1 00:00:03,800 --> 00:00:09,080 In this session, we want to see how to calculate maximum number of neurons per layer. 2 00:00:09,830 --> 00:00:11,800 Let's take a look at this example. 3 00:00:11,810 --> 00:00:18,140 If you have this equation to explore, tree y equals 12, can you solve it? 4 00:00:18,860 --> 00:00:27,200 The answer is no, because we need more information by another hand of our indeterminate are more than 5 00:00:27,380 --> 00:00:28,290 determinate. 6 00:00:28,580 --> 00:00:37,670 But if we just give it another one, let's say six X minus two Y equals seven, then we can solve it 7 00:00:37,670 --> 00:00:45,280 because the number of determination, an indeterminate in this example are the same based on this rule, 8 00:00:45,710 --> 00:00:52,520 we can say for solving an equation or any problem, the number of indeterminate must be less or equal. 9 00:00:52,520 --> 00:00:59,420 Dan Determinates, based on this fact, we are going to calculate the number of neurons per layer. 10 00:00:59,630 --> 00:01:06,120 So first, let's see how many determinants do we have when we want to design our network? 11 00:01:06,380 --> 00:01:18,380 Supposing your cell phone, you have some inputs, here are your inputs and one here is over X, so 12 00:01:18,380 --> 00:01:18,830 fine. 13 00:01:18,830 --> 00:01:24,320 We have a column of inputs and then here we have over outputs. 14 00:01:25,610 --> 00:01:31,940 And this is another column that can be actually several columns for this one. 15 00:01:31,940 --> 00:01:39,320 We call it an off o and then we have K elements or K samples of H. 16 00:01:39,720 --> 00:01:48,440 This part would be OK and here are several columns and several rows. 17 00:01:48,950 --> 00:01:58,150 If we want to calculate total number of determinants, we can say it's K times in parentheses and I 18 00:01:58,190 --> 00:02:00,190 plus an O. 19 00:02:00,800 --> 00:02:06,020 This is how we can calculate the total determinant in our problem. 20 00:02:07,040 --> 00:02:11,780 Let's take a look at this multi-layer neural network supples here. 21 00:02:11,780 --> 00:02:13,190 We have several layers. 22 00:02:13,190 --> 00:02:14,150 We have some inputs. 23 00:02:14,150 --> 00:02:18,680 First, these are inputs which we call them. 24 00:02:18,680 --> 00:02:22,330 And if I let's say here we have two layers. 25 00:02:22,760 --> 00:02:27,290 This is the first layer and this is the second layer. 26 00:02:27,320 --> 00:02:36,650 And finally we have some outputs as well, which we show it with enough for the first layer we have 27 00:02:37,220 --> 00:02:43,880 in one neurons and for the second layer we have in two nephrons. 28 00:02:44,570 --> 00:02:50,180 Now we want to see how many indeterminate do we have for the first layer. 29 00:02:50,680 --> 00:02:51,980 Take a look at this, Neren. 30 00:02:52,550 --> 00:02:59,430 In engineering, we can have a number of inputs plus our bias because we have a bias as well. 31 00:02:59,690 --> 00:03:06,980 So in other hand, we can say a number of indeterminism for the first layer are in one times in apprentice's, 32 00:03:06,980 --> 00:03:12,260 in a number of inputs plus one, which is of our bias. 33 00:03:12,440 --> 00:03:19,100 If we have two neurons, then it would be two off and I plus one. 34 00:03:19,740 --> 00:03:22,120 But what about the second layer? 35 00:03:23,270 --> 00:03:30,080 The number of inputs for the second layer are equal to the number of neurons that we have here. 36 00:03:30,080 --> 00:03:31,890 Each neuron is giving one output. 37 00:03:32,060 --> 00:03:34,470 This one is N one plus one. 38 00:03:34,520 --> 00:03:37,870 Of course we have our bias as well. 39 00:03:38,270 --> 00:03:41,540 And then how many neurons do we have in the second layer? 40 00:03:41,540 --> 00:03:42,770 We have in two neurons. 41 00:03:42,790 --> 00:03:52,610 So number of indeterminate for a second layer are into in apprentice's and one plus one because no one 42 00:03:52,610 --> 00:03:56,240 needs our input for the second layer. 43 00:03:56,360 --> 00:04:05,720 And we already know that number of neurons in a second layer must be equal to the number of other outputs 44 00:04:05,870 --> 00:04:09,080 so that her to say and two is equal to. 45 00:04:09,080 --> 00:04:13,100 And actually this is a mass for multilayer Perceptron. 46 00:04:14,060 --> 00:04:19,790 If we have more outputs, if you have more neurons, each neuron is giving an output. 47 00:04:20,180 --> 00:04:25,880 If, for example, we have two outputs, then what would be the use of tarried narrowed in the second 48 00:04:25,880 --> 00:04:26,240 layer? 49 00:04:26,270 --> 00:04:36,860 We must have two neurons for the second layer as well, so I can already rewrite it as an old enough 50 00:04:36,860 --> 00:04:42,620 output number of neurons in output in apprentices and one plus one. 51 00:04:43,460 --> 00:04:49,040 OK, we can calculate the total off indeterminate for other network. 52 00:04:49,610 --> 00:04:55,490 This will from indeterminacy for our network would be the number of determinates for the first layer 53 00:04:55,490 --> 00:05:00,140 plus the number of indeterminism for the second layer. 54 00:05:02,460 --> 00:05:03,840 And here we have it. 55 00:05:07,060 --> 00:05:08,360 Now, let's check it here. 56 00:05:08,380 --> 00:05:13,630 We know that in determinates must be a less or equal than determinates. 57 00:05:14,200 --> 00:05:21,700 These are other indeterminism which were calculated here and these are the total number of samples and 58 00:05:21,850 --> 00:05:30,400 determinates that we can have in and was actually in reality, we're not usually using all the samples. 59 00:05:30,550 --> 00:05:32,700 Not all the samples are useful. 60 00:05:32,860 --> 00:05:37,320 But however, this can be the maximum of elements that we can have. 61 00:05:38,560 --> 00:05:45,130 I'm looking for a number of concerns for the first layers, so I'm going to keep this and one at one 62 00:05:45,130 --> 00:05:48,140 side and send the rest of them in the other side. 63 00:05:49,390 --> 00:05:54,600 This is what we can have and this is already the upper limit. 64 00:05:55,060 --> 00:05:58,040 How about the lower limit for the lower limit? 65 00:05:58,360 --> 00:06:07,420 We really can say it's just based on experience, but we can just write it as two times off number of 66 00:06:07,420 --> 00:06:10,120 inputs plus a number of outputs. 67 00:06:10,450 --> 00:06:17,870 We can just put this one for the lower limit and set Dysport for upper upper limit. 68 00:06:18,610 --> 00:06:25,270 So here is how we can calculate the number of neurons for each layer. 69 00:06:27,100 --> 00:06:31,090 Now let's back to Matlab and have more examples.