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-Machine Learning Systems: Design and Implementation
-The first open-source book to comprehensively cover machine learning systems
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- The first open-source book to comprehensively cover machine learning systems
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- MindSpore Architect
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[C/C++编程接口](chapter_programming_interface/c_python_interaction.md) - - [机器学习框架的编程范式](chapter_programming_interface/ml_programming_paradigm.md) - - [总结](chapter_programming_interface/summary.md) -- [计算图](chapter_computational_graph/index.md) - - [计算图的设计背景和作用](chapter_computational_graph/background_and_functionality.md) - - [计算图的基本构成](chapter_computational_graph/components_of_computational_graph.md) - - [计算图的生成](chapter_computational_graph/generation_of_computational_graph.md) - - [计算图的调度](chapter_computational_graph/schedule_of_computational_graph.md) - - [总结](chapter_computational_graph/summary.md) - -# 进阶篇 - -- [导读](chapter_preface_advanced/index.md) -- [AI编译器和前端技术](chapter_frontend_and_ir/index.md) - - [AI编译器设计原理](chapter_frontend_and_ir/ai_compiler_design_principle.md) - - [AI编译器前端技术概述](chapter_frontend_and_ir/overview_of_frontend.md) - - [中间表示](chapter_frontend_and_ir/intermediate_representation.md) - - [自动微分](chapter_frontend_and_ir/ad.md) - - [类型系统和静态分析](chapter_frontend_and_ir/type_system_and_static_analysis.md) - - [常见前端编译优化方法](chapter_frontend_and_ir/common_frontend_optimization_pass.md) - - [总结](chapter_frontend_and_ir/summary.md) -- [编译器后端和运行时](chapter_backend_and_runtime/index.md) - - [概述](chapter_backend_and_runtime/overview.md) - - [计算图优化](chapter_backend_and_runtime/graph_optimizer.md) - - [算子选择](chapter_backend_and_runtime/kernel_selecter.md) - - [内存分配](chapter_backend_and_runtime/memory_allocator.md) - - [计算调度与执行](chapter_backend_and_runtime/compute_schedule_and_execute.md) - - [算子编译器](chapter_backend_and_runtime/op_compiler.md) - - [总结](chapter_backend_and_runtime/summary.md) -- [硬件加速器](chapter_accelerator/index.md) - - [概述](chapter_accelerator/accelerator_introduction.md) - - [加速器基本组成原理](chapter_accelerator/accelerator_architecture.md) - - [加速器基本编程原理](chapter_accelerator/accelerator_programming.md) - - [加速器实践](chapter_accelerator/accelerator_practise.md) - - [总结](chapter_accelerator/summary.md) -- [数据处理框架](chapter_data_processing/index.md) - - [概述](chapter_data_processing/requirements.md) - - [易用性设计](chapter_data_processing/program_model.md) - - [高效性设计](chapter_data_processing/performance.md) - - [保序性设计](chapter_data_processing/data_order.md) - - [单机数据处理性能的扩展](chapter_data_processing/extension.md) - - [总结](chapter_