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Quantization

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

PyTorch 1.3 doesn't provide quantized operator implementations on CUDA yet - this is direction of future work. Move the model to CPU in order to test the quantized functionality.

Quantization-aware training (through :class:`~torch.quantization.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'

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

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.

Operation coverage

Quantized Tensors support a limited subset of data manipulation methods of the regular full-precision tensor. (see list below)

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

Current quantized operation list is sufficient to cover typical CNN and RNN models:

Quantized torch.Tensor operations

Operations that are available from the torch namespace or as methods on Tensor for quantized tensors:

torch.nn.functional

Basic activations are supported.

torch.nn.intrinsic

Fused modules are provided for common patterns in CNNs. Combining several operations together (like convolution and relu) allows for better quantization accuracy

torch.nn.qat

Layers for the quantization-aware training

torch.quantization

Observers for computing the quantization parameters

torch.nn.quantized

Quantized version of standard NN layers.

torch.nn.quantized.dynamic

Layers used in dynamically quantized models (i.e. quantized only on weights)

torch.nn.quantized.functional

Functional versions of quantized NN layers (many of them accept explicit quantization output parameters)

Quantized dtypes and quantization schemes

Quantization Workflows

PyTorch provides three approaches to quantize models.

  1. Post Training 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. Applying dynamic quantization to a whole model can be done with a single call to :func:`torch.quantization.quantize_dynamic()`. See the quantization tutorials

  2. Post Training Static Quantization: This is the most commonly used form of quantization where the weights are quantized ahead of time and the scale factor and bias for the activation tensors is pre-computed based on observing the behavior of the model during a calibration process. Post Training Quantization is typically when both memory bandwidth and compute savings are important with CNNs being a typical use case. The general process for doing post training quantization is:

    1. Prepare the model: a. Specify where the activations are quantized and dequantized explicitly by adding QuantStub and DeQuantStub modules. b. Ensure that modules are not reused. c. Convert any operations that require requantization into modules
    2. Fuse operations like conv + relu or conv+batchnorm + relu together to improve both model accuracy and performance.
    3. Specify the configuration of the quantization methods '97 such as selecting symmetric or asymmetric quantization and MinMax or L2Norm calibration techniques.
    4. Use the :func:`torch.quantization.prepare` to insert modules that will observe activation tensors during calibration
    5. Calibrate the model by running inference against a calibration dataset
    6. Finally, convert the model itself with the torch.quantization.convert() method. This does several things: it quantizes the weights, computes and stores the scale and bias value to be used each activation tensor, and replaces key operators quantized implementations.

    See the quantization tutorials

  3. Quantization Aware Training: In the rare cases where post training quantization does not provide adequate accuracy training can be done with simulated quantization using the :class:`torch.quantization.FakeQuantize`. Computations will take place in FP32 but with values clamped and rounded to simulate the effects of INT8 quantization. The sequence of steps is very similar.

    1. Steps (1) and (2) are identical.
    1. Specify the configuration of the fake quantization methods '97 such as selecting symmetric or asymmetric quantization and MinMax or Moving Average or L2Norm calibration techniques.
    2. Use the :func:`torch.quantization.prepare_qat` to insert modules that will simulate quantization during training.
    3. Train or fine tune the model.
    4. Identical to step (6) for post training quantization

    See the quantization tutorials

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.
  2. Specify which parts of the model need to be quantized either by assigning `.qconfig attributes on submodules or by specifying qconfig_dict

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 :class:`~torch.quantization.QuantStub` and :class:`~torch.quantization.DeQuantStub` modules.
  2. Use :class:`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 :func:`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]

torch.quantization

.. automodule:: torch.quantization

This module implements the functions you call directly to convert your model from FP32 to quantized form. For example the :func:`~torch.quantization.prepare` is used in post training quantization to prepares your model for the calibration step and :func:`~torch.quantization.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.

Top-level quantization APIs

.. autofunction:: quantize

.. autofunction:: quantize_dynamic

.. autofunction:: quantize_qat

.. autofunction:: prepare

.. autofunction:: prepare_qat

.. autofunction:: convert

.. autoclass:: QConfig

.. autoclass:: QConfigDynamic

Preparing model for quantization

.. autofunction:: fuse_modules

.. autoclass:: QuantStub

.. autoclass:: DeQuantStub

.. autoclass:: QuantWrapper

.. autofunction:: add_quant_dequant

Utility functions

.. autofunction:: add_observer_

.. autofunction:: swap_module

.. autofunction:: propagate_qconfig_

.. autofunction:: default_eval_fn

Observers

.. autoclass:: Observer
    :members:

.. autoclass:: MinMaxObserver

.. autoclass:: MovingAverageMinMaxObserver

.. autoclass:: PerChannelMinMaxObserver

.. autoclass:: MovingAveragePerChannelMinMaxObserver

.. autoclass:: HistogramObserver

.. autoclass:: FakeQuantize

.. autoclass:: NoopObserver

Debugging utilities

.. autofunction:: get_observer_dict

.. autoclass:: RecordingObserver

torch.nn.intrinsic

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

.. automodule:: torch.nn.intrinsic

ConvBn2d

.. autoclass:: ConvBn2d
    :members:

ConvBnReLU2d

.. autoclass:: ConvBnReLU2d
    :members:

ConvReLU2d

.. autoclass:: ConvReLU2d
    :members:

ConvReLU3d

.. autoclass:: ConvReLU3d
    :members:

LinearReLU

.. autoclass:: LinearReLU
    :members:

torch.nn.instrinsic.qat

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

.. automodule:: torch.nn.intrinsic.qat

ConvBn2d

.. autoclass:: ConvBn2d
    :members:

ConvBnReLU2d

.. autoclass:: ConvBnReLU2d
    :members:

ConvReLU2d

.. autoclass:: ConvReLU2d
    :members:

LinearReLU

.. autoclass:: LinearReLU
    :members:

torch.nn.intrinsic.quantized

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

.. automodule:: torch.nn.intrinsic.quantized

ConvReLU2d

.. autoclass:: ConvReLU2d
    :members:

ConvReLU3d

.. autoclass:: ConvReLU3d
    :members:

LinearReLU

.. autoclass:: LinearReLU
    :members:

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.

.. automodule:: torch.nn.qat

Conv2d

.. autoclass:: Conv2d
    :members:

Linear

.. autoclass:: Linear
    :members:

torch.nn.quantized

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

Functional interface

.. automodule:: torch.nn.quantized.functional


.. autofunction:: relu

.. autofunction:: linear

.. autofunction:: conv2d

.. autofunction:: conv3d

.. autofunction:: max_pool2d

.. autofunction:: adaptive_avg_pool2d

.. autofunction:: avg_pool2d

.. autofunction:: interpolate

.. autofunction:: upsample

.. autofunction:: upsample_bilinear

.. autofunction:: upsample_nearest



.. automodule:: torch.nn.quantized

ReLU

.. autoclass:: ReLU
    :members:

ReLU6

.. autoclass:: ReLU6
    :members:

Conv2d

.. autoclass:: Conv2d
    :members:

Conv3d

.. autoclass:: Conv3d
    :members:

FloatFunctional

.. autoclass:: FloatFunctional
    :members:

QFunctional

.. autoclass:: QFunctional
    :members:

Quantize

.. autoclass:: Quantize
    :members:

DeQuantize

.. autoclass:: DeQuantize
    :members:

Linear

.. autoclass:: Linear
    :members:

torch.nn.quantized.dynamic

.. automodule:: torch.nn.quantized.dynamic

Linear

.. autoclass:: Linear
    :members:

LSTM

.. autoclass:: LSTM
    :members: