量化知识体系汇总

量化方法与高效神经网络推断综述

介绍-实现高效神经网络的方向

设计高效的NN模型

微观结构优化

• 卷积核调整为depthwise
• 低秩分解
• inception
• 残差结构
• 自动化机器学习（Automl）

宏观结构优化

自动搜索网络结构（EfficienNet）

•     旨在以自动化方式，在给定的模型大小，深度和/或宽度的约束下，找到正确的模型架构

• 神经网络结构搜索（NAS）
• 非结构剪枝-移除不显著的神经元

联合NN架构和硬件条件共同考虑

NN架构调整用于特定的目标硬件平台

剪枝

具有较小响应的神经元被移除，从而得到稀疏的计算图

•     优点：可以进行主动剪枝，去除大部分神经网络参数，对模型的泛化性能影响很小

•     缺点：会导致稀疏矩阵运算，众所周知，稀疏矩阵运算很难加速，而且通常内存有限[21,65]

• 结构剪枝-去除一组参数（例如，整个卷积滤波器）

•     优点：有改变层和权重矩阵的输入和输出形状的效果，因此仍然允许密集的矩阵运算。

•     缺点：过度的结构化剪枝往往会导致精确度显著降低

知识蒸馏

训练一个大模型，然后用它作为老师来训练一个更紧凑小巧的模型

量化

用于推理的量化是本文的重点

量化与神经科学

连续形式存储的信息将不可避免地受到噪声的破坏，离散信号表示对噪声更具鲁棒性

量化的基础概念

问题及符号标记

基础量化概念

均匀量化

• 量化函数

•    

 

• 逆量化函数

•    

 

• 最重要的是缩放因子S的选择，缩放因子的本质是将真实值r的范围一定数量的分区上去

•    

 

• [α,β]是真实值的裁剪范围，b是量化bit宽度，所以想要确定缩放因子S，先要确定[α,β]，选择裁剪范围的过程称为“校准calibration”
• 非对称量化

对称量化和非对称量化

•     裁剪范围选择为−α != β，常见例如：α = r_min,β=r_max

•     非对称量化相比对称量化会有更小的剪切范围

•     当目标权重或激活需要被平衡时，这一点尤其重要，例如，ReLU 之后的激活始终是非负值

• 对称量化

•     裁剪范围选择为−α = β，常见例如：−α=β=  max(|r_max|,|r_min|)

•     两种方法去选择缩放因子S

•     全范围对称量化

•     使用INT8的全部范围，[-128，127]

 

•     限制范围对称量化

•     量化范围是[-127，127]。S的值是

 

•     全范围方法更准确

• 不同的校准(calibration)方法，（α，β）的选择

•     min/max比较常见

•     这种方法容易受到激活中的异常值影响，会增大量化范围，降低量化分辨率

•     使用x/max百分比

•     选择β和α，使得真实值与量化值之间的KL散度（也就是信息损失）最小

• 对称与非对称量化比较

•     对称量化在量化权重的实践中被广泛采用，因为零点归零会导致推论期间计算成本的降低 [247]，并且使实现更加简单。

•     对于剪切范围会变动的，或者不对称的情况，对称量化不如非对称量化

•  

 

静态与动态量化

• 量化激活的方法有两种

•     动态量化

•     范围在运行期间对每个激活映射进行动态计算

•     计算开销大，精度好

•     （常用）静态量化

•     范围是预先计算的，并且在推理期间是静态的

•     不增加计算开销，精度低点

•     范围预计算方法

•     运行一系列校准输入来计算典型的激活范围[112,259]

•     （常用）最小化原始未量化的权重分布和对应的量化值之间的均方误差(MSE)[40,214,221,273]，熵[184]

•     NN训练期间学习该裁剪范围[36,144,268,278]

•     这里值得注意的工作是LQNets[268]、PACT[36]、LSq[56]和LSq+[15]，它们在训练期间联合优化NN中的裁剪范围和权重。

量化粒度

• 如何计算权重的限幅范围[α，β]的粒度

•     逐层量化

•     考虑[131]一层卷积滤波器中的所有权重来确定限幅范围

•     分组量化

•     对层内的多个不同通道进行分组，以计算(激活或卷积内核的)剪切范围

•     逐通道量化

•     对每个卷积滤波器使用固定值，独立于其他通道[104,112,131,215,268,276]

非均匀量化

• 量化步长以及量化级别非均匀间隔

•    

 

•     Xi表示离散量化级别和∆i量化步长(阈值)，∆i和Xi都不是均匀的

•     对于固定的位宽，非均匀量化可能会实现更高的精度，因为人们可以通过更关注重要价值区域或找到适当的动态范围来更好地捕获分布

•     非均匀量化方法

•     典型的非均匀量化是使用对数分布[175,274]

•     其中量化步长和级别以指数而不是线性增加

•     基于二进制代码的量化

•    

 

•     非均匀量化器公式化为一个优化问题

•    

 

fine-tuning方法

量化感知训练(QAT)