data_processing/summary.md) -- [模型部署](chapter_model_deployment/index.md) - - [概述](chapter_model_deployment/model_deployment_introduction.md) - - [训练模型到推理模型的转换及优化](chapter_model_deployment/model_converter_and_optimizer.md) - - [模型压缩](chapter_model_deployment/model_compression.md) - - [模型推理](chapter_model_deployment/model_inference.md) - - [模型的安全保护](chapter_model_deployment/model_security.md) - - [总结](chapter_model_deployment/summary.md) -- [分布式训练](chapter_distributed_training/index.md) - - [系统概述](chapter_distributed_training/overview.md) - - [实现方法](chapter_distributed_training/methods.md) - - [机器学习集群架构](chapter_distributed_training/cluster.md) - - [集合通信](chapter_distributed_training/collective.md) - - [参数服务器](chapter_distributed_training/parameter_servers.md) - - [总结](chapter_distributed_training/summary.md) - -# 拓展篇 - -- [导读](chapter_preface_extension/index.md) -- [深度学习推荐系统](chapter_recommender_system/index.md) - - [系统基本组成](chapter_recommender_system/system_architecture.md) - - [多阶段推荐系统](chapter_recommender_system/multi_stage_recommender_system.md) - - [模型更新](chapter_recommender_system/model_update.md) - - [案例分析：支持在线模型更新的大型推荐系统](chapter_recommender_system/case_study.md) - - [小结](chapter_recommender_system/summary.md) -- [联邦学习系统](chapter_federated_learning/index.md) - - [概述](chapter_federated_learning/overview.md) - - [横向联邦学习](chapter_federated_learning/horizontal_fl.md) - - [纵向联邦学习](chapter_federated_learning/vertical_fl.md) - - [隐私加密算法](chapter_federated_learning/privacy_encryption_algorithm.md) - - [展望](chapter_federated_learning/outlook.md) - - [小结](chapter_federated_learning/summary.md) -- [强化学习系统](chapter_reinforcement_learning/index.md) - - [强化学习介绍](chapter_reinforcement_learning/rl_introduction.md) - - [单节点强化学习系统](chapter_reinforcement_learning/single_node_rl.md) - - [多智能体强化学习](chapter_reinforcement_learning/marl.md) - - [多智能体强化学习系统](chapter_reinforcement_learning/marl_sys.md) - - [小结](chapter_reinforcement_learning/summary.md) -- [可解释性AI系统](chapter_explainable_AI/index.md) - - [背景](chapter_explainable_AI/explainable_ai.md) -- [机器人系统](chapter_rl_sys/index.md) - - [机器人系统概述](chapter_rl_sys/rl_sys_intro.md) - - [通用机器人操作系统](chapter_rl_sys/ros.md) - - [案例分析：使用机器人操作系统](chapter_rl_sys/ros_code_ex.md) - - [总结](chapter_rl_sys/summary.md) - -# 附录 - -- [机器学习介绍](appendix_machine_learning_introduction/index.md) - - [神经网络](appendix_machine_learning_introduction/neural_network.md) - - [梯度下降与反向传播](appendix_machine_learning_introduction/gradient_descent.md) - - [经典机器学习方法](appendix_machine_learning_introduction/classic_machine_learning.md) diff --git a/zh_chapters/appendix_machine_learning_introduction/classic_machine_learning.md b/zh_chapters/appendix_machine_learning_introduction/classic_machine_learning.md