering Sea by then, so it will have a combination of both and 28:09.030 --> 28:09.590 B here. 28:11.560 --> 28:20.440 Because she's a product of both, and so this is what Barillas, which means that if Y is equal to your 28:20.440 --> 28:27.790 faith and ecology of you, so human body is equal to your faith that this is a function of C. 28:29.660 --> 28:39.020 And so if this is a function of Sandy and I want to find out the value or the change in it, then I 28:39.020 --> 28:44.870 can find it out with respect to the change in Sydney FC and they are functional. 28:45.140 --> 28:50.120 And then the change in E can be found both in terms of. 28:51.970 --> 28:56.230 Changing it with respect to C, with respect to a. 28:57.130 --> 29:03.640 That is changing with respect to the with respect to the so this can be done in this particular way 29:03.640 --> 29:09.490 that is dealt with by delegates is equal to the value in value by benitz. 29:10.900 --> 29:17.230 So the intermediate, which is present that become come like this just the way it is something you. 29:18.440 --> 29:25.790 So they need vitality in daily vitality is equal to the Leviathan, so here we have the intermediate 29:25.790 --> 29:26.530 evidence. 29:26.840 --> 29:27.650 They love the. 29:28.750 --> 29:30.430 So this is what Jane Willis. 29:31.640 --> 29:35.420 Now, how we actually use this, we will think of something. 29:37.540 --> 29:38.080 So. 29:39.650 --> 29:41.640 Legacy won back propagation. 29:42.290 --> 29:50.870 So back propagation is calculating the gradient approaching, we always start from the familiar and 29:50.870 --> 29:55.830 propagate backwards of the beats and biases for each year. 29:56.510 --> 30:01.580 So we start from the end note and for the words the. 30:02.710 --> 30:03.880 Input values. 30:05.020 --> 30:10.930 And by going towards the input values, we obey the values of the gates which are in. 30:12.730 --> 30:17.590 And based on the values of faith, we can actually find out the outward values. 30:17.800 --> 30:24.040 So the main thing here is that what happens is that this is the next book, which we have. 30:25.640 --> 30:30.230 And in this network, we have these input values, which we know of. 30:30.950 --> 30:35.150 We know these sigmoid functions and we know about these output values. 30:35.510 --> 30:38.810 But the only things which we don't know about are debates. 30:39.800 --> 30:46.700 Now, in one forward buzz, we can find out dysfunction and find out these values, and then we find 30:46.700 --> 30:47.150 out the. 30:48.380 --> 30:49.950 Predicted output value. 30:50.360 --> 30:58.340 So based on some random values, we can predict the output right now because these output values are 30:58.340 --> 31:01.910 actually not exactly equal to these output values. 31:02.300 --> 31:06.150 That is, the predicted values will be different from the actual value. 31:06.350 --> 31:08.180 So we will have to find out. 31:08.510 --> 31:16.700 We will have the gold in the back for addiction to obey the bits, because only of the weights can actually 31:16.700 --> 31:18.200 improve the output values. 31:19.190 --> 31:27.410 So what we do, we find out what is the change which needs to be done and we go back and based on the 31:27.410 --> 31:32.930 change, we backtrack what the value of these weights and inputs should be and correspondingly, the 31:32.930 --> 31:35.210 input of the value of the wheat. 31:35.900 --> 31:42.260 Now, again, the former vice principal and again, the input values will be multiplied by the updated 31:42.340 --> 31:43.130 values. 31:43.340 --> 31:46.250 And again, the sigmoid function will be calculated. 31:46.460 --> 31:50.740 And based on the updated sigmoid value, the output will be delivered. 31:51.710 --> 31:59.840 Now, again, if the output value is not equal to the actual output value, it will find the error and 31:59.990 --> 32:06.030 back propagation to these input values so that it can actually have these rates. 32:06.740 --> 32:08.930 So this is what will keep on going. 32:08.940 --> 32:17.390 It will all keep on going the forward and backward pass until it actually gets the output values, which 32:17.390 --> 32:19.340 are very close to the actual value. 32:20.940 --> 32:23.410 So this is what neural networks is all about. 32:23.730 --> 32:30.840 It is all about going forward and backward, but until we are able to improve the way it's a high. 32:33.150 --> 32:40.890 So we adjust the leads and biases throughout the network so that we get the desired output in the output. 32:41.490 --> 32:41.940 Now. 32:43.330 --> 32:47.260 This is what it looks like, so we have the input value. 32:48.090 --> 32:51.450 I'm the input value is multiplied by some one. 32:52.410 --> 32:58.800 Then indicate the while we have this activation function, so what goes inside this activation function 32:59.100 --> 33:03.660 in this activation function input into one who's. 33:04.670 --> 33:14.480 So after this one comes out, so we get activation, we get input value into the blue one applied activation 33:14.480 --> 33:17.750 function, and then what value comes out of this? 33:17.750 --> 33:23.660 We multiply, they'll be then again, activation function is applied on top of it. 33:23.780 --> 33:32.630 So we get the union function and then we again apply multiply it with the WP and then again apply the 33:32.630 --> 33:35.840 activation function and we get the answer from this one. 33:36.350 --> 33:37.190 So what does a. 33:38.420 --> 33:42.140 So now if we read this, this entire thing, what is the. 33:43.680 --> 33:53.280 The output is nothing but activation function of light on WTT multiplied by the result of the Hadler 33:53.280 --> 33:53.520 to. 33:54.940 --> 34:05.110 What is the result of his desire is nothing but activation function applied on the menu to include dessert 34:05.110 --> 34:06.210 of the Italian one. 34:07.930 --> 34:14.620 And what is he, the one who delivered one result is nothing like the blue one multiplied with the input. 34:15.760 --> 34:22.210 So you can see the again going forward, very similar to calculating the value and the back prediction 34:22.210 --> 34:26.260 also for calculating the input, values and the values. 34:26.880 --> 34:34.810 So in this particular deal, if we go in this particular process, so the output value will be activation 34:34.810 --> 34:44.170 of light on W3 in the activation of light on W2, the activation of light on the blue one in. 34:46.770 --> 34:53.880 You can read this for a while and actually see the entire thing, me, you can cause the video and have 34:53.880 --> 34:58.610 a look at it right on the understand, because this is what which will be creating the concept. 35:00.330 --> 35:07.530 Now, if people want to find out the change in the output value, what change we want to have in the 35:07.530 --> 35:12.840 output value to improve our prediction, then how would that be calculated? 35:13.200 --> 35:22.290 That will be calculated by then output by Delver, W1 that this change in output, one with respect 35:22.290 --> 35:23.880 to change in W1. 35:25.050 --> 35:29.860 How W1 will change actually impact the change in the output value. 35:30.420 --> 35:38.190 So what this bill is, we will do this will be will do change in output with respect to the delayed 35:38.190 --> 35:38.490 one. 35:39.580 --> 35:47.700 The change in the lead, one with respect to the one in two, changing the earlier one with respect 35:47.700 --> 35:49.020 to the blue one. 35:50.980 --> 35:54.970 We're just changing our vote with respect to the little one. 35:55.930 --> 36:05.260 And the change in the land won with respect to the land, one in the change in the land with respect 36:05.750 --> 36:07.860 to the land won with respect to the blue one. 36:08.560 --> 36:10.710 So it's just going this way. 36:17.350 --> 36:20.150 This is the entire equation now. 36:20.200 --> 36:23.320 We will try to understand this photo. 36:24.700 --> 36:25.270 So. 36:27.540 --> 36:31.050 For us, the output of activation function. 36:33.240 --> 36:43.170 Is they give the the world because we will be subtracting this output with the actual value so that 36:43.170 --> 36:44.540 they give us the added value. 36:45.810 --> 36:53.700 Now we want to minimize this, everybody, so what we will be doing is we will be back tracking this 36:53.700 --> 37:00.300 error value to W1 so that we can gradually update the value of the bits. 37:00.600 --> 37:01.870 So how are we going to do that? 37:02.250 --> 37:06.390 The change in error with respect to W1 is equal to. 37:07.410 --> 37:13.710 The change in attitude with respect to the everyone will be equal to the change in Ed with respect to 37:14.160 --> 37:15.090 the output. 