# Basic Functionalities¶

## Quantization function¶

`tensor_quant`

and `fake_tensor_quant`

are 2 basic functions to
quantize a tensor. `fake_tensor_quant`

returns fake quantized tensor
(float value). `tensor_quant`

returns quantized tensor (integer value)
and scale.

```
tensor_quant(inputs, amax, num_bits=8, output_dtype=torch.float, unsigned=False)
fake_tensor_quant(inputs, amax, num_bits=8, output_dtype=torch.float, unsigned=False)
```

Example:

```
from pytorch_quantization import tensor_quant
# Generate random input. With fixed seed 12345, x should be
# tensor([0.9817, 0.8796, 0.9921, 0.4611, 0.0832, 0.1784, 0.3674, 0.5676, 0.3376, 0.2119])
torch.manual_seed(12345)
x = torch.rand(10)
# fake quantize tensor x. fake_quant_x will be
# tensor([0.9843, 0.8828, 0.9921, 0.4609, 0.0859, 0.1797, 0.3672, 0.5703, 0.3359, 0.2109])
fake_quant_x = tensor_quant.fake_tensor_quant(x, x.abs().max())
# quantize tensor x. quant_x will be
# tensor([126., 113., 127., 59., 11., 23., 47., 73., 43., 27.])
# with scale=128.0057
quant_x, scale = tensor_quant.tensor_quant(x, x.abs().max())
```

Backward of both functions are defined as Straight-Through Estimator (STE).

## Descriptor and quantizer¶

`QuantDescriptor`

defines how a tensor should be quantized. There are
also some predefined `QuantDescriptor`

, e.g.
`QUANT_DESC_8BIT_PER_TENSOR`

and
`QUANT_DESC_8BIT_CONV2D_WEIGHT_PER_CHANNEL`

.

`TensorQuantizer`

is the module for quantizing tensors and defined by
`QuantDescriptor`

.

```
from pytorch_quantization.tensor_quant import QuantDescriptor
from pytorch_quantization.nn.modules.tensor_quantizer import TensorQuantizer
quant_desc = QuantDescriptor(num_bits=4, fake_quant=False, axis=(0), unsigned=True)
quantizer = TensorQuantizer(quant_desc)
torch.manual_seed(12345)
x = torch.rand(10, 9, 8, 7)
quant_x = quantizer(x)
```

If `amax`

is given in the `QuantDescriptor`

, `TensorQuantizer`

will use it to quantize. Otherwise, `TensorQuantizer`

will compute amax then quantize. amax will be computed w.r.t `axis`

specified. Note that `axis`

of QuantDescriptor specify remaining axis as oppsed to axis of max().

## Quantized module¶

There are 2 major types of module, `Conv`

and `Linear`

. Both can
replace `torch.nn`

version and apply quantization on both weight and
activation.

Both take `quant_desc_input`

and `quant_desc_weight`

in addition to
arguments of the original module.

```
from torch import nn
from pytorch_quantization import tensor_quant
import pytorch_quantization.nn as quant_nn
# pytorch's module
fc1 = nn.Linear(in_features, out_features, bias=True)
conv1 = nn.Conv2d(in_channels, out_channels, kernel_size)
# quantized version
quant_fc1 = quant_nn.Linear(
in_features, out_features, bias=True,
quant_desc_input=tensor_quant.QUANT_DESC_8BIT_PER_TENSOR,
quant_desc_weight=tensor_quant.QUANT_DESC_8BIT_LINEAR_WEIGHT_PER_ROW)
quant_conv1 = quant_nn.Conv2d(
in_channels, out_channels, kernel_size,
quant_desc_input=tensor_quant.QUANT_DESC_8BIT_PER_TENSOR,
quant_desc_weight=tensor_quant.QUANT_DESC_8BIT_CONV2D_WEIGHT_PER_CHANNEL)
```

# Post training quantization¶

A model can be post training quantized by simply by calling `quant_modules.initialize()`

```
from pytorch_quantization import quant_modules
model = torchvision.models.resnet50()
```

If a model is not entirely defined by module, than TensorQuantizer should be manually created and added to the right place in the model.

## Calibration¶

Calibration is the TensorRT terminology of passing data samples to the quantizer and deciding the best amax for activations. We support 3 calibration method:

`max`

: Simply use global maximum absolute value`entropy`

: TensorRT’s entropy calibration`percentile`

: Get rid of outlier based on given percentile.`mse`

: MSE(Mean Squared Error) based calibration

In above ResNet50 example, calibration method is set to `mse`

, it can
be used as the following example:

```
# Find the TensorQuantizer and enable calibration
for name, module in model.named_modules():
if name.endswith('_input_quantizer'):
module.enable_calib()
module.disable_quant() # Use full precision data to calibrate
# Feeding data samples
model(x)
# ...
# Finalize calibration
for name, module in model.named_modules():
if name.endswith('_input_quantizer'):
module.load_calib_amax()
module.enable_quant()
# If running on GPU, it needs to call .cuda() again because new tensors will be created by calibration process
model.cuda()
# Keep running the quantized model
# ...
```

# Quantization Aware Training¶

Quantization Aware Training is based on Straight Through Estimator (STE) derivative approximation. It is some time known as “quantization aware training”. We don’t use the name because it doesn’t reflect the underneath assumption. If anything, it makes training being “unaware” of quantization because of the STE approximation.

