Shortcuts

Quantization

Warning

Quantization is in beta and subject to change.

Introduction to Quantization

Quantization refers to techniques for performing computations and storing tensors at lower bitwidths than floating point precision. A quantized model executes some or all of the operations on tensors with integers rather than floating point values. This allows for a more compact model representation and the use of high performance vectorized operations on many hardware platforms. PyTorch supports INT8 quantization compared to typical FP32 models allowing for a 4x reduction in the model size and a 4x reduction in memory bandwidth requirements. Hardware support for INT8 computations is typically 2 to 4 times faster compared to FP32 compute. Quantization is primarily a technique to speed up inference and only the forward pass is supported for quantized operators.

PyTorch supports multiple approaches to quantizing a deep learning model. In most cases the model is trained in FP32 and then the model is converted to INT8. In addition, PyTorch also supports quantization aware training, which models quantization errors in both the forward and backward passes using fake-quantization modules. Note that the entire computation is carried out in floating point. At the end of quantization aware training, PyTorch provides conversion functions to convert the trained model into lower precision.

At lower level, PyTorch provides a way to represent quantized tensors and perform operations with them. They can be used to directly construct models that perform all or part of the computation in lower precision. Higher-level APIs are provided that incorporate typical workflows of converting FP32 model to lower precision with minimal accuracy loss.

Today, PyTorch supports the following backends for running quantized operators efficiently:

  • x86 CPUs with AVX2 support or higher (without AVX2 some operations have inefficient implementations)

  • ARM CPUs (typically found in mobile/embedded devices)

The corresponding implementation is chosen automatically based on the PyTorch build mode.

Note

At the moment PyTorch doesn’t provide quantized operator implementations on CUDA - this is the direction for future work. Move the model to CPU in order to test the quantized functionality.

Quantization-aware training (through FakeQuantize) supports both CPU and CUDA.

Note

When preparing a quantized model, it is necessary to ensure that qconfig and the engine used for quantized computations match the backend on which the model will be executed. Quantization currently supports two backends: fbgemm (for use on x86, https://github.com/pytorch/FBGEMM) and qnnpack (for use on the ARM QNNPACK library https://github.com/pytorch/QNNPACK). For example, if you are interested in quantizing a model to run on ARM, it is recommended to set the qconfig by calling:

qconfig = torch.quantization.get_default_qconfig('qnnpack')

for post training quantization and

qconfig = torch.quantization.get_default_qat_qconfig('qnnpack')

for quantization aware training.

In addition, the torch.backends.quantized.engine parameter should be set to match the backend. For using qnnpack for inference, the backend is set to qnnpack as follows

torch.backends.quantized.engine = 'qnnpack'

Quantization API Summary

There are three types of quantization supported in PyTorch:

  1. dynamic quantization (weights quantized with activations read/stored in floating point and quantized for compute.)

  2. static quantization (weights quantized, activations quantized, calibration required post training)

  3. quantization aware training (weights quantized, activations quantized, quantization numerics modeled during training)

Please see our Introduction to Quantization on Pytorch blog post for a more comprehensive overview of the tradeoffs between these quantization types.

Dynamic Quantization

This is the simplest to apply form of quantization where the weights are quantized ahead of time but the activations are dynamically quantized during inference. This is used for situations where the model execution time is dominated by loading weights from memory rather than computing the matrix multiplications. This is true for for LSTM and Transformer type models with small batch size.

Diagram:

# original model
# all tensors and computations are in floating point
previous_layer_fp32 -- linear_fp32 -- activation_fp32 -- next_layer_fp32
                 /
linear_weight_fp32

# dynamically quantized model
# linear and conv weights are in int8
previous_layer_fp32 -- linear_int8_w_fp32_inp -- activation_fp32 -- next_layer_fp32
                     /
   linear_weight_int8

API example:

import torch

# define a floating point model
class M(torch.nn.Module):
    def __init__(self):
        super(M, self).__init__()
        self.fc = torch.nn.Linear(4, 4)

    def forward(self, x):
        x = self.fc(x)
        return x

# create a model instance
model_fp32 = M()
# create a quantized model instance
model_int8 = torch.quantization.quantize_dynamic(
    model_fp32,  # the original model
    {torch.nn.Linear},  # a set of layers to dynamically quantize
    dtype=torch.qint8)  # the target dtype for quantized weights

# run the model
input_fp32 = torch.randn(4, 4, 4, 4)
res = model_int8(input_fp32)

To learn more about dynamic quantization please see our dynamic quantization tutorial.

