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In this lesson,

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you will leverage the tools
that you have just built in order

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to create your own quantizer to quantize
any model in eight-bit precision.

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This quantizer is modality agnostic,
meaning you can apply it on

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vision,
audio texts, and even multimodal models.

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Let's get started
and quantize some models.

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In this lesson,

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we will learn together about how to make
our own quantizer to quantize any model

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in eight-bit precision
using the per channel linear

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quantization scheme that you have seen
in the lesson previously.

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So for that, we'll break down our project
into multiple sub steps.

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So we'll first deep dive into creating a
W8A16 linear layer class.

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And "W8" stands for eight-bit weights
and "A16"

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simply stands for 16 bits activations.

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We use this class to store
eight-bit weights and scales,

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as you have seen previously
on the previous lesson,

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and then we will see how we can replace
all instances

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of torch nn layers
with that new class.

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And then we will build a quantizer
to quantize our model end to end.

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And we will test our quantizer
on many scenarios.

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And we will study the impact of the eight
bit quantization on different models.

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So let's start with the first subtask
that we have defined before.

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So building the W8A16
linear layer class.

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So for this task we'll also break it down
into different multiple subtasks.

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First of all you will build a forward
method called W8A16 forward

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that will take as input eight-bit weights,

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16 bit inputs,

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scales, and optional bias.

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Once you have built this method,
the idea is to call

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that method inside the linear
layers forward pass

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and pass
the 8 bit weights of the linear layer,

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input, the scales that are stored inside
the layer, and the optional bias as well.

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So let's get started.

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So what the W8A16 forward
method will do under the hood

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is to first cast the eight bit weights

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into the same data type as the input.

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So for example, in the case
the input is in float16 or b float16,

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cast the weights into that precision
while keeping

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the weights into the same range as before.

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So between -128 and 127,

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we'll just cast the data type of those weights in,

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half precision so that it will match the data
type of the input.

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Then we will perform, the linear
operation.

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So classic matrix

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multiplication
between the input and the casted weights.

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We will multiply these results together
with the scales

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of the model and optionally add the bias

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once this is done.

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So let's get started.

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So let's first import those modules that
we will use for implementing our method.

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And I'm also I'm also defining here
some random inputs a random int8 matrix,

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random hidden states, random scales,
and random bias.

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So, typically the workflow
would be something as follows.

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So we first cast the weights

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into the same data
type as the hidden states.

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Then on top of that,
you will perform the matrix multiplication

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by calling f.linear from PyTorch.

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All right.

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And then we'll multiply that
with the input scales

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and optionally add a bias term

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at the end of the operation.

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Perfect.

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And notice also for the weight matrix.

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So it has the shape output dimension
input dimension.

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When you perform the matrix multiplication
between the weight matrix

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and the input hidden states, you will have
a vector of batch size output dimension.

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So 132.

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So it's important that the scales have this

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the same shape
as the output shape of your weight matrix.

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And same comment for the bias
so that you can broadcast the operations

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between the output from here
and the scales and the whole output here

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and the bias. Perfect.

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So let's wrap everything
in a single method.

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Perfect.

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And let's also quickly try it out.

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With and without bias.

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Great. So it seems to work fine.

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So I guess we can move forward
with the next building block

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that will leverage the method
that we have just created. To continue

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building our linear layer class,

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we'll start implementing
the init method of that class.

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So recall for this linear layer
we need to store the int8 weights,

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the scales and the bias.

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Let's first start by implementing
the skeleton of the init method.

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So it has to kind of match,

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the signature of the init
method of a torch in our layer.

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So it has to contain
input features, output features

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in order to correctly initialize
the input matrix.

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The weights matrix bias, whether
the linear layer has a bias term or not,

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and data type which would correspond
to the data type of the bias.

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Because our weight matrix
will have a torch that int8 as data type.

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So here

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we're going to define our int8
weights, together with the scales

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that are going to be stored
in the linear layer.

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So if you have done any PyTorch
before this lab,

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you might be directly trying your hands on
doing something like this

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to create your int8 weights,
assigning the new attributes int8 weights,

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being a parameter.

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And then maybe do something like this.

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So the issue with this, with this approach
is that when you create

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an nn. parameter, PyTorch expects

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that parameter where it's able to compute
gradients on it.

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The issue is that with PyTorch,
you can't explicitly compute gradients

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on int8 tensors, yet,
so you should get an error

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if you try just to initialize
a dummy layer

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with this approach.

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So if you try that out, you get an error

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saying "only tensors of floating point
and complexity can require gradients."

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So, the right approach to store int8
weights

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is instead of saving attributes as being

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an endless parameter, is to call
this method called register buffer.

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That way instead of storing a parameter,
we just store a buffer, meaning

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we don't need to compute
gradients on the tensor,

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and you can initialize it
with whatever dtype that you want.

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So if you try that out and
initialize, it just works.

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So let's
continue designing our linear layer.

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So we have our int8 weights.

