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Hello, everyone, and welcome to this new and amazing section in which we are going to treat the mobile

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net architecture.

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This was first developed by Google researchers in 2017 and we have the mobile net version one and 2019.

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The again, develop the mobile net version two.

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And after this, there was a mobile version three.

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But yeah, we are just going to focus on this mobile net version two entitled Inverted Residuals and

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Linear Bottlenecks.

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By just looking at the title, we could guess the type of environments for which this model was built

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for.

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In fact, the mobile nets have been built for environments with low compute resources like the mobile

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and edge devices.

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So in this section we are going to focus on what permits this model that is the mobile net v two to

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perform quite well in terms of speed while producing high quality results.

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There are two major techniques which make the mobile net version two very powerful, all which permits

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them all which permits us work at higher speeds while still maintaining reasonable quality results.

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Now these two are the dep y separable convolutions and the inverted residual bottleneck which we have

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right here.

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Yours, those separable convolutions, this irregular convolution, your separable convolution.

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And we'll start by explaining what that separable convolution is.

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A deep, separable convolution is simply a combination of a depth wise convolution and a point y convolution.

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Now this point why convolution is not in different from a normal convolution layer, but with kernel

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size of one so one by one convolution.

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Here, that's the point where it's convolution and before this we have the depth wise convolution.

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Now to understand like this, now the deep separable convolution which is this to put together in sequence

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or sequentially.

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Now to understand what this depth wise convolution is, actually let's get back to this demo where we

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saw how usual convolution operation works.

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As you could see here, we have this inputs.

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Basically let's let's have this, let's toggle the movement.

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So yeah, we have some inputs.

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Now this input is three dimensional.

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As you see here we have one, two, three, So 012 we have this three dimensions.

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Let's change the color so it's clear for you to see.

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We have this first dimension, we have the second dimension, and then we have this other third dimension.

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Now, what goes on during the convolution operation is that we have this canal, so we have this year

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and then we have also some canal.

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So in this case, three by three canal.

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We have this on a canal here, three by three.

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And the reason why it is three by three is because we have three channels here and the input.

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So because the inputs are three channel or have three channels, we have a three channel canal.

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Now, here we could add this, we could add a foot channel right here at this four channel.

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And then we'll also have here four of this canals.

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And then what happens is going here during the convolution operation is exactly what we're seeing here.

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So we have this one which is placed at a given position.

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Let's pick its color is place at this position, for example.

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And then we multiply all the values, like let's say we add this point here.

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You see at this point we can see how this filter in this case, this filter.

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So this filter is actually we match this filter with this one, we match this one with this in red.

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We match this one with this in green.

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Now, since there are three, obviously we don't have four.

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Now let's get back to this operation where we take this one and multiply with all the values we have

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here.

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So when we multiply all the values we have here, we get, for example, in this case one by zero plus

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zero times zero plus one times zero.

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You see all this at the top canceled.

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And then we have zero times zero zero times one.

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On council.

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We have one times one year, so we have one and then we have 100 negative, one times one negative one.

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So we have negative one and then negative one times two.

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We have negative two.

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So this gives us a value of negative two and then we move to the next one.

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This one, let's change the color.

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You see, we have one times.

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All this at the top is zero.

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So when we multiply all this by because it's just simply matching.

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So when we have one times zero, we have zero zero times zero zero, one times zero zero, one times

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zero zero, negative one times two, negative two, then negative one times zero.

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We have zero negative one times zero zero, negative one times to negative two.

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So this gives us negative four.

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At this point we have negative four.

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We move to the next one.

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Here we have negative one.

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All this is zero, obviously.

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So we just get to this one one times one.

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we have one zero or negative one and then zero.

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So we have one.

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Let's write that we have one and minus one because this is negative one times one minus one, it gives

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us zero.

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So here we have negative six.

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When you add all this up, basically we taken this, we multiply and then we add, yeah, we take this

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multiply, we add, take this multiply, we add and we add all these values.

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And this gives us your negative six.

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Now, because we have this bias of one, we add plus one, it gives us negative five.

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That's how we obtain this value here.

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So we obtain this one right here.

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Now we'll repeat the same process for all these filters and all the different positions.

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So basically, let's toggle this so you see what happens.

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You see we repeat this process, we move, we move, we go down and that's it.

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There we go.

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So we repeat this to the end and we have this final value right here.

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Then if we want to have you see that we get this.

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So what we have is let's take this off, let's take this orange off.

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What we have is now we have this output.

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So we have the input, which is of the of channel, which has a number of channels to read here.

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We also have this number of channels three, and then we have an output which has a number of channels

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one.

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But if we want the number of channels to be equal, say to like in this case for the output, we have

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one channel and this other channel, then we need to increase the number of filters we have here.

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So basically here we have how many filters.

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We, we, we could create this again.

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So we will have now two.

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If we want to have output two, then we will need to have two of this of this three dimensional filter.

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So we will have this again, we would have this with its own weights, obviously, and we will have

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this and that's it.