Static Quantization

Static quantization quantizes the weights and activations of the model. It fuses activations into preceding layers where possible. It requires calibration with a representative dataset to determine optimal quantization parameters for activations. Post Training Quantization is typically used when both memory bandwidth and compute savings are important with CNNs being a typical use case. Static quantization is also known as Post Training Quantization or PTQ.

Diagram:

# original model
# all tensors and computations are in floating point
previous_layer_fp32 -- linear_fp32 -- activation_fp32 -- next_layer_fp32
                    /
    linear_weight_fp32

# statically quantized model
# weights and activations are in int8
previous_layer_int8 -- linear_with_activation_int8 -- next_layer_int8
                    /
  linear_weight_int8

API Example:

import torch

# define a floating point model where some layers could be statically quantized
class M(torch.nn.Module):
    def __init__(self):
        super(M, self).__init__()
        # QuantStub converts tensors from floating point to quantized
        self.quant = torch.quantization.QuantStub()
        self.conv = torch.nn.Conv2d(1, 1, 1)
        self.relu = torch.nn.ReLU()
        # DeQuantStub converts tensors from quantized to floating point
        self.dequant = torch.quantization.DeQuantStub()

    def forward(self, x):
        # manually specify where tensors will be converted from floating
        # point to quantized in the quantized model
        x = self.quant(x)
        x = self.conv(x)
        x = self.relu(x)
        # manually specify where tensors will be converted from quantized
        # to floating point in the quantized model
        x = self.dequant(x)
        return x

# create a model instance
model_fp32 = M()

# model must be set to eval mode for static quantization logic to work
model_fp32.eval()

# attach a global qconfig, which contains information about what kind
# of observers to attach. Use 'fbgemm' for server inference and
# 'qnnpack' for mobile inference. Other quantization configurations such
# as selecting symmetric or assymetric quantization and MinMax or L2Norm
# calibration techniques can be specified here.
model_fp32.qconfig = torch.quantization.get_default_qconfig('fbgemm')

# Fuse the activations to preceding layers, where applicable.
# This needs to be done manually depending on the model architecture.
# Common fusions include `conv + relu` and `conv + batchnorm + relu`
model_fp32_fused = torch.quantization.fuse_modules(model_fp32, [['conv', 'relu']])

# Prepare the model for static quantization. This inserts observers in
# the model that will observe activation tensors during calibration.
model_fp32_prepared = torch.quantization.prepare(model_fp32_fused)

# calibrate the prepared model to determine quantization parameters for activations
# in a real world setting, the calibration would be done with a representative dataset
input_fp32 = torch.randn(4, 1, 4, 4)
model_fp32_prepared(input_fp32)

# Convert the observed model to a quantized model. This does several things:
# quantizes the weights, computes and stores the scale and bias value to be
# used with each activation tensor, and replaces key operators with quantized
# implementations.
model_int8 = torch.quantization.convert(model_fp32_prepared)

# run the model, relevant calculations will happen in int8
res = model_int8(input_fp32)

To learn more about static quantization, please see the static quantization tutorial.

Quantization Aware Training

Quantization Aware Training models the effects of quantization during training allowing for higher accuracy compared to other quantization methods. During training, all calculations are done in floating point, with fake_quant modules modeling the effects of quantization by clamping and rounding to simulate the effects of INT8. After model conversion, weights and activations are quantized, and activations are fused into the preceding layer where possible. It is commonly used with CNNs and yields a higher accuracy compared to static quantization. Quantization Aware Training is also known as QAT.