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And then we'll do the same thing
for scales

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as well by initializing
with the correct shape.

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And we're also going to call register
buffer on scales

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because again, here, we're just expecting
to do simple inference.

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We're not interested in doing training.

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So just calling registered
buffer is sufficient.

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And then we're going to store
an optional bias.

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So if bias is set to true we're just
starting a new buffer called bias.

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Otherwise we'll set it to none.

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So let's quickly try that out and create
a dummy instance of a linear layer

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and see if our attributes
have been correctly saved.

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Perfect. So yeah.

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So all the expected attributes have,
the expected shape.

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So output shape input
shape output output shape or the scales.

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I guess we can move forward with the next task,

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which is building the
forward pass of that class.

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So we're going to copy

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what we did here.

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And we're going to call the method that
we have defined in the first sub task.

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And we're just simply going to call it on
self.int8

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weights,
self.skills, and self.bias.

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And this method will do everything
under the hood for us.

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And we'll take care of casting the weights
into the correct dtype and multiplying

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everything with the scales and optionally
add the whole results with bias.

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All right. So let's create a new module.

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Some dummy hidden states with the shape
batch size,

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sequence length, hidden shape,
which should match the input

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hidden states shape
that we have, passed here.

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Perfect.

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So we still have batch
size, sequence length.

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And here, instead of input
shape, we have output shape.

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It's also check data type.

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So the dtype is correct Float32.

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Because we have initialized
a random tensor

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and by default PyTorch initialize
everything in torch, not Float32.

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Great.

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Now that we have a forward pass
that is working a linear layer class

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that has all the needed attributes,
we need to build, quantize method

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in order to perform
the linear quantization algorithm

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that you have seen in the previous lesson,
so that the weights gets correctly,

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quantized.

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Because right now everything is random.

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So you need to replace all the layers
with this, linear layer,

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you'll get gibberish output most likely.

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So just to give you more idea,

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once we have defined that quantize method,
the workflow will be the following.

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So, you have your base model
that is let's say in half precision.

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So either Fp16 or Vf16.

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Will loop over all the linear
layer classes, replace them

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with our new linear class,
and then call quantize

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by passing the old weights in order
to quantize the old weights into int8.

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So let's redefine our class again.

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And here start
thinking about the quantize method.

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So as I said the quantize method
will take the original weights as input.

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It will quantize the weights in Int8
precision,

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get the scales of the quantization,
and then manually assign int8

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weights and scales to the computed
quantized weights and scales.

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So let's do that step by step.

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So first of all, I would recommend
to upcast the weights in FP32

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for stability.

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So we'll get the weights in Fp32 first
and then we will use

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this simple formula
that you have seen in the previous lesson.

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So we'll first
get the absolute values of the weights.

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Get the maximum on the last dimension
and divide it by

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yeah 127 in order to get the scales.

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So we're going to assign
that to scales variable.

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And make sure that scales
has the same datatype as the input weights

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by calling two weights the dtype.

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And to get the int8 weights,
we'll just apply the formula

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that you have seen on the previous lesson
on linear quantization.

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So this is the per channel,

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linear quantization

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as you're getting the maximum

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on each element of the last dimension.

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So yeah basically
this is how you get the int8 weights.

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Again, it's based on the previous lesson
unrolled.

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We're just simply assigning self

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dot int8 weights and scales

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with these tensors.

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Perfect.

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And the forward pass will stay the same.

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Perfect.

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Okay.

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So let's let's try that out.

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So let's first initialize
the dummy module.

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Maybe print
the int8 weights before quantizing

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and we'll compare the results
afterwards as well.

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I might just take a smaller.

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Yeah.

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All right.

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Let's also pass some dummy random

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original weights.

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So this random matrix will act
as the original weights

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that we're going to use
to quantize your module.

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So let's call module.quantize.

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Perfect.

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So as you can see the weights tensor
are completely different.

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And because we quantized the module
with the correct weights.

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And also

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the int8 weights

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are now between -128 and 127.

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So those values did not exist before
because the module has been

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initialized randomly.

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And since here we're performing
abs max quantitzation.

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We always have these values
in the quantized int8 weights.

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Yeah.

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We can also inspect the scales
of our quantized module

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which look like this.

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I want you to quickly inspect
also the shape of scales.

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So you have a tensor of size four
which is the expected output shape.

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So we're going to do the same for

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int8 weights.

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So four eight.

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So if we directly multiply the two tensors
it won't work.

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So you have to add a new dimension
here in scales.

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All right.

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So let's compare
that against our original weights.

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Yeah. So as you can see,

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if you quickly look into it, the weights
look pretty close.

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We can have also a better idea
by computing the quantization error

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that can be done through this formula.

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So we just,

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subtracting both tensors.

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So the quantized weights
the original weights absolute value.

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So this is the average quantization error
for each element

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between the original weights
and the dequantized weights.

244
00:13:32.211 --> 00:13:32.745
Perfect.