8 位线性量化的数学表达

• 将 32 位浮点(实数)模型转换为 8 位整数模型
  $$\begin{gathered} F_{32}=Scale\ast (I_{int8}-Z) \\ 量化公式：I_{int8}=\frac{F_{32}}{Scale}+Z \end{gathered}$$

对称量化	仿射量化
$Z=0$	$Z\ne 0$
$S=\frac{2\ast max(abs(F_{max}),abs(F_{min}))}{I_{max}-I_{min}}$	$S=\frac{F_{max}-F_{min}}{I_{max}-I_{min}}$
s =max(abs(A1), abs(A2))/(2^7) ,z =0	s = (A1-A2)/(2^8 + 1) ,z = -(ROUND(A2 * s)) - 2^(8-1)
量化到[-127,127]	一般可量化到[-128,127] ([0,255])

卷积的量化（对称量化）

$$\begin{gathered} y_{1,1} \\ =x_{1,1}\ast w_{1,1}+x_{1,2}\ast w_{2,1}+x_{1,3}\ast w_{3,1} \\ =s_a\ast X_{1,1}\ast s_b\ast W_{1,1}+ \\ {s}_c\ast X_{1,2}\ast s_d\ast W_{2,1}+ \\ {s}_e\ast X_{1,3}\ast s_f\ast W_{3,1}(量化) \\ =s_A\ast s_B(X_{1,1}\ast W_{1,1}+X_{1,2}\ast W_{2,1} \\ +X_{1,3}\ast W_{3,1})(需满足s_A=s_a,s_c,s_e才行) \end{gathered}$$

手动实现的一些细节（代码来自github,A simple network quantization demo using pytorch from scratch）

• 基础公式

def quantize_tensor(x, scale, zero_point, num_bits=8, signed=False):if signed:qmin = - 2. ** (num_bits - 1)qmax = 2. ** (num_bits - 1) - 1else:qmin = 0.qmax = 2. ** num_bits - 1.q_x = zero_point + x / scaleq_x.clamp_(qmin, qmax).round_()return q_xdef dequantize_tensor(q_x, scale, zero_point):return scale * (q_x - zero_point)

• 重新定义梯度 pytorch实现简单的straight-through estimator(STE)

class QConv2d(QModule):def __init__(self, conv_module, qi=True, qo=True, num_bits=8):super(QConv2d, self).__init__(qi=qi, qo=qo, num_bits=num_bits)self.num_bits = num_bitsself.conv_module = conv_moduleself.qw = QParam(num_bits=num_bits)self.register_buffer('M', torch.tensor([], requires_grad=False))  # 将M注册为bufferdef freeze(self, qi=None, qo=None):if hasattr(self, 'qi') and qi is not None:raise ValueError('qi has been provided in init function.')if not hasattr(self, 'qi') and qi is None:raise ValueError('qi is not existed, should be provided.')if hasattr(self, 'qo') and qo is not None:raise ValueError('qo has been provided in init function.')if not hasattr(self, 'qo') and qo is None:raise ValueError('qo is not existed, should be provided.')if qi is not None:self.qi = qiif qo is not None:self.qo = qoself.M.data = (self.qw.scale * self.qi.scale / self.qo.scale).dataself.conv_module.weight.data = self.qw.quantize_tensor(self.conv_module.weight.data)self.conv_module.weight.data = self.conv_module.weight.data - self.qw.zero_pointself.conv_module.bias.data = quantize_tensor(self.conv_module.bias.data, scale=self.qi.scale * self.qw.scale,zero_point=0, num_bits=32, signed=True)def forward(self, x):if hasattr(self, 'qi'):self.qi.update(x)x = FakeQuantize.apply(x, self.qi)self.qw.update(self.conv_module.weight.data)x = F.conv2d(x, FakeQuantize.apply(self.conv_module.weight, self.qw), self.conv_module.bias, stride=self.conv_module.stride,padding=self.conv_module.padding, dilation=self.conv_module.dilation, groups=self.conv_module.groups)if hasattr(self, 'qo'):self.qo.update(x)x = FakeQuantize.apply(x, self.qo)return x

PTQ(Post Training Quantization)

• 一个帮助理解量化过程的demo
• A simple network quantization demo using pytorch from scratch

    def quantize(self, num_bits=8):self.qconv1 = QConvBNReLU(self.conv1, self.bn1, qi=True, qo=True, num_bits=num_bits)self.qmaxpool2d_1 = QMaxPooling2d(kernel_size=2, stride=2, padding=0)self.qconv2 = QConvBNReLU(self.conv2, self.bn2, qi=False, qo=True, num_bits=num_bits)self.qmaxpool2d_2 = QMaxPooling2d(kernel_size=2, stride=2, padding=0)self.qfc = QLinear(self.fc, qi=False, qo=True, num_bits=num_bits)