37:16.610 --> 37:23.550 In go change in output with respect to the net include the change in the labor with respect to. 37:25.130 --> 37:31.430 Fewer didn't run into the change and he didn't run with respect to the new one, so this is what we 37:31.430 --> 37:31.790 are doing. 37:32.690 --> 37:33.200 This is. 37:34.380 --> 37:39.720 James and Ed, with respect to the blue one in blue jeans and Ed, with respect to output into output, 37:39.990 --> 37:46.800 with respect to to into change in hereinto with respect to one single change, including one with respect 37:46.800 --> 37:50.130 to the W one. 37:54.640 --> 38:00.070 So let us calculate the error values, we will calculate these. 38:01.090 --> 38:06.820 So in this scenario, let's consider the this as one of the. 38:07.870 --> 38:17.770 So for any length for the first year, this be the legacy, then this is the output layer or any layer 38:17.770 --> 38:18.780 intermediately. 38:19.090 --> 38:22.540 So in this year, there will be an activation function, the. 38:23.520 --> 38:25.980 And there will be an output exergy. 38:27.280 --> 38:28.300 For leered in. 38:29.330 --> 38:36.890 And there will be an input value that is the sigmoid function, the product of every time, everything 38:37.130 --> 38:46.340 as an object and what is in store and sees nothing but multiplication of X1 into W.M. plus X2 into the 38:46.340 --> 38:49.310 video plus extra into the battery from different modes. 38:50.900 --> 38:55.370 So in the case, we want to find out the change in. 38:56.190 --> 39:03.480 And if you want to find out the change in edit or with respect to the change in weight. 39:04.700 --> 39:10.040 That is the change in area with respect to the change in weight. 39:10.100 --> 39:13.960 So how will we do that again with the same function which we learned in the. 39:15.360 --> 39:22.980 So the change in L.A. with respect to we will be equal to the change in era with respect to this sigmoidal 39:22.980 --> 39:23.460 function. 39:26.260 --> 39:32.710 I multiplied by this sigmoid function change in sigmoid function with respect to the change in. 39:34.040 --> 39:34.460 So. 39:35.640 --> 39:36.790 What will this be? 39:37.140 --> 39:44.760 Now, the change in this is with respect to W. is nothing by expanding. 39:46.360 --> 39:47.170 What is this? 39:47.410 --> 39:54.500 This is this is nothing but Xingdou W and X is a constant W is the variable. 39:54.760 --> 40:03.940 So if we take a derivative of of a constant and the variable, then be out with no power on top of it. 40:03.940 --> 40:05.870 So the output will be the constant value. 40:06.370 --> 40:10.540 So we get X minus one, which is from the previous year. 40:12.220 --> 40:17.680 Now we need to find out the change in Ayda with respect to the. 40:19.250 --> 40:24.080 S, which is the sigmoidal the segment of this letter. 40:24.620 --> 40:25.610 So what is this? 40:26.110 --> 40:27.610 This is legacy. 40:27.660 --> 40:28.700 This is day. 40:28.910 --> 40:30.320 This is this Valentine's Day. 40:31.010 --> 40:32.510 Now, how do we find now? 40:33.490 --> 40:36.590 So let us say we want to find out for the final. 40:37.240 --> 40:45.370 So this will be equal to change and e with respect to this, so for the final leg changing, even with 40:45.370 --> 40:54.850 respect to S will be equal to now here, the what will be added value will be the function of X minus 40:54.850 --> 40:57.010 Y value for with. 40:58.450 --> 41:03.190 That is predictive value minus the actual value will split. 41:03.880 --> 41:06.500 Now, this is Gwen, is there. 41:06.560 --> 41:08.380 Now, what is this one? 41:11.380 --> 41:14.020 This X1 is nothing but. 41:15.370 --> 41:19.390 Sigmoid function of light or t, the function of light on is. 41:20.920 --> 41:21.300 Right. 41:21.400 --> 41:24.340 This is the definition of light on is what was. 41:26.300 --> 41:31.620 X is X, Y, plus W, one extra W2 this extra on. 41:32.060 --> 41:37.760 And this is what is going inside this, that the summation value which is going inside, this is the 41:37.760 --> 41:38.900 activation function. 41:40.530 --> 41:44.460 And X is the output value after applying the activation function. 41:45.060 --> 41:46.090 So what do we get? 41:46.500 --> 41:52.100 So it's it's and is nothing but sigmoid function applied on the summation value. 