00:00going to get 8, 90 and 75 and you can multiply it with 0.4, 0.3 and 0.2.
00:09We can do a multiplication
00:11or instead of doing this we can also do W transpose x. What is the W transpose x? We
00:18are taking 0.4, 0.3 and 0.2 that is getting multiplied with 8, 90 and then 75. So,
00:28that
00:28is the reason you can see the very first operation that is happening inside a neuron is you are
00:35multiplying the input with its associated weight W transpose x and next comes the concept there
00:43is b, b is a constant that is been added to it. For example, let us assume if all of
00:53these
00:53input values are 0, the very first you know understanding why we require bias is if the
01:03value x1, x2, x3 if the values are 0, then this whole term becomes 0. Then there is ideally
01:12there is nothing that this particular neuron is a processing, there is no information this
01:18particular neuron sends it to a next neuron. So, in order to avoid it I do not want to send
01:24a 0 to a next neuron. So, if you want to avoid sending 0 to next neuron, what is the
01:29only way?
01:30We can add to this 0, we can add some small constant value. So, that instead of sending
01:360 at least we are sending 0.1 which is a small value at least is been processed from this
01:42particular
01:43neuron. So, that is one reason why we add one constant which is b always a very small value
01:51that is been added. Now comes the question why we need to add a very small value, why not
01:57a large value is been why not add a large value. Now say for example, it is just for an
02:04example
02:04when you multiply input with the weight. For example, let us assume the resultant of it we
02:10are getting some 23.5. I am just giving an example when you multiply some values of input with its
02:16weight, we are getting this 23.5. For this if you are going to add a very large value, then
02:23the entire resultant we are going to change it, we are changing the value. So, which is not correct.
02:30So, because of this we are adding a very small value which is 0.1. So, that the resultant by
02:37adding
02:37this 0.1 whatever the value that we are going to get there is no much difference to what that
02:44summation
02:44value we had got. So, the bias terms bias is been added in order to avoid the summation value being
02:530.
02:54So, that you can avoid this neuron not processing any information. The second most important concept
03:02why bias is being added is how can you understand what is the importance, what is the role of the
03:08bias
03:09is? If you look into this, it is an straight line equation. So, mx plus c, so this is a
03:18straight line equation.
03:20Suppose if we does not have this term, then always the line will pass through an origin, the line will
03:28pass through
03:28origin. Now, what is the problem if a line passes through an origin? There is a very high possibility
03:34that the learning will not be correct, there is a high possibility that there can be a misclassification.
03:42Now, by adding the bias how is that we are avoiding the misclassification? Let us understand this.
03:47When a bias term is being added, the line not necessarily will go through the origin,
03:53the line will be shifted either above, below, right, left, the line will be shifted.
03:58As you are seeing here, when a line is being shifted, the learning is appropriate and there
04:04is a very high chances that you can avoid a misclassification. That is the role of bias
04:10in this particular in this particular concept. So, from this slide what is that we are understanding?
04:18We are seeing a mathematical representation of a neuron. So, how is what is a mathematical representation
04:24inside a neuron? There are 2 operations that are taking place. One, we are performing a summation
04:29and whatever is the resultant of this summation is then passed to an activation function. Yeah. So,
04:37let us try to understand what is the role of an activation function here. Now, whatever is the result
04:43that is obtained from this summation that is given to an activation function? This activation function
04:50is then decides whether it decides whether sufficient signal is been whether the strength of a signal
04:55is sufficient so that we can trigger a response. So, how biological neural system once there is a
05:03sufficient once the signal is strong enough how a neuron is going to trigger a response that is
05:10been mimicked by using an activation function concept in artificial neuron. Now, so what activation function is
05:19been used that we will be seeing shortly, but for now you understand that it has been passed to an
05:24activation function and the role of an activation function here is whether you should trigger or
05:30whether you should fire a neuron or not firing a neuron. So, this is what is the biological representation
05:37of a neuron. From this we are entering into the first and the oldest form of a neural network called
05:47a
05:47perceptron. Perceptron is an algorithm which is invented in the year 1958 by Frank Rosenbelt. It is an algorithm
05:58which is mainly designed for a supervised learning problems only and more specifically perceptron is
06:06designed only for a binary classification. What is the binary classification? Where you just have
06:12only two classes, we can have either 0, 1 or it can be yes or no or it can be
06:18true or false. So,
06:20the perceptron is mainly designed to solve a supervised learning problems only. If this is the case,
06:26how do the architecture of a perceptron model looks like? The perceptron consists of an input layer and
06:33we will have an output layer. So, there is no hidden layer in a perceptron model or we can say
06:41a single
06:41layer perceptron that we will be seeing shortly. The term single layer perceptron you will learn shortly.
06:48Now, this is so what was the main aim of designing this perceptron initially when the perceptron was
06:55designed it was designed. It was designed to solve a logical problem such as
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