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Hello.

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Welcome back.

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So let's see how to build these multiple input multiple output neural network.

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I'm gonna make a copy of the last project

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can open it

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right.

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So let's take a look at the um the neural network again.

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So this what we have.

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So we set this time given the temperature humidity and air quality we not only we don't want to only

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predict whether you are sad or happy.

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We also want to predict whether you are sick or healthy active or inactive.

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So given the three inputs we want to get three outputs from it.

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And this is what we have right.

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So a way of viewing this as we mentioned earlier is to view this as a multiple input single output neural

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network.

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We can view this as three multiple inputs single output neural networks put together.

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And what do I mean by this.

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See if we take the the input we can just map all of them to a single output.

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If we take the input again we map all of them to another single output and then we take all the input

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we map all of them to a single output again.

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So essentially this is three X multiple inputs single output neural networks put together.

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So let's see how to implement this.

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I'm going to come to our neural network to see file and what we're going to do is create a function

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known as matrix vector multiplication.

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And why am I saying matrix vector multiplication is because our weights are going to be stored in a

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matrix right.

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We're going to have the weight we're going to have a two dimensional array.

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And when I say matrix just think of a two dimensional array.

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For those of you who don't know.

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Um.

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So over here we have a two dimensional array.

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The first row belongs to side the first row it's made up of weight that we use to compute the sad result.

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The second row belongs to weight that we used to compute the sick resort.

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The third row belongs to weight that we used to compute the active resort.

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And when we want to view them in column in terms of columns all fares columns belong to weight that

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we compute with the temperature input all second columns belong to weights that we compute with the

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humidity input and all third columns belong to weights that we compute the air quality input.

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So we're going to keep all of this back together in a matrix or two dimensional array and then we're

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going to

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and then we're going to sort of multiplied by effector rights and the vector is going to be our input

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because we have just three inputs and we have this weight.

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The input is going to be one dimensional Larry.

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Therefore it is a vector.

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And the weight as we've described here is a matrix two dimensional.

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Hence we going to write a function to perform matrix vector multiplication or vector make matrix multiplication.

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However you want to call it so.

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Okay I'll come down here and then

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let's see come down here.

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I'll create a new function void.

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I'm assuming a bit

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void matrix

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vector multiplication like this.

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The first argument is going to be of type double and we're going to take a pointer to the input for

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actual

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The second argument is gonna be the inputs length.

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We can see you into 30 to 40

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inputs land.

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The third argument is going to be effector to store the output because the output is going to be three

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different values.

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So we can store them in a one dimensional array.

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So we are going to go back to you into 30 to underscore t and we said a vector to store the output.

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So we see a double star you can call this output vector

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and we can to improve readability.

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We can just see another variable to store the outputs leant in.

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In our case the output length is the same as the inputs length.

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It's not always the case.

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If we said we just wanted to uh if we said if we said we just wanted to predict sad and sick without

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active then the outputs length it would be just too.

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But this is just a coincidence that the input length is the same as the output length.

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So if you want to try with a different neural network then let's make the output length flexible such

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that you can pass an argument for your new output length or your custom output land.

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I'm gonna say in that to underscore T over here you outlined

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and the last argument is going to be a matrix to hold the weights and it's gonna be of type double

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going to call this weight matrix

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put an S over here and the size of this

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is gonna be output length.

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How do we know the size we can see from our image here.

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The size of this is going to be the rows equal to the number of output at the columns because the number

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of input you see the first row belongs to side which is an output.

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Second row sic output third row active.

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So the rows number of rows of course number of output and number of columns because number of inputs

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so the size here is going to be output length

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and input length here like this

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and open

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and close.

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Right.

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So now we can implement this and we are going to use a that for loop to help us do this.

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Let's see you start off by saying for

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I say 4 into K equals zero K is less than the output lent

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K plus plus an inside this I'm going to do for I

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for int i equals your eye is less than the input line.

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And a plus plus open and close.

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And what we are essentially trying to do is come over here take this.

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Finish processing this row and then go to the next row.

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Because remember input Len represent the rows.

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The number of rows so the outer loop is the number of rows the inner loop is the number of input.

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So when we come we first come to rule 1 and then we we process these values and then we go to row to

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process these values and they rule 3.

