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Okay.

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So we're going to do that in pure PyTorch.

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Let's first import torch and then define
the signature of the method pack_weights.

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That is going to take the unsigned
int8 tensor and the number of bits.

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So the reason why we're using unsigned int
instead of int8 is that for int8 tensor,

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the first bit is used to determine
the sign of the tensor.

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So, just for simplicity
we're going to use unsigned int

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so that we don't have to deal
with the sign bit.

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So recall also
what I've said at the beginning.

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So for simplicity it's better
to have, the shape of the input tensor

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being a multiple of four eight
divided by number of bits.

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So we're just going to add
a small condition here checking

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that if the tensor does
not have the right shape,

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then we're going to raise a small error
saying that the input shape needs

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to be a multiple of the expected number
and print it to the users.

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So, now let's get the

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number of

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values
expected values of the packed tensor.

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So if we come back to our example.

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So this of course
depends on the number of bits that you use

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to encode your values.

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So in case of two bits
we have four values.

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So the number of expected packed values
is simply going to be

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the shape of your input tensor
multiplied by the number of bits.

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So here we have two bits per value.

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And then we have four values.

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So eight bit divided by eight

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because our packed tensor

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is going to be eight bits.

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So number of expected value
is simply going to be number of input

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low bits values
that you're going to retrieve with dot

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shape of zero times the number of bits.

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If either you are in 2 or 4 bits,

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everything divided by eight.

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Perfect.

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So let's come back again
to the example that we had before.

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So in case of two bits, each packet weight
will contain four values two bit.

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We're processing
four parameters per packed parameter.

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So this is going to be our number
of processing steps.

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So we're calling this value num steps.

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That is simply going to be
the number of bits

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of the pack tensor
divided by number of bits.

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Again in our example this should be

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four because of a processing
for two bit values for packed tensor.

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And we're going to

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declare this index

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because we're going to have a four loop.

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And then we initialize our packed tensor
which should contain num values

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and which should be in a
dtype of unsigned eight.

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Perfect.

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Let's first loop on each packed value.

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And then for each packed
value we pack num steps,

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low bit values.

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So we need to loop again here
using a new variable.

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And then we're going to use unpacked index
in order to keep track of

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which values
are we trying to pack in our algorithm.

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So, in the first iteration again

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if we consider the tensor
that we had in our example.

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So I'm going to write it here.

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So 1,0,3,2

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which should be in two bit.

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And then we have our

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so this is uint8 tensor.

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So it's encoded in Int8.

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And we only want to extract those bits.

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And then we have our plain packed tensor
which should only contain

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one value in uint8.

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All right.

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For each num steps here.

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So for each,

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num step.

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So each two bits, we're going to retrieve
the corresponding value.

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So here for example it should be one.

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And then,

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we're going to perform bitwise
shifting on the left

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for this tensor but encoded in eight bits.

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So let me try to break it down below.

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So here,

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this value.

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So it's encoded in uint8.

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So it should give us this value.

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All right.

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And then the idea is
that we're going to take this value

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shifted on the left by bits times J.

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So here since we are on
the first iteration it's going to be zero.

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So nothing is going to be applied here.

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So no shifting on the left.

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So this value should stay like this.

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All right.

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And then we're going to perform bitwise

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or operation on the current packed tensor.

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So let me explain you that.

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So in the first iteration this is how
the packed tensor would look like.

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And this is how the right side
of the equation would look like.

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Here.

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And again we want to pack this here.

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Then this here, this here, and this here.

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So we're going to perform
an bitwise or operation.

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So that zero and 0 or 1 would give us one

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0 or 0 zero and so on.

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So here after the first iteration
the packed tensor

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would exactly look like this. Okay.

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And then on the second iteration
then we're going to increment

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our unpacked index here.

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All right.

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And then on the second iteration
we're going to take this tensor

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but encoded in uint8.

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So now the packed tensor

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would look like this
because of the bitwise or operation.

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And this time the shifting coefficient
is going to be two.

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So you're going to take this tensor.

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It's 000.

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Shift it on the left by two.

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So again it's going to be 000.

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And then you're going to perform
bitwise Or operation

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between the shifted tensor
and the pack tensor.

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And it's still going to be 1000000.

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That's fine because we pack
the first tensor here in two bit.

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We pack the second
thing off here in two bits,

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and then
we're ready to move on to the next one.

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And then on the next iteration

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we're going to have this tensor.

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Okay. Again so encode you in uint8.

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We're going to shift it on the left
this time by.

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So J is going to be equal to two.

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So two times two four.

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So we're going to shift that by four bit.

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And it's going to look like this.

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And then you're going to perform
bitwise or operation.

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And the new pack tensor would look like

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this. Perfect.

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And then on the last iteration
you'll do the same thing

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but this time shifting by six on the left.

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So one zero would be here.

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And then bitwise or at the very end
you would end up like this.

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So the final packed tensor
would look theoretically like this.

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Perfect.

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Yeah.

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Let's try out quickly
our methods and test it.

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And we're going to test it on our toy
example.

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Let's say our unpacked tensor is encoded
as follows:

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1032.

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Again everything encoded in two bit.

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And yeah let's pack the weights
to see if it works.

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Perfect.

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So 177 should be encoded

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exactly like this in uint8.

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You can try that out
verifying the results.

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But yeah that should be
the correct result.

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Perfect. So yeah.

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You can pause the video

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and maybe try to understand
this whole logic.

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Try also maybe to enhance it a bit.

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Optimize it.

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You can also try out with four bits
and yeah, maybe you can also try out

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different combinations.

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For example, you can also battle test

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the method a bit if we add these values.

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So three and two which should be one one.

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So we should have 11111 here everywhere.

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And the second tensor should be 255

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which is the case.