deleted file mode 100644 index e573e1d..0000000 --- a/zh_chapters/appendix_machine_learning_introduction/classic_machine_learning.md +++ /dev/null @@ -1,72 +0,0 @@ -## 经典机器学习方法 - -大量经典机器学习算法，如 支持向量机(Support Vector Machine，SVM), -K最近邻(K-Nearest Neighbor, KNN)分类算法 和K均值聚类算法(K-Means -Clustering Algorithm)等， -虽然它们有的有网络参数，有的没有网络参数，有的是监督学习算法，有的是无监督学习算法， -训练过程也不一样，但是从系统的角度，它们都是以矩阵运算为基础的。下面，我们来简要介绍一下这些算法。 - -### 支持向量机 - -**支持向量机**(Support Vector -Machine，SVM)，是一种经典的机器学习分类算法，其核心思想在于最大化决策边界到数据点的距离。在这里，我们以线性可分数据为例；对于非线性可分的数据，运用**核方法**(Kernel -Method)即可类似处理。 - -如果训练数据是线性可分的，SVM的目标则是最大化**间隔**(Margin)。首先，我们先来定义最大化间隔的分类器，如下： -$$\min_{{w},b} ~~~\frac{1}{2} ||{w}||^2$$ -$$s.t. ~~~y_i ({w}^T {x_i} + b) \geq 1, ~~~\forall 1 \leq i \leq n$$ -其拉格朗日乘子为 -$$L({w},b,{\lambda}) = \frac{1}{2} ||{w}||^2 + \sum_{i=1}^n \lambda_i (1-y_i({w}^T {x_i} + b))$$ -由于$\frac{1}{2} ||{w}||^2$是凸的，并且$\lambda_i (1-y_i({w}^T {x_i} + b))$是线性的（也是凸的），所以优化问题的解为 -$$\max_{\lambda>0} \min_{{w},b} L({w},b, {\lambda})$$ -求$L$关于${w},b$的导数有 -$$\nabla_{{w}} L= {w} - \sum_{i=1}^n \lambda_i y_i {x_i}$$ -$$\nabla_b L = - \sum_{i=1}^n \lambda_i y_i$$ -令$L$关于${w},b$的导数均为0得到，${w}^* = \sum_{i=1}^n \lambda_i y_i {x_i}$以及$\sum_{i=1}^n \lambda_i y_i = 0$。 -由于当$\lambda$固定的时候，$b$的值对目标函数无贡献，所以可以令$b^* = 0$。 -这时，由对偶性理论和KTT条件，我们得到： -$$y_i ({w}^{*T} {x_i} + b^*) > 1 \Rightarrow \lambda_i^* = 0$$ -$$\lambda_i^* > 0 \Rightarrow y_i ({w}^{*T} {x_i} + b^*) = 1$$ -$${w}^* = \sum_{i=1}^n \lambda_i^* y_i {x_i}$$ -如果$y_i ({w}^{*T} {x_i} + b^*) = 1$，那么${x_i}$就是离超平面$({w}^*,b^*)$最近的点之一，否则就不是。因此，${w}^*$就是离超平面$({w}^*,b^*)$最近的点${x_i}$的线性组合。 - -如此，通过SVM算法，我们实现了数据的分类，并且能够最大化了决策边界到最近点的距离。 -我们定义满足$y_i ({w}^{*T} {x_i} + b^*) = 1$的${x_i}$为**支持向量**(Support -Vectors)，同时把分类器$\hat{y}=sgn({w}^{*T} {x_i} + b^*)$称为支持向量机。 - -### K最近邻算法 - -**K最近邻算法**(K-Nearest -Neighbor，KNN)也是一种传统的机器学习算法，可用于分类、回归等基本的机器学习任务。和上面介绍的SVM算法不同，K最近邻算法的核心思想并不是用一个决策边界把属于不同类的数据分开，而是依靠每个数据点周围几个距离最近的数据的性质，来预测数据点本身的性质。 - -KNN用于分类时，为了预测某个样本点的类别，会进行一次投票。投票的对象为离这个观测样本点最近的K个样本点，每个要投票的样本点可能会被赋予不同的权重，而投票的"内容"则是样本点的类别。处理投票结果的时候，采用的是少数服从多数的决策方法(Majority -Vote)。也就是说，若一个样本点最近的K个样本点中大多数属于某个类别，那么该样本点也属于这个类别。 - -KNN算法的具体描述如下：（1）计算待分类点到各已知类别点的距离；（2）将这些点按照距离排序，并按照距离挑选出最近的K个点；（3）按照每个点的权重进行"统票"，票面内容为点所处的类别；（4）返回得票最高的类别，并作为待分类点的预测类别。 - -KNN算法有几个需要注意的关键问题，包括超参数K的选择，距离的度量方式，还有分类决策规则。对于超参数K，不宜过大，否则会导致很大的近似误差，反之亦不宜过小，否则会导致很大的估计误差。距离的度量，则可以选择曼哈顿距离、欧式距离和闵可夫斯基距离等等。为了降低K值对于预测结果产生的误差和影响，我们通常可以对分类决策规则做一定的规定，比如在投票决策时让距离小的点有更大的权重，距离较大的点权重较小。在编程实现KNN算法的时候，权重等参数都会以矩阵的形式进行运算，以提高运算效率。 - -### K均值聚类算法 - -**K均值聚类算法**(K-Means Clustering -Algorithm)是机器学习中一种常见的无监督聚类算法。在这里，我们首先定义聚类问题：给定数据点${x_1},\cdots, {x_n} \in \mathbb{R}^d$和$K\in \mathbb{N}$，需要划分为$K$个簇${C_1}, \cdots, {C_K} \in \mathbb{R}^d$以及每个数据点所对应的分类中心点${ C_{(1)}}, \cdots, {C_{(n)}}$，以最小化距离和$\sum_i ||{x_i} - {C_{(i)}}||^2$。 - -K均值聚类算法是一种解决聚类问题的算法，算法过程如下： - -- 随机选择${C_1}, \cdots, {C_K}$ - -- 把${x_i}$所对应的分类置为距离其最近的聚类中心点的分类 - -- 计算并赋值${C_K} = \frac{\sum_{{C_{(i)}}={C_K}} {x_i}}{\sum_{{C_{(i)}}={C_K}} 1}$ - -- 重复以上步骤直到算法收敛 - -可以证明，K均值聚类算法会使得距离和$\sum_i ||{x_i} - {C_{(i)}}||^2$不断地单调减小，并且最终能够收敛。不过，算法可能收敛到局部最小值。 - -本章结束语： - -在系统角度，机器学习的算法无论是什么算法，涉及到高维数据任务的现都是矩阵运算实现的。 - -## 参考文献 - -:bibliography:`../references/appendix.bib` \ No newline at end of file diff --git a/zh_chapters/appendix_machine_learning_introduction/gradient_descent.md b/zh_chapters/appendix_machine_learning_introduction/gradient_descent.md deleted file mode 100644 index e7db43c..0000000 --- a/zh_chapters/appendix_machine_learning_introduction/gradient_descent.md +++ /dev/null @@ -1,93 +0,0 @@ -## 梯度下降与反向传播 - -上面大体上介绍了经典神经网络的内容，那么现在有一个问题，这些网络中的参数是如何确定的呢？如果要解决的问题是一个小感知器就能解决的话，参数可以人为地去确定。但是如果是一个深度网络的话，参数的确定需要自动化，也就是所谓的网络训练，而这个过程需要我们设定一个**损失函数**（Loss -Function）来作为训练优化的一个方向。 -常见的损失函数有：1）用来衡量向量之间距离的均方误差(Mean Squared -Error，MSE) -$\mathcal{L} = \frac{1}{N}\|{y}-\hat{{y}}\|^{2}_{2} = \frac{1}{N}\sum_{i=1}^N(y_{i}-\hat{y}_{i})^{2}$ -和 平均绝对误差(Mean Absolute Error，MAE) -$\mathcal{L} = \frac{1}{N}\sum_{i=1}^{N}|y_{i}-\hat{y}_{i}|$ -，其中$N$代表数据样本的数量，用以求平均用，而$y$代表真实标签（Ground -Truth）、$\hat{y}$代表网络输出的预测标签。 -2）分类任务可以用的交叉熵损失（Cross Entropy） -$\mathcal{L} = - \frac{1}{N} \sum_{i=1}^N \bigg(y_{i}\log\hat{y}_{i} + (1 - y_{i})\log(1 - \hat{y}_{i})\bigg)$来作为损失数，当且仅当输出标签和预测标签一样的时候损失值才为零。 - -有了损失值之后，我们就可以利用大量真实标签的数据和优化方法来更新模型参数了，其中最常用的方法是**梯度下降**（Gradient -Descent）。如 :numref:`gradient_descent2`所示， -开始的时候，模型的参数${w}$是随机选取的，然后求出损失值对参数的偏导数$\frac{\partial \mathcal{L}}{\partial {w}}$，通过反复迭代 -${w}:={w}-\alpha\frac{\partial \mathcal{L}}{\partial {w}}$完成优化。这个优化的过程其实就可以降低损失值以达到任务目标，其中$\alpha$是控制优化幅度的**学习率**（Learning -Rate）。 -在实践中，梯度下降最终得到的最小值很大可能是一个局部最小值，而不是全局最小值。不过由于深度神经网络能提供一个很强的数据表达能力，所以局部最小值可以很接近全局最小值，损失值可以足够小。 - -![梯度下降介绍。（左图）只有一个可以训练的参数$w$；（右图）有两个可以训练的参数${w}=[w_1,w_2]$。在不断更新迭代参数后，损失值$\mathcal{L}$会逐渐地减小。但是由于存在很多局部最优解，我们往往不能更新到全局最优解。](../img/ch_basic/gradient_descent2.png) -:width:`600px` -:label:`gradient_descent2` - -那么接下来，在深度神经网络中如何实现梯度下降呢，这需要计算出网络中每层参数的偏导数$\frac{\partial \mathcal{L}}{\partial {w}}$，我们可以用**反向传播**（Back-Propagation） :cite:`rumelhart1986learning,lecun2015deep`来实现。 -接下来， -我们引入一个中间量${\delta}=\frac{\partial \mathcal{L}}{\partial {z}}$来表示损失函数$\mathcal{L}$ -对于神经网络输出${z}$（未经过激活函数，不是$a$）的偏导数， -并最终得到$\frac{\partial \mathcal{L}}{\partial {w}}$。 - -我们下面用一个例子来介绍反向传播算法， -我们设层序号为$l=1, 2, \ldots L$（输出层（最后一层）序号为$L$）。 -对于每个网络层，我们有输出${z}^l$，中间值${\delta}^l=\frac{\partial \mathcal{L}}{\partial {z}^l}$和一个激活值输出${a}^l=f({z}^l)$ -（其中$f$为激活函数）。 -我们假设模型是使用Sigmoid激活函数的多层感知器，损失函数是均方误差（MSE）。