00:00we should update all 3. So, w1 is something associated with x1. So, substitute the values,
00:05what is learning rate? Learning rate is given as 0.1, what is the error that we have got?
00:10The error we got is 1 and what is x1 value? x1 value is 1, what is change in the
00:16what
00:18is this value? We are going to get 0.1 delta w. With this go back and then substitute back
00:25in this, what is the old weight? The old weight value is 0.2 and what is this delta? It
00:31is
00:320.1. Therefore, the new w1 what we have got is 0.3, this is w1 0.3. Similar way
00:44you calculate
00:45w2 and then see let us see what is the value that we are going to get. I am going
00:51to solve
00:51here for w2. w2 since the formula is here, I am looking into this formula and then substituting.
00:57What is first let us calculate delta w. Delta w is learning rate 0.1 and what is the error
01:05that we have got? The error is 1 and what is x2? Now, we are updating w2. w2 is something
01:12is the weight which is associated with x2. What is x2? It is 2. So, what is delta w2 value
01:19here?
01:19It is 0.2. So, go back and then calculate what is w2 new weight? What is w2 old weight?
01:28It is
01:28minus 0.5 plus change 0.2. So, w2 value what we are going to get is minus 0.3.
01:38Can you see here?
01:39What is that we have done? Initially, the weights were 0.2 and minus 0.5, but that is not
01:46the correct
01:46weights. The correct by changing the weight what we got is w1 value as 0.3 and w2 value what
01:57we
01:57have got is minus 0.3. Now, with this we should also calculate the bias term. Let us see how
02:05do you update the bias? Let us solve calculating the bias. Let us see how to calculate the how
02:20do we update the bias. So, what is the formula to update the bias? Bias is the old bias plus
02:27the learning rate the error. So, what is the old bias value? 0.1. What is the learning rate?
02:360.1 and what is the error? The error is 1. So, what is the bias? 0.1 plus 0
02:41.1 it is 0.2.
02:42So, with this the new parameters what we have got? W is it is 0.3 minus 0.3 and
02:55the bias what
02:56we have got is 0.2. Can you see the difference? Earlier the weights were 0.2 minus 0.5
03:04and the
03:04bias is 0.1. Now, the new parameters the new weights are 0.3 and minus 0.3 and the
03:13bias is
03:140.2. Now, does it mean that these are the standard or correct values? Now, for this let us go
03:21back
03:21and then solve the problem again to understand what what is our input x1 and x2 value from
03:28our previous we have seen it is 1 and 2 ok. So, let us calculate again first step is calculating
03:36z it is x1 w1 plus x2 w2 plus bias. What is x1? It is 1. What is the weight?
03:44Now, you will
03:45use the updated weight. What is x2? It is 2. What is the new minus 0.3 plus bias 0
03:52.2. So,
03:53z value what we are going to so calculate this we get 0.3 minus 0.6 plus 0.2.
04:01What we are going
04:02to get is minus 0.1 this is the z value. Now, so summation part is done. Now, you have
04:08to pass
04:09it to an activation function. What is activation function? If the value is less than or equal
04:13to 0 it is 0. So, therefore, y hat what we are going to get is 0. With this we
04:20are calculating
04:20the error. What is error? Target minus computed. What is target 1? Computed is 0. So, error value
04:29what we are getting is 1. Still there is an error. So, because there is an error again we are
04:34going
04:34back and then we are updating the weights. How are we updating the weights? By now you should know
04:39the formula w new is w old plus delta wf. What is delta wf? It is the learning rate error
04:48and
04:49which weights we are updating both x1 x2 weights and bias. So, input x1. So, let us solve what
04:57is learning rate eta 0.1 and what is the error? Error is 1. What is the input? Input is
05:021. So,
05:03what is delta w? Delta w what we are going to get is 0.1. With this w new weight
05:10once again
05:10let us see what is the old weight? Old weight is now 0.3 plus 0.1 which is now
05:150.4 w1 value
05:18be 0.4. I think you are getting the concept. Similar way let us calculate w2 because since
05:25you are now familiarized I am directly solving w2 value. So, the old w2 value is 0.3 plus the
05:35learning rate is 0.1 and then what is the error? Error is 1 and 1 it is 0. ok.
05:45Let us take
05:45w2 is learning rate is 0.1 error is this and then the input is 2. So, we have 0.
05:52we have
05:53w2 value here I am sorry. So, we have yeah it is 0.2. So, this entire delta w what
06:16we are
06:16getting? So, when you multiply w2 is minus 0.1 this is our wf 2 value. So, earlier and similar
06:29way when we go back and then calculate the bias. So, let us see bias what is the old bias
06:36value?
06:37The previous bias value was 0.2 plus the learning rate is 0.1 into error is 1. So, the
06:45bias what
06:45we are getting is 0.3 with this the new parameters wf are 0.1 minus 0.2 minus 0
06:54.4 and minus 0.1 and
06:56the bias is 0.3. Can you see?
06:59.
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