Diagram:

# original model
# all tensors and computations are in floating point
previous_layer_fp32 -- linear_fp32 -- activation_fp32 -- next_layer_fp32
                      /
    linear_weight_fp32

# model with fake_quants for modeling quantization numerics during training
previous_layer_fp32 -- fq -- linear_fp32 -- activation_fp32 -- fq -- next_layer_fp32
                           /
   linear_weight_fp32 -- fq

# quantized model
# weights and activations are in int8
previous_layer_int8 -- linear_with_activation_int8 -- next_layer_int8
                     /
   linear_weight_int8

API Example:

import torch

# define a floating point model where some layers could benefit from QAT
class M(torch.nn.Module):
    def __init__(self):
        super(M, self).__init__()
        # QuantStub converts tensors from floating point to quantized
        self.quant = torch.quantization.QuantStub()
        self.conv = torch.nn.Conv2d(1, 1, 1)
        self.bn = torch.nn.BatchNorm2d(1)
        self.relu = torch.nn.ReLU()
        # DeQuantStub converts tensors from quantized to floating point
        self.dequant = torch.quantization.DeQuantStub()

    def forward(self, x):
        x = self.quant(x)
        x = self.conv(x)
        x = self.bn(x)
        x = self.relu(x)
        x = self.dequant(x)
        return x

# create a model instance
model_fp32 = M()

# model must be set to train mode for QAT logic to work
model_fp32.train()

# attach a global qconfig, which contains information about what kind
# of observers to attach. Use 'fbgemm' for server inference and
# 'qnnpack' for mobile inference. Other quantization configurations such
# as selecting symmetric or assymetric quantization and MinMax or L2Norm
# calibration techniques can be specified here.
model_fp32.qconfig = torch.quantization.get_default_qat_qconfig('fbgemm')

# fuse the activations to preceding layers, where applicable
# this needs to be done manually depending on the model architecture
model_fp32_fused = torch.quantization.fuse_modules(model_fp32,
    [['conv', 'bn', 'relu']])

# Prepare the model for QAT. This inserts observers and fake_quants in
# the model that will observe weight and activation tensors during calibration.
model_fp32_prepared = torch.quantization.prepare_qat(model_fp32_fused)

# run the training loop (not shown)
training_loop(model_fp32_prepared)

# Convert the observed model to a quantized model. This does several things:
# quantizes the weights, computes and stores the scale and bias value to be
# used with each activation tensor, fuses modules where appropriate,
# and replaces key operators with quantized implementations.
model_fp32_prepared.eval()
model_int8 = torch.quantization.convert(model_fp32_prepared)

# run the model, relevant calculations will happen in int8
res = model_int8(input_fp32)

To learn more about quantization aware training, please see the QAT tutorial.

Quantized Tensors

PyTorch supports both per tensor and per channel asymmetric linear quantization. Per tensor means that all the values within the tensor are scaled the same way. Per channel means that for each dimension, typically the channel dimension of a tensor, the values in the tensor are scaled and offset by a different value (effectively the scale and offset become vectors). This allows for lesser error in converting tensors to quantized values.

The mapping is performed by converting the floating point tensors using

_images/math-quantizer-equation.png

Note that, we ensure that zero in floating point is represented with no error after quantization, thereby ensuring that operations like padding do not cause additional quantization error.

In order to do quantization in PyTorch, we need to be able to represent quantized data in Tensors. A Quantized Tensor allows for storing quantized data (represented as int8/uint8/int32) along with quantization parameters like scale and zero_point. Quantized Tensors allow for many useful operations making quantized arithmetic easy, in addition to allowing for serialization of data in a quantized format.

Quantization Operation coverage

Quantized Tensors support a limited subset of data manipulation methods of the regular full-precision tensor. For NN operators included in PyTorch, we restrict support to:

  1. 8 bit weights (data_type = qint8)

  2. 8 bit activations (data_type = quint8)

Note that operator implementations currently only support per channel quantization for weights of the conv and linear operators. Furthermore the minimum and the maximum of the input data is mapped linearly to the minimum and the maximum of the quantized data type such that zero is represented with no quantization error.