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So because we have this two now, we will no longer have an output with one channel, but now an output

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with two channels, as you could see here.

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Now notice how as we click this, we move to this next.

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So this is the this year is this one year.

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Let's pause this.

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So this year is this one right here.

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And this one is this one right here.

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Now, with this, we are able to get this other channel for the output.

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And so that's how the convolution operation works for a normal convolution.

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Now, if we get to the depth wise convolution, we will find that this be different from this method

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for the depth wise convolution.

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As the name goes, this computations are done depth wise.

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So first of all, now here this output will only be gotten from interactions of this channel and this

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channel right here.

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So what goes on here is we take this and then we pass it around, as we usually do, and then we obtain

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this new output right here.

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So if this is three by three, then we obtain some values one, two, three, four, five, six, seven,

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eight, nine.

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So these values will be different from this one, because the way we compute these values is different

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from the way these values were computed.

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The way we computed this value was we take this year, pass it here, take this, pass this, take this,

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pass this here, and then add all our resulting sums to obtain this value of negative five as we saw.

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But in this case, what we'll obtain for this.

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Value will be this five.

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What we'll obtain here will be one times zero zero times zero plus one times 0001 times one.

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We will have one and then you will have zero year one times one.

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Negative one, negative two, negative one, negative two.

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It gives us negative two.

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So what we'll obtain here will be negative two, and then we'll move on to the next, we'll move on

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to the next, we'll go to this next position.

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We'll get some value, as we've seen here and up to this last value right here.

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So the way we got this was we took all this in different four different channels and then we added them

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up to get this bigger.

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We just get this directly by taking for each and every channel and just producing the output like this.

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So this means that with this we are going to have like here, let's take this off with this because

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we are having the each channel all for the filters producing its own output.

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We're going to have this three producing three different outputs.

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So you already we have three outputs, unlike here where we had to output and the two outputs here were

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controlled by the number of canals we used, because here we use two canals, we have two outputs.

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But here we this doesn't matter.

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You're the number of output or the number of input channels we have here will dictate the number of

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outputs.

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So here we have three channels.

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So we just obviously have these three different outputs.

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Now since we have the three output and we want to be able to control the number of output channels,

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what we'll do now after the depth wise convolution, which is in fact what we've just explained here

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is we're going to add now the one by one convolution.

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That's the point where it's convolution after adding the one by one convolution, we are going to specify

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the number of channels here and this number of channels of this one by one convolution that will permit

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us leave from a certain number of channels like in this case three to another number of channel or to

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give a number of channels, let's say two.

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So after getting this three channels or getting up with three channels, we now get, we pass to this

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point where it's convolution and now we're going to get just two channels.

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To better understand this.

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Let's take this dead wide convolution image from papers with code.

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So you're.

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Let's try to reduce this anyway.

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Let's have this.

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You see, we have one, two, three.

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You see this?

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One, two, three.

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This is a five by five canal.

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And then we pass this.

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Notice how each and every one is now responsible for its own output.

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See this?

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See, we have this orange with this foil for this particular channel.

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It gives us an output.

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The red gives us an output.

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The yellow gives us an output unlike previously, where we'll take this pass this year and then add

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all this together.

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But now instead, what we do is we just simply carry out that addition at the level of the channel,

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and then we get this output right here.

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Now, let's see why that wise or that separable convolution is more efficient.

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And we'll do this by calculating the number of filters.

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So here we find the number of filters we need to get from this input, which is one, two, three,

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four, five, six, seven.

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So we have this seven by seven by three inputs which we want to convert to this, three by three by

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two output.

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And here the number of filters and the more parameters we used can be calculated as here we have nine

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times three.

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Obviously in this, nine times three comes from the fact that we have for each of this, we have nine

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and times three.

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The three is from here actually, because we have three input channels, then we'll have three filter

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channels.

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And so we're going to have the filter size, which is three by three.

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I think we should change this color so it makes it clearer.

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Let's change this.

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So here we have seven by seven by three.

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The three is for this number of channels.

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Here we have three by three and then this is three by three, four single one, then times three, this

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number of weights.

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But now, because we want to have let's change this color again here, because we want to have an output

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with two channels, then we would multiply this again by the number of output channels two.

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So this is like some general formula to get a number of parameters.

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We're going to omit the biases.

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So here we have three by three by three, two and seven times 254 parameters.

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Now this means that if we have or we want to have a number of channels of, say, 16, then this will

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give us 432.

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Now, let's consider that we are dealing with depth wise convolution and the point where is convolution

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which both form the depth separable convolution with a depth wise we will have.

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First of all, we have to note that this is no more needed.

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We just need this.

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So what we have will be three by three by.

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Three.

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Now the story comes from the number of inputs by now to get the number of outputs.

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We wouldn't carry out any multiplication here because basically the output from the depth wise convolution

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is a three by three by 3/10 or in this case or more.

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Or we could just say it's a three channel output.

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Since we have three channel inputs, we'll have three channel output.