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That is what our nested for loop here would do for us and all we have to do here is say output vector

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index K plus we use our accumulator we say input vector index I times.

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Wait wait.

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Matrix index K index I.

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So you understand index K here.

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So we first though it k equals zero.

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And then ask k equals zero.

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We do K equals zero equals zero K.

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Cause your I equals 1 k equals zero aqueous 2.

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So K equals zero represent this rule.

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K equals zero equals zero is zero point two K.

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Close your eyes because 1 it represents you point one K cause your eye equals to represent zero point

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five.

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So we process this and then it becomes k equals 1 and then we do K K was 1 equals U K equals 1 I of

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course one in a K cos one equals two.

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And then it becomes k equals 2.

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Over here I know you get it.

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Okay.

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So that's how we will process this.

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So this all we have to write for this and we can wrap it around our function known as multiple input

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multiple output and n come over here.

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Void

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what will inputs

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which will outputs n n.

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And we take the same document a copy over here.

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Okay

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um let's see

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come down here and open and close.

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Right.

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And we simply need to call our function our matrix vector multiplication function

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and we pass the same document the first one is input vector

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the second one is input lent

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the first output vector

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then outputs land and then way to matrix

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right.

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So put a semicolon here and we can expose this function

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bring it over here

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patient over here on a semicolon here

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right.

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So we can try it out in our main file.

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We can start off okay.

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We have sat here at zero point nine.

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We don't need this.

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We can just clean everything to prevent confusion.

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Right.

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So I'm gonna put some defined statements here to hold the indices.

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I'm gonna see a sad prediction index.

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So the resort offside is going to be stored in the first index of the output vector.

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Then we're gonna have six prediction index.

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So it's sad or happy sick or healthy active or inactive

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and then when I say define output length here

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defined in Poland

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and we know our input is three in our output is three as well.

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That's why I'm pausing three and three here and we have to create the effect or to hold the predicted

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values

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like this.

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Right.

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So this what we have now.

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Okay let's declare our wait let's say double.

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Remember we said a way is a two dimensional array and I'm going to say weights and the sizes outputs

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led by inputs Len.

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So the first row belongs to the decide prediction.

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So we can see it a way to minus zero point two

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hope on nine point five.

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And then let's see two points 0 1 over there and then we go to row 2.

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This is going to be for the sake of prediction

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C minus four point eight seven point two six point three.

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And then we can go to the third row.

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There's going to be for the active prediction.

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C minus four point five point four five.

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And let's say zero point nine

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like this.

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And so I just put a bit of comment here.

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The first column belongs to temperature.

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The temperature puts the second column as humidity and this one the last one is air quality.

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And when we want to view it according to Rose The first rule belongs to Saad

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Sardo happy.

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The second rule is sick or healthy and the last rule is active or inactive.

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Right.

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So once we've done this less let's say we have some input I'm going to create an input vector here

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and the length of the vector is the inline

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and we can see temperatures 30 degrees Celsius and humidity we can see it's 87.

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Air quality can be at 110 and it will be helpful to have a comment here showing you our input arrangement

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as well

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right.

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So once they start we can call our new network function.

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So I'm going to come over here and say

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multiple inputs multiple up and the first document as you can see over here is the input vector which

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we call input or input vector here.

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The second argument as you can see over here is the output vector.

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And we call that I think the second argument is the input length and we have a defined statement to

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that in Len.

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The third argument is the output vector which we call predicted output.

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The next argument is the output length which we have out Len.

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The argument following that is the the weight matrix which we call weight

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and that's all right.

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So we can print some resorts here or come over here and see print f

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sad prediction but this percentage F and then output courage return and then what I want is a one to

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go to our predicted output vector and navigate to the sad prediction sad prediction index and I can

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do the same for the rest sake prediction and active prediction

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right.

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So this order is I've got to build and see what it looks like.

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We've got no arrow Click here to download onto the board let us open to return

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or reset my board.

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So this what we have.

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Right.

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So based on the weight this what we get sad prediction is this sick prediction is that an active prediction

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and like I said the meaning of all of this can just be a way of encode in words to numbers such that

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we know a particular numerical value represents what are you sad or sick.

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And that I want to represent what you are you know whether you are sad or happy and I want to represent

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what I you are sick or healthy etc. So this how to implement the multiple input multiple output neural

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network and I'll see you in the next lesson.