00:000 and what is the weight? Weight is 0.1 and what is x2? x2 is also 0 and the
00:05weight is
00:060.3. So, definitely the value is 0. So, and this is less than a threshold, what is a threshold
00:13value that is defined? The threshold is 0.5. Since the value is less than threshold, the
00:18predicted value is 0. So, we can say the computed value is 0. Now, the next step is that is
00:26what we have seen the computed value is 0. And the target directly we are taking it from
00:32the data set that is given to us, you can see there is a target, we have taken that a
00:37target
00:37as it is. The next step what we are doing? We have to calculate the error. What is the
00:41formula to calculate the error? Target minus computed. What is the target value? 0. What
00:47is the computed? The computed is also 0. So, the error what we are getting is 0 ok. Once
00:54we get an error is 0, now we have to ideally there is you know you have to go back
01:00and
01:00then update the weight. Now, how is that you will be updating the weight? Although in this
01:05particular example you do not for this instance we do not require because the error is 0. But
01:11still let us see how do you update the weight? The update weight is let us see how we are
01:16getting
01:17this 0. So, the learning rate is 0.2 and the error is 0 and you are updating the weights
01:23with respect to x1, x1 is also 0. So, delta w value is 0. So, we have seen delta w
01:30value
01:31is 0. Similar way let us see how delta w 2 value we are getting. So, let us look into
01:38how delta
01:38w 2. So, delta w 2 is error learning rate is 0.2 and the error value is 0 and
01:49with respect
01:50to x2 we are calculating x2 is also 0. Therefore, delta w 2 value we are getting 0. Now, once
01:58we get this what is the total complete formula w nu is equal to w old plus delta w f.
02:06Now, what
02:06is when we are doing for w 1 what is w 1 old value 0.1 and what is this
02:14delta w what we got
02:15is 0. Therefore, w 1 value is still 0.1 only and similar way if you have to do w
02:222, w 2 is
02:24old weight what is old weight of w 2 0.3 and what is change in what is this delta
02:30w 2 this
02:31is also 0. So, when you add you get 0.3. So, the weights are w 1 and w 2
02:38for the next input will be
02:40this 0.1 and 0.3 only. So, with this I hope you have understood how it is being solved.
02:47I will show
02:48you for one complete epoch whatever you are seeing on this table I will be solving this. Now, the next
02:54input that we are considering is 0 and 1 we are considering the next input. Now, for this
03:00input what is the target the target is 1 ok. So, what is the first step as usual we have
03:05to calculate
03:06z which is x1 w 1 plus x2 w 2 once again I am saying there is a bias term
03:12but here we are not
03:13considering it what is x1 0 what is w f. So, w f is 0.1 and what is x2
03:19x2 is 1 and w 2 value is 0.3.
03:22What is the z value this term becomes 0. So, this is 0.3 which is less than a threshold
03:28therefore y dash
03:30is 0. So, computed value what we are getting is 0. Now, what is the target value for this input?
03:38The target value for this input is 1. So, what is the next step? We have to calculate the error.
03:43How is the error is calculated? Target minus computed. Target is 1. So, the error is 1. So,
03:49now we have to update the weights. So, what is the formula to update the weights? It is w nu
03:55is equal
03:56to w old plus delta w. So, now since both w 1 and w 2. So, first let us calculate
04:03delta w 1. So,
04:05how is that we calculate delta w 1 learning rate? So, what is the learning rate? So, let us erase
04:12this
04:13part and then take the value directly. So, the learning rate here is 0.2 and what is the error
04:21that we have got? The error we got is 1 and with respect to input x1 we are updating. Therefore,
04:27this is 0 delta w 1 is 0 that is what is the 0 that we have got here. Now,
04:33let us update delta w 2. So,
04:37here only I am changing how do we go for w 2 learning rate is 0.1 error is 1
04:43and the input is
04:45now 1 instead of 0 previous now we will be taking input 1. So, for this let us calculate what
04:52is
04:53the value that we get? The value that we are getting is 0.2 that is the 0.2 value
04:57that we have written.
04:58Now, if there is a change now you have to update back into this w new value. So, there was
05:06no change
05:07with respect to delta w 1. So, let us not see let us look into how do we update w
05:132. w 2 what is the
05:15old weight? The old weight was 0.3 for this change in delta w is 0.2 therefore, it is
05:230.5. So, the new
05:26weights are w 1 since there was no change it is 0.1 and w 2 value is 0.5
05:33that is what you are seeing
05:35that for the next input it is no more 0.5 it is I mean 0.3 it is 0
05:42.5 now. So, what is the next input
05:45that we are considering? Let us erase. So, we have seen it is now 0.5. The next input is
05:521 under 0. So,
05:53on a similar lines when you compute the first step is z you will calculate x1 into 0.1 we
06:02will get 0.1
06:04plus x2 since it is 0 it is 0. So, it is 0.1 which is less than the threshold
06:09value. So, y hat is 0. So,
06:12y hat is 0 and what is the target for this input? The target for this input is 1. So,
06:19what is the error?
06:20The target minus computed which is 1 minus 0 which is 1 ok. Once this is what is the target
06:27and error.
06:28Now, we have to calculate delta w 1. So, what is the learning rate? 0.2 what is the error?
06:351 and what
06:36is the input? Input is 1. So, it is 0.2 delta w 1 is 0.2 and what is
06:43the new weight? The new weight is
06:46what was the old weight? 0.1 and the change 0.2. So, now we are updating w 1 to
06:530.3. We have updated w 1
06:57to 0.3. So, similar way you can check for w 2 and you can see how we are going
07:07to. So, this is for
07:08one single epoch which I have solved the problem. I will be pausing here for a few seconds where I
07:17want
07:17to you to
Comments