After calibration is done, Quantization Aware Training is simply select a training schedule and continue training the calibrated model. Usually, it doesn’t need to fine tune very long. We usually use around 10% of the original training schedule, starting at 1% of the initial training learning rate, and a cosine annealing learning rate schedule that follows the decreasing half of a cosine period, down to 1% of the initial fine tuning learning rate (0.01% of the initial training learning rate).

## Some recommendations¶

Quantization Aware Training (Essentially a discrete numerical optimization problem) is not a solved problem mathematically. Based on our experience, here are some recommendations:

For STE approximation to work well, it is better to use small learning rate. Large learning rate is more likely to enlarge the variance introduced by STE approximation and destroy the trained network.

Do not change quantization representation (scale) during training, at least not too frequently. Changing scale every step, it is effectively like changing data format (e8m7, e5m10, e3m4, et.al) every step, which will easily affect convergence.

# Export to ONNX¶

The goal of exporting to ONNX is to deploy inference by TensorRT, not ONNX runtime. So we only export fake quantized model into a form TensorRT will take. Fake quantization will be broken into a pair of QuantizeLinear/DequantizeLinear ONNX ops. In future, TensorRT will take the graph, and execute it in int8 in the most optimized way to its capability.

Pytorch doesn’t support exporting fake quantize ops to ONNX yet, but the
code is simple. Add the following code to
`torch/onnx/symbolic_opset10.py`

```
@parse_args('v', 't', 'i', 'i', 'i')
def fake_quantize_per_tensor_affine(g, inputs, scale, zero_point, quant_min=-128, quant_max=127):
if quant_min not in [0, -128] or quant_max not in [127, 255]:
raise TypeError("ONNX defines [0, 255] for quint8 and [-128, 127] for int8, got [{}, {}]".format(
quant_min, quant_max))
scale = scale.float() # Avoid exportor generating double type
zero_point = torch.tensor(zero_point, dtype=torch.int8) # ONNX requires zero_point to be tensor
return g.op("DequantizeLinear", g.op("QuantizeLinear", inputs, scale, zero_point), scale, zero_point)
@parse_args('v', 'v', 'v', 'i', 'i', 'i')
def fake_quantize_per_channel_affine(g, inputs, scale, zero_point, axis, quant_min=-128, quant_max=127):
if quant_min not in [0, -128] or quant_max not in [127, 255]:
raise TypeError("ONNX defines [0, 255] for quint8 and [-128, 127] for int8, got [{}, {}]".format(
quant_min, quant_max))
# ONNX defines zero_point to be int8 or uint8
if quant_min == 0:
zero_point = g.op("Cast", zero_point, to_i=sym_help.cast_pytorch_to_onnx['Byte'])
else:
zero_point = g.op("Cast", zero_point, to_i=sym_help.cast_pytorch_to_onnx['Char'])
return g.op(
"DequantizeLinear",
g.op("QuantizeLinear", inputs, scale, zero_point, axis_i=axis),
scale, zero_point, axis_i=axis)
```

Then set static member of TensorQuantizer to use Pytorch’s own fake quantization functions

```
from pytorch_quantization import nn as quant_nn
quant_nn.TensorQuantizer.use_fb_fake_quant = True
```

Fake quantized model can now be exported to ONNX as other models, follow the instructions in torch.onnx. For example:

```
from pytorch_quantization import nn as quant_nn
from pytorch_quantization import quant_modules
quant_nn.TensorQuantizer.use_fb_fake_quant = True
quant_modules.initialize()
model = torchvision.models.resnet50()
# load the calibrated model
state_dict = torch.load("quant_resnet50-entropy-1024.pth", map_location="cpu")
model.load_state_dict(state_dict)
model.cuda()
dummy_input = torch.randn(128, 3, 224, 224, device='cuda')
input_names = [ "actual_input_1" ]
output_names = [ "output1" ]
# enable_onnx_checker needs to be disabled. See notes below.
torch.onnx.export(
model, dummy_input, "quant_resnet50.onnx", verbose=True, opset_version=10, enable_onnx_checker=False)
```

Note

Note that `axis`

is added to `QuantizeLinear`

and `DequantizeLinear`

in opset13.