00:042 plus h 2 w 2 1 2 plus h 3 w 3 1 2 ok. Now, what is your
00:19h? h is nothing but h sorry
00:23h 1 is nothing but your sigma z 1 1, h 2 is equal to sigma z 2 1, h
00:373 is equal to sigma
00:39z 3 1 ok, done. Therefore, what I can write? Therefore, I can write partial derivative
00:56of y with respect to w 1 1 2 is equal to y into 1 minus y, this I have
01:07got already and
01:08using that one into for the third term only h 1 is coming ok. So, this is my partial derivative
01:17of y with respect to w 1 1 2. Putting all these values in equation 1.1, we get what
01:36was our
01:36equation 1.1 that was the full equation for getting the partial derivative of the loss function
01:44with respect to w 1 1 2 which was our starting problem statement ok. So, we can write partial
01:49derivative of l with respect to w 1 1 2 is equal to 1 by n summation y minus t
02:00into y 1 minus
02:04y into h 1. So, this is how we get you know the partial derivative of l with respect to
02:15this
02:16weight. Now, as I told for gradient descent algorithm to work, we need to find out the partial derivative
02:29of the loss function of the loss function with respect to all the weights in the network. So,
02:33similarly, we can do it for you know a partial derivative of l with respect to w 2 1 2,
02:39partial
02:40derivative of l with respect to w 3 1 2 and so on. So, I have shown one for this
02:46layer, the output layer,
02:48whatever is going in the output layer. So, that portion. Now, I will take another one which is I want
02:55to show something how do I get the partial derivative of l with respect to w 1 1 1 because
03:03that also is required.
03:04These are all 1 1 1, 1 2 1, 1 3 1, 2 1 1, 2 2 1, 2 3
03:101 all are weights. These are the weights associated
03:14with the you know first layer that is between the hidden layer and the input layer. So, now, I will
03:20show
03:20how we can get this. Now, let us calculate and write it. Now, let us calculate partial derivative of l
03:36with
03:36respect to w 1 1 1 1. What is w 1 1 1 that is here? So, we have to
03:43do this one. We will write partial
03:47derivative of l with respect to w 1 1 1 1 as del l by del h 1 into del
03:57h 1 by del w 1 1 1.
04:01What is my h 1? h 1 was this one, this was my h 2 and this is my h
04:063. So, I have written
04:09the partial derivative of l with respect to w 1 1 1 1 as partial derivative of l with respect
04:14to h 1 1 1 1 with respect to w 1 1 1 1. We have started for the you
04:24know layers which
04:25are inside, we start from the you know nearest layer. And then what we will do is we will
04:32use whatever we have calculated for the you know the layers which are near to the output.
04:43Now, we have seen ok, what is h 1 h 2 h 2 h 2 we have seen. Now, h
04:483 we have seen. Now,
04:50what we will do is del l by del w 1 1 1 1, I will write once again as
04:58partial derivative
04:59of l with respect to sigma z 1 1 1, why I am writing this one ok. So, because your
05:10h 1 is nothing
05:11but your sigma sigmoid activation function working on z 1 1 ok. So, for h 1 I have written it
05:18here. Then del of sigmoid of z 1 1 1 into partial derivative of z 1 1 with respect to
05:351 1 1 w 1
05:38ok. So, this I will put as equation number 2. Here we will keep the first term as it is
05:48del
05:48l l by del sigma z 1 1 1 into this one. Once again I can see it is derivative
06:00of the sigmoid
06:00activation function. So, this I can write as sigmoid of z 1 1 into 1 minus sigmoid of z 1
06:121. This
06:13is from equation 1.3 I remember from equation 1.3. Now, the derivative of a sigmoid function
06:23is it can be written as sigma x into 1 minus sigma x into the last term I will get
06:30it as
06:30it is z 1 1 with respect to w 1 1 y ok. So, I will continue writing this one
06:41as derivative
06:43partial derivative of L with respect to partial derivative of L with respect to sigmoid of
06:49z 1 1 1 into h 1 into 1 minus h 1 into x 1 ok. So, why I have
07:00written h 1 into 1 minus h 1
07:02this one because,
07:03I have written h 1 1 1 into h 1 1 into this one. It is so controversial and what
07:06I have written
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