Hello.
Welcome back.
Let's say we have a truly a new network like this.
We don't often include the input layer when we talk about the layers of shared neural network has a
two layer neural network would look like this the input layer is always denoted as a zero in the next
layer is denoted as a one and the one after that is denoted as a to the hidden layer.
A one has 4 unit D superscript represent the Layer number and the subscript represents the unit number.
Let's see how to compute unit a subscript 1 and superscript 2 1 to complement this we begin by compute
in Z subscript 1 z subscript 1 is computed by weight subscript 1 transpose x plus b subscript 1 superscript
1.
As we can see over here remember we use subscript to denote the unit number and superscript to denote
the Layer number.
Once we have found Z subscript 2 1 we apply our activation function to it to get a subscript 1 superscript
2 1.
This is how we find the output of the first unit.
We find the output of the second third and fourth unit using the same method but we have to use our
respective weight and biases like shown in these equations to compute Zi superscript 1 which means the
Zi output of the entire layer.
Number one we've put all of the weight together in a matrix and all of the inputs in effect so and all
of the bias is in effect all and perform you transpose x plus B on the weight matrix and vectors.
The result would look like this like we see over here we end up with a vector containing the ze result
of the of all the units in the layer 1.
As you can see over here by applying our activation function to this resort we get a new vector containing
all the end result of layer one right.
So you can post the video and take a look at this.
This slide over here it's all been arranged nicely.
If you have any questions you can let me know.
Also take note of the dimensions of the parameters the dimension of the weight matrix.
4 by 3 four rows three columns four rows because Layer 1 has four units and three columns because we
have three inputs entering each unit which will spend more time talking about how to fully understand
the dimensions later.
So this order is for this lesson and I shall see you in the next lesson.