也就是说，我们设定： - -- 网络结构${z}^{l}={W}^{l}{a}^{l-1}+{b}^{l}$ - -- 激活函数${a}^l=f({z}^l)=\frac{1}{1+{\rm e}^{-{z}^l}}$ - -- 损失函数$\mathcal{L}=\frac{1}{2}\|{y}-{a}^{L}\|^2_2$ - -我们可以直接算出激活输出对于原输出的偏导数： - -- $\frac{\partial {a}^l}{\partial {z}^l}=f'({z}^l)=f({z}^l)(1-f({z}^l))={a}^l(1-{a}^l)$ - -和损失函数对于激活输出的偏导数： - -- $\frac{\partial \mathcal{L}}{\partial {a}^{L}}=({a}^{L}-{y})$ - -有了这些后，为了进一步得到损失函数对于每一个参数的偏导数，可以使用**链式法则**（Chain -Rule），细节如下： - -首先，从输出层（$l=L$，最后一层）开始向后方传播误差，根据链式法则，我们先计算输出层的中间量： - -- ${\delta}^{L} - =\frac{\partial \mathcal{L}}{\partial {z}^{L}} - =\frac{\partial \mathcal{L}}{\partial {a}^{L}}\frac{\partial {a}^L}{\partial {z}^{L}}=({a}^L-{y})\odot({a}^L(1-{a}^L))$ - -除了输出层（$l=L$）的中间值${\delta}^{L}$，其他层（$l=1, 2, \ldots , L-1$）的中间值${\delta}^{l}$如何计算呢？ - -- 已知模型结构${z}^{l+1}={W}^{l+1}{a}^{l}+{b}^{l+1}$，我们可以直接得到$\frac{\partial {z}^{l+1}}{\partial {a}^{l}}={W}^{l+1}$；而且我们已知$\frac{\partial {a}^l}{\partial {z}^l}={a}^l(1-{a}^l)$ - -- 那么根据链式法则，我们可以得到 ${\delta}^{l} - =\frac{\partial \mathcal{L}}{\partial {z}^{l}} - =\frac{\partial \mathcal{L}}{\partial {z}^{l+1}}\frac{\partial {z}^{l+1}}{\partial {a}^{l}}\frac{\partial {a}^{l}}{\partial {z}^{l}} - =({W}^{l+1})^\top{\delta}^{l+1}\odot({a}^l(1-{a}^l))$ - -根据上面的计算有所有层的中间值${\delta}^l, l=1, 2, \ldots , L$后，我们就可以在此基础上求出损失函数对于每层参数的偏导数：$\frac{\partial \mathcal{L}}{\partial {W}^l}$和$\frac{\partial \mathcal{L}}{\partial {b}^l}$，以此来根据梯度下降的方法来更新每一层的参数。 - -- 已知模型结构${z}^l={W}^l{a}^{l-1}+{b}^l$，我们可以求出 - $\frac{\partial {z}^{l}}{\partial {W}^l}={a}^{l-1}$ 和 - $\frac{\partial {z}^{l}}{\partial {b}^l}=1$ - -- 那么根据链式法则，我们可以得到$\frac{\partial \mathcal{L}}{\partial {W}^l}=\frac{\partial \mathcal{L}}{\partial {z}^l}\frac{\partial {z}^l}{\partial {W}^l}={\delta}^l({a}^{l-1})^\top$ - , - $\frac{\partial \mathcal{L}}{\partial {b}^l}=\frac{\partial \mathcal{L}}{\partial {z}^l}\frac{\partial {z}^l}{\partial {b}^l}={\delta}^l$ - -求得所有偏导数$\frac{\partial \mathcal{L}}{\partial {W}^l}$ 和 -$\frac{\partial \mathcal{L}}{\partial {b}^l}$后，我们就可以用梯度下降更新所有参数${W}^l$ -和 ${b}^l$： - -- ${W}^l:={W}^l-\alpha\frac{\partial \mathcal{L}}{\partial {W}^l}$, - ${b}^l:={b}^l-\alpha\frac{\partial \mathcal{L}}{\partial {b}^l}$ - -但是还有一个问题需要解决，那就是梯度下降的时候每更新一次参数，都需要计算一次当前参数下的损失值。然而，当训练数据集很大时（$N$很大），若每次更新都用整个训练集来计算损失值的话，计算量会非常巨大。 -为了减少计算量，我们使用**随机梯度下降**（Stochastic Gradient -Descent，SGD）来计算损失值。具体来说，我们计算损失值不用全部训练数据，而是从训练集中随机选取一些数据样本来计算损失值，比如选取16、32、64或者128个数据样本，样本的数量被称为**批大小**（Batch -Size）。 -此外，学习率的设定也非常重要。如果学习率太大，可能无法接近最小值的山谷，如果太小，训练又太慢。 -自适应学习率，例如Adam :cite:`KingmaAdam2014`、RMSProp :cite:`tieleman2012rmsprop`和 -Adagrad :cite:`duchi2011adagrad`等，在训练的过程中通过自动的方法来修改学习率，实现训练的快速收敛，到达最小值点。 