WEBVTT
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Now, let's go

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even smaller and do per group
quantization.

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In per group quantization we perform
quantization on groups of n elements.

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Common values for n are 32,

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64, or 128. Per group

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quantization can require a lot of memory.

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Let's say,

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we want to quantize a tensor in four-bit,
and we choose a group size equal to 32.

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We use symmetric mode.

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That means that the zero point
is equal to zero,

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and we store the scales
in floating point 16.

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It means that we are actually quantizing
the tensor in 4.5 bits.

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Since we have four bits, since each
element is stored using four bit

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and we have 16 divided by 32 bit.

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Since we need to store a scale in 16 bits

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for every 32 elements for each element,
you store it in four bit,

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but you also have quantization parameters
and you need to store once

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a scale in 16 bits,
so 16 bits every 32 elements.

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Now let's jump to the code.

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For simplicity,
we will restrict ourselves to the case

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where the tensor is of dimension two
and we will be using the symmetric mode.

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You don't

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need to pay attention to this code
since we will be coding in the notebook.

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Now let's code it.

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So we define the following function.

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Linear q symmetric per group.

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This will take as argument the tensor,

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the group size and the d-type.

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We set the default value torch.int8.

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First,
we need to get the shape of the tensor.

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Then, another restriction for this function

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is that we will be performing
quantization on the rows.

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This is why we also need to make sure
that each row is divisible by group size.

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To confirm that,
we will just use assertion

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so that the shape of the tensor along the
rows is indeed divisible by group size.

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Then, as I said,
we will be restricting ourselves

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to tensors of dimension two.

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Now all we need to do
is to reshape the tensor

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so that we end up with rows of group
size elements.

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To do that, we will use the view function
that we learned about.

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So as you can see, what we do here

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is to make sure that each row contains
group size elements.

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And we put the minus one here
so that it infers

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automatically the right dimension
to have in the first dimension.

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And now if you look at the tensor
we has the setup

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for performing positional quantization.

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We resized this tensor
so that we have rows of group size

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so that we can use the function
that we coded previously.

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That is to say the linear q
symmetric channel quantization.

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So we have quantized tensor

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and scale

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which is equal to linear
q symmetric per channel function.

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And we need to put the tensor
the right dimension.

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So along the rows and the d-type.

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After quantizing the tensor

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we still need to reshape it
to its original shape.

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So we will use the shape
that we stored before.

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Here the d shape.

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To reshape the tensor,

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we use the view
and we just pass this shape.

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Then we can return the quantized tensor
and the scale.

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Now that we have coded

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the per group quantization, now let's code
the linear quantization

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for the quantization
in order to verify our results.

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So we need to define

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this function.

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In that function
we need the quantized tensor

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to scale.

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But we also need the group size.

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Then we need to get the shape
of the quantized tensor.

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That will be useful.

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Then we need to reshape

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the quantized tensor
so that we have rows that contain

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only group size elements.

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To do that,
we put in the view methods minus

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one for the first value and group size
for the second one.

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Then we can reuse the linear

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dequantization methods
we coded before to dequantize the tensor.

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We need to pass the quantized tensor,
the scale and decimal point.

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But since we are
doing symmetric quantization,

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the zero point is equal to zero.

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Then all we need to do is to reshape
the dequantized tensor

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with the shape of the original tensor,
and the shape is stored in q shape.

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Then we return the dequantized tensor.

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Now let's test our implementation.

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We will test a random tensor of size six

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by six and

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let's set group size to be equal to three.

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So, we will get the quantized tensor
and the scale

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using the linear q symmetric group function.

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And we need to pass the test

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tensor as well as the group size.

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Then to verify our results
we also need to

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dequantize the tensor using

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the linear dequantization function
where we need to pass

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the quantized tensor,

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the scale, and the group size.

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Finally, to have the summary
of the quantization process,

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we just need to pass inside the plot
quantization error.

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The following arguments.

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So test tensor,
quantized tensor and dequantized tensor.

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And as you can see,
if you look at the quantized tensor

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you will see that
every three elements in each row

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you will have the maximum value 127.

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It shows that we indeed managed
to quantize

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each three elements in this matrix
along the rows.

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So three elements
here, three here, and so on.

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And you have the quantized tensor.

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As you can see on the right.

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And you can see also that the quantization
error tensor is very, very low

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and that the dequantized tensor is

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practically the same
as the original tensor.

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Let's also print the dequantization error
using the dequantization error function.

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And we just need to pass the test tensor
and the quantized tensor.

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And indeed we have a very very low
quantization error.

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Now is a good time to pause the video
and try a couple of things.

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You can try to change the test tensors.

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Or you can also change the group size.

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And to see what is the effect of the
group size on the dequantization process.