• 量化之后重新训练模型，来调整NN的参数

•     反向传播的量化算子微分方法

•     直通估计器（STE）[13]

•     本质上忽略了舍入操作，而用恒等函数来逼近它

•     随机神经元方法作为STE的替代方法[13]

•     组合优化[65]

•     目标传播[138]

•     Gumbel-Softmax[115]

•     消除了在EQ2中使用不可微量化运算符的需要

•     非STE方法[4，8，39，98,142,179,274]

•     使用脉冲训练来近似不连续点的导数[45]

•     Ada round[177]

•     一种自适应舍入方法来代替舍入方法

训练后量化(PTQ)

• 不重新训练模型，来量化调整NN的参数

•     主要论文有：[11，24，40，60，61，68，69，88,107,140,146,170,178,273]

•     优劣

•     PTQ有一个额外的优势，那就是它可以应用于数据有限或未标记的情况，但是精度低了点

•     优化方向

•     偏差校正

•     [11，63]观察量化后权值的均值和方差的固有偏差，并提出偏差校正方法

•     跨层/通道均衡

•     [170,178]表明均衡不同层或通道之间的权重范围(和隐含的激活范围)可以减少量化误差

•     最佳裁剪范围和通道位宽设置

•     ACIQ[11]解析地计算PTQ的最佳裁剪范围和通道位宽设置。       

•     ACIQ可以实现较低的精度下降，但ACIQ中使用的通道激活量化很难在硬件上有效地实现

•     OMSE方法[40]去除了激活时的通道方式量化

•     建议通过优化量化张量和相应的浮点张量之间的L2距离来进行PTQ

•     缓解离群点对PTQ的不利影响，在文献[273]中提出了一种离群点通道分裂(OCS)方法

•     该方法将含有离群点的通道复制并减半。

•     round

•     Adaround[177]

•     它表明朴素的四舍五入量化方法可能会反直觉地导致次优解，并提出了一种自适应舍入方法，更好地减少了损失。

•     AdaQuant[107]

•     相比Adaround,提出了一种更通用的方法，允许量化权重根据需要进行更改。

零点量化（ZSQ）

• 级别1：无数据和无微调(ZSQ+PTQ)

•     [178]的工作，该方法依赖于均衡权值范围和校正偏差误差

•     然而，由于该方法基于(分段)线性激活函数的比例等变特性，因此对于具有非线性激活的NNs，该方法可能是次优的

• 级别2：无数据但需要微调(ZSQ+QAT)

•     gan生成与真实数据相似的合成数据

•     存在问题

•     没有考虑内部统计的合成数据可能不能正确地表示真实数据分布

•     解决方案

•     使用存储在批归一化(BatchNorm)[111]中的统计量，即通道的均值和方差，来生成更真实的合成数据。

•     [84]通过直接最小化内部统计量的KL散度来产生数据

•     ZeroQ方案，待了解

随机量化方法

随机量化将浮点数向上或向下映射为与权重更新的大小相关的概率

• [29，78]中，EQ2中的Int运算符被定义为

•    

 

• 42]将其扩展到二进制量

•    

 

• Quant Noise[59]中：随机权重子集

•     QuantNoise在每次前向传播过程中随机量化不同的权重子集，并使用无偏梯度训练模型

• 随机量化方法的一个主要挑战是为每次权重更新创建随机数的开销，因此它们在实践中还没有被广泛采用
•  

高级概念：量化低于 8 bit

模拟和纯整数量化区别

模拟量化(也称为伪量化)

 

•     伪量化方法对于带宽限制大于计算限制的问题是有益

纯整数量化(也称为定点量化)

•  

 

•     激活函数是relu

•     [151]将批量归一化融合到先前的卷积层中

•     [112]提出了批量归一化残差网络的仅整数计算方法。

•     突破激活函数是relu的限制

•     [130]最近的工作通过用整数算法近似Gelu[93]、Softmax和层归一化[6]来解决这一限制，并进一步将仅限整数的量化扩展到Transformer[235]体系结构。

•     二元量化的思路

•     所有的定标都是用二进数执行的，二进数是分子为整数值、分母为2的幂的有理数[259]

•     所有的加法(例如剩余连接)都强制具有相同的并矢规模，这可以使加法逻辑更简单，效率更高

混合精度量化

每一层都以不同的bit精度进行量化，[51，81,101,182,193,204,231,238,241,255,277]

• 存在的挑战

•     可选择的bit设置的搜索空间与层数成指数关系

• 解决方案

•     基于强化学习

•     [238]提出了一种基于强化学习(RL)的量化策略自动确定方法，并使用硬件模拟器将硬件加速器的反馈纳入RL代理反馈中

•     基于神经网络结构搜索（NAS）

•     [246]将混合精度构型搜索问题描述为一个神经结构搜索(NAS)问题，并用微分NAS(DNAs)方法有效地搜索搜索空间

•     基于周期函数正则化

•     方法是自动区分不同的层及其相对于精度的不同重要性，同时获得它们各自的位宽[179]