diff --git a/zh_chapters/appendix_machine_learning_introduction/index.md b/zh_chapters/appendix_machine_learning_introduction/index.md deleted file mode 100644 index 680737b..0000000 --- a/zh_chapters/appendix_machine_learning_introduction/index.md +++ /dev/null @@ -1,12 +0,0 @@ -# 附录：机器学习介绍 - -本书假设读者有一定的机器学习算法基础，因此本章只会简略地介绍一下机器学习，其中的梯度下降方法对本书机器学习系统来说尤为重要，是必须掌握的内容。 - -```toc -:maxdepth: 2 -:numbered: - -neural_network -gradient_descent -classic_machine_learning -``` \ No newline at end of file diff --git a/zh_chapters/appendix_machine_learning_introduction/neural_network.md b/zh_chapters/appendix_machine_learning_introduction/neural_network.md deleted file mode 100644 index f9ef31c..0000000 --- a/zh_chapters/appendix_machine_learning_introduction/neural_network.md +++ /dev/null @@ -1,175 +0,0 @@ -## 神经网络 - -### 感知器 - -:width:`600px` -:label:`single_neuron` - - :numref:`single_neuron`是一个神经元的例子，输入数据$x$根据连线上的权重$w$做加权求和得到输出$z$，我们把这样的模型叫作**感知器**（Perceptron）。 - 因为输入和输出之间只有一层神经连接，这个模型也叫做单层感知器。 :numref:`single_neuron`的模型计算可以写为：$z = w_{1}x_{1}+ w_{2}x_{2} + w_{3}x_{3}$。 - -当输入数据用列向量${x}=[x_1,x_2,x_3]^T$表示，模型权重用行向量${w}=[w_1,w_2,w_3]$表示，那么输出的标量$z$可以写为： - -$$z = -\begin{bmatrix} -w_1,w_2,w_3\\ -\end{bmatrix} -\begin{bmatrix} -x_1\\ -x_2\\ -x_3 -\end{bmatrix} -={w}{x}$$ - -我们可以利用输出标量$z$为输入的加权组合来实现特定任务。 -比如，可以对"好苹果"和"坏苹果"进行分类，输入的$x_1,x_2,x_3$分别代表三种不同的特征：1）红色的程度，2）有没有洞，3）大小。如果苹果的大小对这个判断没有影响，那么对应的权重就为零。 -这个神经网络的训练，其实就是选择合适的权重，来实现我们的任务。比如我们可以选择合适的权重，使得当$z$小于等于$0$时代表"坏苹果"，而当$z$大于$0$时则是"好苹果"。 -则最终的分类输出标签$y$如下，为$1$时代表好，$0$代表坏。这个神经元的输入和输出之间只有一层，所以可以成为单层神经网络。 - -$$ -y = -\begin{cases} -1 & z>0 \\ -0 & z \leq 0 \\ -\end{cases}$$ - -### 决策边界vs.偏置 - -通过选择合适的权重以$z$大于或小于$0$来对输入数据做分类的话，可以在数据空间上获得一个**决策边界** -（Decision Boundary）。如 :numref:`single_neuron_decision_boundary2`所示，以神经元输出$z=0$作为输出标签$y$的决策边界， -没有偏置时决策边界必然经过坐标原点，如果数据样本点不以原点来分开，会导致分类错误。 -为了解决这个问题，可以在神经元上加入一个**偏置**（Bias）。 :numref:`single_neuron_bias2` -是一个有偏置$b$的神经元模型，可以用 :eqref:`singleneuron_bias`表达： -$$z = w_{1}x_{1}+ w_{2}x_{2}+ w_{3}x_{3} + b$$ -:eqlabel:`singleneuron_bias` - - -:width:`600px` -:label:`single_neuron_decision_boundary2` - - -:width:`600px` -:label:`single_neuron_bias2` - -有了偏置以后，决策边界（直线、平面或超平面）可以不经过坐标原点，因此能更好地分类样本。 -准确来说，决策边界把这些样本数据分成两个不同的类别，这个边界是 -$\{x_1, x_2, x_3 | w_{1}x_{1}+ w_{2}x_{2}+ w_{3}x_{3} + b = 0\}$。 - -### 逻辑回归 - -上述神经元的输入和输出是线性关系，为了提供非线性的数据表达能力，可以在神经元输出上加上**激活函数**（Activation -Function），最常见的激活函数有Sigmoid、Tanh、ReLU和Softmax等。 -比如，上述神经元以$z=0$为分界来做分类任务，那么我们可不可以让神经元输出一个概率呢？比如输出$0~1$，$1$代表输入数据$100\%$为某一类。 -为了让神经元输出$0~1$，可以在$z$上加一个逻辑函数**Sigmoid**， -如 :eqref:`sigmoid`所示，Sigmoid把数值限制在0和1之中，通过一个简单的临界值（如：0.5）来决定最终输出的标签是否属于某个类别。这个方法叫做**逻辑回归**（Logistic -Regression）。 - -$$a = f({z}) = \frac{1}{1+{\rm e}^{-{z}}}$$ -:eqlabel:`sigmoid` - -### 多个神经元 - - -:width:`600px` -:label:`two_neurons2` - -上述网络只有一个输出，若多个神经元在一起就可以有多个输出。 :numref:`two_neurons2`是有两个输出的网络，每个输出都和所有输入相连，所以也被称**全连接层**（Fully-Connected(FC) Layer）， -可由下述式子 :eqref:`fc_cal`表示X。 - -$$z_{1} &= w_{11}x_{1} + w_{12}x_{2} + w_{13}x_{3} + b_1 \notag \\ z_{2} &= w_{21}x_{1} + w_{22}x_{2} + w_{23}x_{3} + b_2$$ -:eqlabel:`fc_cal` - -如下式子表示了矩阵方法的实现： - -$$ -{z} = -\begin{bmatrix} -z_1 \\ -z_2 -\end{bmatrix} -= -\begin{bmatrix} -w_{11} & w_{12} & w_{13}\\ -w_{21} & w_{22} & w_{23}\\ -\end{bmatrix} -\begin{bmatrix} -x_1\\ -x_2\\ -x_3 -\end{bmatrix} -+ -\begin{bmatrix} -b_1 \\ b_2 -\end{bmatrix} -= {W}{x} + {b}$$ - - -多输出的网络可以实现多分类问题，比如有10个数值输出，每个数值分别代表一类物品的概率，每个输出在$0$到$1$之间，10个输出之和为$1$。 -可用 :eqref:`e_softmax`的**Softmax** 函数来实现，$K$为输出的个数： - -$$f({z})_{i} = \frac{{\rm e}^{z_{i}}}{\sum_{k=1}^{K}{\rm e}^{z_{k}}}$$ -:eqlabel:`e_softmax` - -### 多层感知器 - - - -**多层感知器**（Multi-Layer -Perceptron，MLP） :cite:`rosenblatt1958perceptron`通过叠加多层全连接层来提升网络的表达能力。相比单层网络，多层感知器有很多中间层的输出并不暴露给最终输出，这些层被称为**隐含层**（Hidden -Layers）。这个例子中的网络可以通过下方的串联式矩阵运算实现，其中$W^l$和$b^l$代表不同层的权重矩阵和偏置，$l$代表层号，$L$代表输出层。 - -$${z} = f({W^L}f({W^3}f({W^2}f({W^1}{x} + {b^1}) + {b^2}) + {b^3}) + {b^L})$$ - -在深度学习时代，网络模型基本都是多层的神经网络层连接起来的，输入数据经过多层的特征提取，可以学到不同抽象层级的**特征向量**（Feature -Vector）。下面我们介绍一下其他常用的神经网络层。 - -### 卷积网络 - - -:width:`600px` -:label:`conv_computation_v4` - -**卷积神经网络** （Convolutional Neural -Network，CNN） :cite:`lecun1989backpropagation`由多层**卷积层**（Convolutional -Layer）组成，常用于计算机视觉任务 :cite:`krizhevsky2012imagenet,he2016deep`。 - :numref:`conv_computation_v4`描述了一个卷积运算的例子。 -根据卷积的特点，我们可以知道两个事实：1）一个卷积核的通道数，等于输入的通道数；2）输出的通道数，等于卷积核的数量。 - - :numref:`conv_computation_v4`例子中，卷积核每次滑动一个数值的范围来进行卷积操作，我们称它的**步长**（Stride）为1。此外，如果希望输入的边缘数值也能被考虑在内的话，则需要对边缘做**填零**（Zero -Padding）操作。 :numref:`conv_computation_v4`例子中，如果输入的每个通道上下左右都填充一圈零，那么输出的大小则为$4\times 4\times 1$。填零的圈数取决于卷积核的大小，卷积核越大则填零圈数越大。 - -为了对输入的图像数据做特征提取，卷积核数量往往比输入数据的通道数据要多，这样的话输出数据的数值会很多，计算量变大。然而图像数据中相邻像素的特征往往相似，所以我们可以对相邻的输出特征进行聚合操作。**池化层**就是为了实现这个目的，我们通常有两种池化方法最大值池化（Max -Pooling）和平均值池化（Mean -Pooling）。如 :numref:`pooling_v3`所示，假设池化的卷积核高宽为$2\times2$，输入$4\times4$的数据，步长为2（步长为1时，则输出等于输入），则输出为$2\times2$。 - - -:width:`600px` -:label:`pooling_v3` - -卷积层和全连接层都是很常用的，但是卷积层在输入是高维度的图像时，需要的参数量远远小于全连接层。卷积层的运算和全连接层是类似的，前者基于高维度张量运算，后者基于二维矩阵运算。 - -### 时序模型 - -现实生活中除了图像还有大量时间序列数据，例如视频、股票价格等等。**循环神经网络**（Recurrent -Neural Networks，RNN） :cite:`rumelhart1986learning`是一种处理序列数据的深度学习模型结构。序列数据是一串连续的数据$\{x_1, x_2, \dots, x_n\}$，比如每个$x$代表一个句子中的单词。 - -为了可以接收一连串的输入序列，如 :numref:`rnn_simple_cell2`所示，朴素循环神经网络使用了循环单元（Cell）作为计算单元，用隐状态（Hidden -State）来存储过去输入的信息。具体来说，对输入模型的每个数据$x$，根据公式 :eqref:`aligned`，循环单元会反复计算新的隐状态，用于记录当前和过去输入的信息。而新的隐状态会被用到下一单元的计算中。 - -$${h}_t = {W}[{x}_t; {h}_{t-1}] + {b}$$ -:eqlabel:`aligned` - - -:width:`600px` -:label:`rnn_simple_cell2` - -然而这种简单的朴素循环神经网络有严重的信息遗忘问题。