预处理

• ONNX 运行时提供 python API，预处理使用命令python -m onnxruntime.quantization.preprocess
• 官方提供的实例为： python -m onnxruntime.quantization.preprocess --input mobilenetv2-7.onnx --output mobilenetv2-7-infer.onnx

量化（ 动态量化& 静态量化）

静态量化

• 官方提供的实例为：python run.py --input_model mobilenetv2-7-infer.onnx --output_model mobilenetv2-7.quant.onnx --calibrate_dataset ./test_images/
  静态量化方法首先使用一组称为校准数据的输入来运行模型。在这些运行期间，我们计算每个激活的量化参数。这些量化参数作为常量写入量化模型并用于所有输入。

import numpy as np
import onnxruntime
from onnxruntime.quantization import QuantFormat, QuantType, quantize_staticimport resnet50_data_reader
dr = resnet50_data_reader.ResNet50DataReader(calibration_dataset_path, input_model_path
)# Calibrate and quantize model
# Turn off model optimization during quantization
quantize_static(input_model_path,output_model_path,dr,quant_format=args.quant_format,# default=QuantFormat.QDQ, 有两种表示量化 ONNX 模型的方法：面向操作符（QOperator）的所有量化运算符都有自己的 ONNX 定义，如 QLinearConv、MatMulInteger 等。面向张量（QDQ；量化和反量化）。此格式在原始运算符之间插入 DeQuantizeLinear(QuantizeLinear(tensor)) 以模拟量化和反量化过程per_channel=args.per_channel,weight_type=QuantType.QInt8,optimize_model=False,
)

动态量化

• 动态量化动态计算激活的量化参数（比例和零点）。这些计算增加了推理成本，但与静态计算相比通常可以获得更高的准确性。

import onnx
from onnxruntime.quantization import quantize_dynamic, QuantTypemodel_fp32 = 'path/to/the/model.onnx'
model_quant = 'path/to/the/model.quant.onnx'
quantized_model = quantize_dynamic(model_fp32, model_quant)# 
quantized_model = quantize_dynamic(model_fp32, model_quant, weight_type=QuantType.QUInt8)

调试与优化

• 调试与优化见官方的例子
• console python run_qdq_debug.py --float_model mobilenetv2-7-infer.onnx --qdq_model mobilenetv2-7.quant.onnx --calibrate_dataset ./test_images/

参考与更多

• 此工具可用于量化选定的 ONNX 模型。支持基于模型中的运算符。使用详情请参考 ，示例请参考

• 基于离群值去除的卷积神经网络模型训练后量化预处理方法

• Quantizing deep convolutional networks for efficient inference: A whitepaper

• https://zhuanlan.zhihu.com/p/622334595 量化语言模型

FX

• TORCH.FX第二篇——PTQ量化实操

• aware ( a 表加强 + ware 注视 )adj. 意识到的; 意识到; 知道; 明白; 察觉到; 发觉; 发现; 对…有兴趣的; 有…意识的

• Quantization Aware Training 量化感知训练

• 训练同时消弭量化的噪声

• https://zhuanlan.zhihu.com/p/158776813

• 基于OneFlow实现量化感知训练

• Quantization (QAT) Demo on CIFAR10

• Inference of quantization aware trained networks using TensorRT

• https://github.com/666DZY666/micronet

• 还有一个好处是, 你拿到的int8的pytorch模型, 可以无缝的部署到任何支持的框架上, 而不需要再其他框架上再进行量化.

• 使用 TensorFlow 模型优化工具包进行量化感知训练 - 性能与准确性

• Pytorch实现量化感知训练QAT(一)

• Brevitas: quantization-aware training in PyTorch

• 在本研究中，使用了Brevitas工具。它是一个基于流行的PyTorch工具的库，该工具允许训练量化神经网络（QNN）

• Quantization library for PyTorch. Support low-precision and mixed-precision quantization, with hardware implementation through TVM(优化计算图的包）.

• Implements quantized distillation. Code for our paper “Model compression via distillation and quantization”

• Summary, Code for Deep Neural Network Quantization

• [CVPR’20] ZeroQ: A Novel Zero Shot Quantization Framework

• PyTorch implementation for the APoT quantization (ICLR 2020)

• 商汤：PPL Quantization Tool (PPQ) is a powerful offline neural network quantization tool.

• AIMET is a library that provides advanced quantization and compression techniques for trained neural network models.

• 4 bits quantization of LLaMa using GPTQ

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- PyTorch量化感知训练（QAT）步骤

• https://github.com/leimao/PyTorch-Quantization-Aware-Training/blob/main/cifar.py

• https://leimao.github.io/blog/PyTorch-Quantization-Aware-Training/

• Codes for paper: Central Similarity Quantization for Efficient Image and Video Retrieval,