•     基于 Hessian

•     HAWQ

•     根据海森矩阵最大特征值确定量化精度与顺序[50]

•     HAWQv2

•     无需任何人工干预即可自动选择不同层的比特精度

•     HAWQv3

•     提出了一种快速整数线性规划方法来为给定的特定应用约束(例如，模型大小或延迟)寻找最优位精度。

硬件感知量化

动机：并不是所有的硬件在某一层/操作被量化后都能提供相同的速度[86，90,238,242,248,248,257,259]

工作[238]使用强化学习代理来确定硬件感知的混合精度量化设置

• 该方法基于不同层的不同位宽的延迟查找表，但是该方法使用模拟的硬件延迟
• 模型蒸馏[3，94,148,173,189,200,260,262,280]是一种利用较高精度的大模型作为教师，帮助训练紧凑的学生模型的方法。

工作[259]直接在硬件中部署量化操作，并测量不同量化位精度下每层的实际部署延迟

蒸馏辅助量化

思路

•     在学生模型的训练过程中，模型蒸馏建议利用教师产生的软概率，这些软概率可能包含更多的输入信息，而不是只使用真实类别标签

•     也就是说，总损失函数包含学生损失和蒸馏损失，通常公式如下

 

方案

• 以往的知识提炼方法侧重于探索不同的知识源
• [94,148,187]使用logits(软概率)作为知识的来源
• [3,200,261]试图利用来自中间层的知识
• [227,265]使用多个教师模型来联合监督学生模型
• [43,269]则在没有教师模型的情况下采用自我蒸馏
• 存在问题

极端低bit量化

二进制量化 [18,25,47,52,77,82,91,92,118,120,122,127,129,133,139,147,152,157,190,192,210,241,243,254,279,281]

•     极端量化很好地提高速度，但不成熟的二值化方法会导致精度显著下降

• 方案

•     BinaryConnect[42]将权重限制为+1或-1

•     权重保持为实值，并且仅在正向和反向传递过程中被二值化，以模拟二值化效果

•     正向传递过程中，基于符号函数将实数值权重转换为+1或-1

•     然后用标准的STE训练方法训练网络，通过不可微符号函数传播梯度。

•     Bi-narized NN(BNN)[106]通过对激活和权重进行二值

•     联合二值化权重和激活还有一个额外的好处，那就是改进了延迟，因为昂贵的浮点矩阵乘法可以被轻量级的XNOR操作取代，然后再进行位计数。

•     [45]中提出的二元权重网络和异或网

•     在权值中加入比例因子并使用+α或-α而不是+1或-1来获得更高的精度。这里，α是选择的比例因子，用于最小化实值权重和结果二值化权重之间的距离。

•     实值权重矩阵W可以表示为W≈αB，其中B是满足以下优化问题的二进制权重矩阵：

 

•     三进制值(例如，+1、0和-1)，显式地允许量化值为零来实现的[143,156]

•     三元二值网络(TBN)[236]，结合二值网络权重和三值激活可以在精度和计算效率之间实现最佳折衷

• 降低极端量化时的精度下降的方案[191]

•     量化误差最小化

•     HORQ[149]和ABC-NET[155]使用多个二进制矩阵的线性组合，即W≈α1b1+···+αmBm，以减少量化误差。

•     改进损失函数

•     [97,98] 减少最终模型损失（不懂，改不改进都要减少模型损失啊）

•     知识蒸馏：全精度的教师模型也有利于提高二值/三值模型的精度 [33, 173, 189, 252]

•     改进训练方法

•     动机

•     STE在通过符号函数反向传播梯度方面的局限性：STE只传播[-1，1]范围内的权重和/或激活的梯度。

•     解决方案

•     符号函数(导数)的近似

•     BNN+[44]：引入了符号函数的导数的连续近似

•     [192,253,264]则用光滑的可微函数替换符号函数，这些函数逐渐锐化并逼近符号函数。

•     Bi-Real Net [160] ：在连续模块中，激活层与激活层之间进行shortcut连接（没看懂）

•     DoReFa-Net[276]：除了对权重和激活进行量化外，还对梯度进行量化

矢量量化

基于k-means量化：[1,30,74,83,116,166,176,184,248]的工作将权重聚类到不同的组中，并在推理过程中使用每组的质心作为量化值

•  

 

基于k-means的矢量量化与剪枝和霍夫曼编码相结合，可以进一步减小模型规模[83]

乘积量化[74,219,248]是矢量量化的扩展，将权重矩阵划分为子矩阵，并对每个子矩阵进行矢量量

问题残留

目前公司用的那个算法较多

fine-tuning时反向传播怎么做的

剪枝，结构化剪枝，去除层和怎么选，去除featuremap,还是去除kernel

非均匀分布(个人想法，概率密度模拟分布)

全范围vs限制范围对称量化

动态量化vs静态量化：微调时只能动态量化呀

模拟量化是量化后运算时逆量化为运算？纯整数量化和模拟量化哪个用的多

量化的困难在哪？工作中的困难

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