Additional data types and quantization schemes can be implemented through the custom operator mechanism.

Many operations for quantized tensors are available under the same API as full float version in torch or torch.nn. Quantized version of NN modules that perform re-quantization are available in torch.nn.quantized. Those operations explicitly take output quantization parameters (scale and zero_point) in the operation signature.

In addition, we also support fused versions corresponding to common fusion patterns that impact quantization at: torch.nn.intrinsic.quantized.

For quantization aware training, we support modules prepared for quantization aware training at torch.nn.qat and torch.nn.intrinsic.qat

The list of supported operations is sufficient to cover typical CNN and RNN models

Quantization Customizations

While default implementations of observers to select the scale factor and bias based on observed tensor data are provided, developers can provide their own quantization functions. Quantization can be applied selectively to different parts of the model or configured differently for different parts of the model.

We also provide support for per channel quantization for conv2d(), conv3d() and linear()

Quantization workflows work by adding (e.g. adding observers as .observer submodule) or replacing (e.g. converting nn.Conv2d to nn.quantized.Conv2d) submodules in the model’s module hierarchy. It means that the model stays a regular nn.Module-based instance throughout the process and thus can work with the rest of PyTorch APIs.

Model Preparation for Quantization

It is necessary to currently make some modifications to the model definition prior to quantization. This is because currently quantization works on a module by module basis. Specifically, for all quantization techniques, the user needs to:

  1. Convert any operations that require output requantization (and thus have additional parameters) from functionals to module form (for example, using torch.nn.ReLU instead of torch.nn.functional.relu).

  2. Specify which parts of the model need to be quantized either by assigning .qconfig attributes on submodules or by specifying qconfig_dict. For example, setting model.conv1.qconfig = None means that the model.conv layer will not be quantized, and setting model.linear1.qconfig = custom_qconfig means that the quantization settings for model.linear1 will be using custom_qconfig instead of the global qconfig.

For static quantization techniques which quantize activations, the user needs to do the following in addition:

  1. Specify where activations are quantized and de-quantized. This is done using QuantStub and DeQuantStub modules.

  2. Use torch.nn.quantized.FloatFunctional to wrap tensor operations that require special handling for quantization into modules. Examples are operations like add and cat which require special handling to determine output quantization parameters.

  3. Fuse modules: combine operations/modules into a single module to obtain higher accuracy and performance. This is done using the torch.quantization.fuse_modules() API, which takes in lists of modules to be fused. We currently support the following fusions: [Conv, Relu], [Conv, BatchNorm], [Conv, BatchNorm, Relu], [Linear, Relu]

Best Practices

  1. Set the reduce_range argument on observers to True if you are using the fbgemm backend. This argument prevents overflow on some int8 instructions by reducing the range of quantized data type by 1 bit.

Modules that provide quantization functions and classes

torch.quantization

This module implements the functions you call directly to convert your model from FP32 to quantized form. For example the prepare() is used in post training quantization to prepares your model for the calibration step and convert() actually converts the weights to int8 and replaces the operations with their quantized counterparts. There are other helper functions for things like quantizing the input to your model and performing critical fusions like conv+relu.

torch.nn.intrinsic

This module implements the combined (fused) modules conv + relu which can then be quantized.

torch.nn.intrinsic.qat

This module implements the versions of those fused operations needed for quantization aware training.

torch.nn.intrinsic.quantized

This module implements the quantized implementations of fused operations like conv + relu.

torch.nn.qat

This module implements versions of the key nn modules Conv2d() and Linear() which run in FP32 but with rounding applied to simulate the effect of INT8 quantization.

torch.nn.quantized

This module implements the quantized versions of the nn layers such as ~`torch.nn.Conv2d` and torch.nn.ReLU.

torch.nn.quantized.dynamic

Dynamically quantized Linear, LSTM, LSTMCell, GRUCell, and RNNCell.

Docs

Access comprehensive developer documentation for PyTorch

View Docs

Tutorials

Get in-depth tutorials for beginners and advanced developers

View Tutorials

Resources

Find development resources and get your questions answered

View Resources