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So here to obtain the outputs or we just need this, we saw this already, we just take this multiplier,

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get the output, get this first one, we take this multiplier, get this next one, take this multiplier,

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get this next one and we're good to go.

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So once we have this, we now add the the weight for the point.

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Why is convolution now for the point twice it's one by one can also see it's quite cheap compared to

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the three by three channels.

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So one by one here we have one by one.

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So let's just put this here.

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We have one by one now times.

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The inputs, just like with the usual convolution.

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It's the same thing actually, because you're for the for the usual convolution.

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Yeah.

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We have to calculate number of weights, just get the kernel size then like one of the the kernel size

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times it cannot size times the number of input channels times number of output channels.

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So here we have the kernel size times kernel size times the number of input channels, which in this

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case is three and the number of output channels which is two.

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So that's what we have Now.

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If we multiply this, we have 27 plus six.

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That gives us something like 33.

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You see that this gives us territory.

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Now, one interesting point to note here is if we multiply, if we modify this and take and say we want

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to have 16 output channel, then we'll change this two and put 16.

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In that case, our answer will be 27.

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Here we have 27 plus 48 now 27 plus 48 or we get that quickly, five seven, that gives us 75.

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So you see that here we have increased this number of channels from 2 to 16, number of weights, 75.

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But when we did that year, number of weights went to 422.

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So clearly that that wise set or the depth separable convolution is one that is way cheaper than the

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normal convolution.

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And in the paper the others argue that this kind of convolution permits us to reduce the computational

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costs by 8 to 9 times than that of standard convolution.

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While we have only a small reduction in the accuracy.

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That said, from this diagram here, you should now understand why when we presenting a regular convolution,

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the others have this filter.

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You see the filter here which has this depth into the input.

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You see this depth right here, See this?

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Whereas when we present the separable convolution, we have this filter which doesn't have any depth.

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And that's because here we have no inter channel computation or calculations as compared to this one.

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And then after we have this point wise, now the point wise is regular convolution.

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So we see we have this depth again, but now it's smaller in size because it's just a one by one filter.

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The next improvement we should look at is this inverted residual block right here.

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So it's first of all called inverted in comparison to the residual block.

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Now, the residual block, as you may notice, you have this large, relatively large channel, and

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then it becomes small in the middle and then it becomes large in the outputs.

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So this means that we have some inputs, we have some inputs, and then we have our residual block and

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then we have some outputs.

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Then we have obviously this link right here from the input to the output.

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Now with this you see this becomes the data or the inputs big.

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He goes to small and then big.

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But here's what we have is we pass in a relatively small channel, small number of channels or an input

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with relatively smaller number of channels.

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So we are small and then in our block it becomes the number of channels increased and then as output

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number of channels reduced, hence the term inverted residual block.

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Now, in addition to the fact that we're using depth wise convolutions instead of the normal convolutions,

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the fact that we have relatively lower dimensional data getting into this block and lower dimensional

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data, getting out means that we could transport very low dimensional data throughout our mobile network.

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So here we have low dimensional data getting in, low dimensional data getting out, and then inside

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we have this expansion layer right here as this expansion layer permits us to capture as much information

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as possible from our input features.

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One thing to also note is the fact that we're using the rate of six.

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The rule of six is different from a usual value in the sense that we the value we have for all x less

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than zero.

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The value is zero for all x greater than zero, the value is x.

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So we have this Y equals x line right here.

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But with the rate of six as from the value six, we actually clipped this output.

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So what we have here is all values or let's get.

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Back.

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What we have here is we have the values.

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It remains X, but once we get to six, it gets clipped.

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So for all values of X greater than six, the value remains at six.

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So that's a value six.

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And then one other important point is the fact that because we are doing or we are carrying out this

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projection from high dimensional data to a low dimensional data, this réélu nonlinearity generally

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will cause us to lose too much information.

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And because of that, there is no real activation in the final layer here.

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You can see this in the summary right here.

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You see we have the input.

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Then we have the expansion factor, which is DT.

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This means that now we have this hyper parameter which we can turn.

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So if we want better results, we can turn this expansion factor so that it permits us to get this better

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results.

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So here we have this expansion factor DT here, which expands number of channels.

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So we get in with K and then we now move to TC and then we have this TCA which now takes us to K Prime.

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Now also note that here we have the realm of six, really six, but here we have no activation.

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Now that said, this is the summary of our mobile net version two.

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So here you have mobile version two, you have the different bottlenecks.

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There we go.

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And then we have this come to the average pull and then come to the this figure right here also shows

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us how the mobile net version two outperforms the mobile net v one shuffle net and the nice net.

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You see that with the mobile net version two right here.

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If you pick this, let's pick for example, this two, you see the number of operations or the computation

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cost here is almost similar, but we see this great difference in accuracy where the mobile net v two

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outperforms the mobile net V one.

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Then apart from classification, the mobile net v two has been used in other tasks like object detection,

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semantic segmentation and other computer vision tasks where we have low compute resource.