41:52.560 --> 41:53.010 So. 41:54.210 --> 42:03.600 Legacy of this dysfunction, this activation function is damage, then the very of and net is equal 42:03.600 --> 42:05.070 to one minus Tusker. 42:05.970 --> 42:08.730 So we can replace it, we can use this value. 42:11.330 --> 42:11.780 So. 42:12.730 --> 42:19.650 If you are checking for the previous year, this is for the last year, we are checking for the existence 42:19.660 --> 42:27.820 of one one previously, Daniel's enemy of those back to the previous years is we will do they love E 42:28.240 --> 42:37.720 with with respect to S Galavis, with respect to the previous year, X into the of previous years, 42:38.320 --> 42:47.500 with respect to the previous year when they this is the final let the previous year and the year before 42:47.500 --> 42:48.510 that date. 42:48.790 --> 42:55.540 So this is how it will just keep on going globally previously and it will just keep on finding out values 42:55.540 --> 42:57.400 from the one layer behind it. 42:57.820 --> 43:01.450 And based on that, it will keep on finding of different values. 43:02.870 --> 43:08.900 So what is the end goal is in which we will be following this, you know, we don't going to the entire 43:09.200 --> 43:15.620 pocket, only thing that we need to know is this entire thing, which is happening so easily. 43:15.620 --> 43:24.220 You will have something in common values and you will think some random values and build up over us 43:24.230 --> 43:32.240 so that the value, the outward value can be calculated now based on the output value and the actual 43:32.240 --> 43:32.690 value. 43:32.690 --> 43:34.650 Some in an amount that we. 43:35.300 --> 43:37.490 And this where we have to be in. 43:38.150 --> 43:46.760 So if we move this into whatever change will be needed, that will be back propagated so that the value 43:46.850 --> 43:48.500 of the wealth can be a big. 43:49.930 --> 43:54.730 And this will be a big theme, the week of each and every live. 43:55.650 --> 44:02.660 So the values each and every year will be big for the week so that we get better. 44:03.330 --> 44:09.500 I think we'll just keep on doing this entire process again and again until you get the results. 44:11.740 --> 44:13.150 So what do we do? 44:13.180 --> 44:20.440 We to make the leads to a small random number and like all the biases, because, you know, we have 44:20.440 --> 44:22.710 not discussed what biases. 44:23.170 --> 44:25.340 So I have this for now. 44:25.360 --> 44:26.590 So what is bias? 44:30.990 --> 44:35.170 Now, here's what we have, is we have this equation. 44:35.580 --> 44:44.970 What does this equation have this equation have W plus W one X, Y plus W two x2. 44:45.420 --> 44:47.850 So these are the V. 44:49.260 --> 44:52.500 And this one, which is being played here. 44:54.220 --> 44:55.540 This is ordered by. 44:57.280 --> 45:00.900 So this is also one, though, which will be a big. 45:03.100 --> 45:05.650 OK, so this is called by. 45:10.510 --> 45:17.600 So the full report is for next March and the activation function. 45:17.920 --> 45:22.750 Now we will go forward and backward buzz by these forces. 45:22.750 --> 45:27.330 Will it be done or whatever they need that we will not take all the data. 45:27.340 --> 45:33.610 And one thing we will take the view that in batches, because it will take a lot of time every day, 45:33.610 --> 45:35.380 all the already that it once. 45:35.740 --> 45:38.470 So we will do this in many batches. 45:38.970 --> 45:43.830 OK, so we will forward, pass and calculate the activation value. 45:44.230 --> 45:52.840 Then we will back what and calculate the gradient and update the gradient by propagating backwards moving. 45:54.280 --> 46:02.590 And we will update the weights and the biases based on the gradient vector calculated from averaging 46:02.590 --> 46:03.750 over the that. 46:04.000 --> 46:10.840 So we will find out the dates by averaging the gradient vector from the many vectors. 46:11.020 --> 46:12.910 So that is what we will be doing. 46:14.020 --> 46:21.730 Now we will have a look at the court in the next session, so I hope that will make this entire thing 46:21.730 --> 46:27.220 a little more clearer so that you will be able to implement these of your own. 46:27.700 --> 46:29.590 So let's meet at the.