比如说我们的输入是"我是中国人，我的母语是___"，隐状态记住了"中国人"的信息，使得网络最后可以预测出"中文"一词；但是如果句子很长的时候，隐状态可能记不住太久之前的信息了，比如说"我是中国人，我去英国读书，后来在法国工作，我的母语是___"，这时候在最后的隐状态中关于"中国人"的信息可能会被因为多次的更新而遗忘了。 -为了解决这个问题，后面有人提出了各种各样的改进方法，其中最有名的是长短期记忆（Long -Short-Term Memory，LSTM） :cite:`Hochreiter1997lstm`。关于时序的模型还有很多很多，比如近年来出现的Transformer :cite:`vaswani2017attention`等等。 diff --git a/zh_chapters/chapter_accelerator/accelerator_architecture.md b/zh_chapters/chapter_accelerator/accelerator_architecture.md deleted file mode 100644 index dfdf338..0000000 --- a/zh_chapters/chapter_accelerator/accelerator_architecture.md +++ /dev/null @@ -1,86 +0,0 @@ -## 加速器基本组成原理 - -上节主要介绍了加速器的意义以及设计思路，讲述了加速器与通用处理器在设计上的区别，可以看到加速器的硬件结构与CPU的硬件结构有着根本的不同，通常都是由多种片上缓存以及多种运算单元组成。本章节主要以GPU的Volta架构作为样例进行介绍。 - -### 硬件加速器的架构 - -现代GPU在十分有限的面积上实现了极强的计算能力和极高的储存器以及IO带宽。在一块高端的GPU中，晶体管数量已经达到主流CPU的两倍，而且显存已经达到了16GB以上，工作频率也达到了1GHz。GPU的体系架构由两部分组成，分别是流处理阵列和存储器系统，两部分通过一个片上互联网络连接。流处理器阵列和存储器系统都可以单独扩展，规格可以根据产品的市场定位单独裁剪。如GV100的组成 :cite:`2017NVIDIA`如 :numref:`gv100`所示： - - -:width:`800px` -:label:`gv100` - -- 6个GPU处理集群（GPU Processing Cluster，GPC）, 每个GPC含有： - - 7个纹理处理集群（Texture Processing Cluster, TPC） (每个TPC含有两个流多处理器（Streaming Multiprocessor, SM）) - - 14个SM -- 84个SM, 每个流多处理器含有： - - 64个32位浮点运算单元 - - 64个32位整数运算单元 - - 32个64位浮点运算单元 - - 8个张量计算核心 - - 4个纹理单元 -- 8个512位内存控制器 - -一个完整的GV100 GPU含有84个SM，5376个32位浮点运算单元，5376个32位整型运算单元，2688个64位浮点运算单元，672个张量运算单元和336个纹理单元。一对内存控制器控制一个HBM2 DRAM堆栈。 :numref:`gv100`中展示的为带有84个SM的GV100 GPU(不同的厂商可以使用不同的配置)，Tesla V100则含有80个SM。 - -### 硬件加速器的存储单元 - -与传统的CPU模型相似，从一个计算机系统主内存DRAM中获取数据的速度相对于处理器的运算速度较慢。对于加速器而言，如果没有缓存进行快速存取，DRAM的带宽非常不足。如果无法快速地在DRAM上获取程序和数据，加速器将因空置而降低利用率。为了缓解DRAM的带宽问题，GPU提供了不同层次的若干区域供程序员存放数据，每块区域的内存都有自己的最大带宽以及延迟。开发者需根据不同存储器之间的存储速度的数量级的变化规律，选用适当类型的内存以及最大化地利用它们，从而发挥硬件的最大算力，减少计算时间。 - -- **寄存器文件（Register File）**：片上最快的存储器，但与CPU不同，GPU的每个SM（流多处理器）有上万个寄存器。尽管如此当每个线程使用过多的寄存器时，SM中能够调度的线程块数量就会受到限制，可执行的线程总数量会因此受到限制，可执行的线程数量过少会造成硬件无法充分的利用，性能急剧下降。所以要根据算法的需求合理使用寄存器。 - -- **共享内存（Shared Memory）**：共享内存实际上是用户可控的一级缓存，每个SM（流多处理器）中有128KB的一级缓存, 开发者可根据应用程序需要配置最大96KB的一级缓存作为共享内存。共享内存的访存延迟极低，只有几十个时钟周期。共享内存具有高达1.5TB/s的带宽，远远高于全局内存的峰值带宽900GB/s。共享内存的使用对于高性能计算工程师来说是一个必须要掌握的概念。 - -- **全局内存（Global Memory）**：全局内存之所以称为全局，是因为GPU与CPU都可以对它进行读写操作。全局内存对于GPU中的每个线程都是可见的，都可以直接对全局内存进行读写操作。CPU等其他设备可以通过PCI-E总线对其进行读写操作。全局内存也是GPU中容量最大的一块内存，可达16GB之多。同时也是延迟最大的内存，通常有高达上百个时钟周期的访存延迟。 - -- **常量内存（Constant Memory）**：常量内存其实只是全局内存的一种虚拟地址形式，并没有真正的物理硬件内存块。常量内存有两个特性，一个是高速缓存，另一个更重要的特性是它支持将某个单个值广播到线程束中的每个线程中。 - -- **纹理内存（Texture Memory）**：纹理内存是全局内存的一个特殊形态。当全局内存被绑定为纹理内存时，执行读写操作将通过专用的纹理缓存来加速。在早期的GPU上没有缓存，因此每个SM上的纹理内存为设备提供了唯一真正缓存数据的方法。然而随着硬件的升级，一级缓存和二级缓存的出现使得纹理缓存的这项优势已经荡然无存。纹理内存的另外一个特性，也是最有用的特性就是当访问存储单元时，允许GPU实现硬件相关的操作。比如说使用纹理内存，可以通过归一化的地址对数组进行访问，获取的数据可以通过硬件进行自动插值，从而达到快速处理数据的目的。此外对于二维数组和三维数组，支持硬件级的双线性插值与三线性插值。纹理内存另一个实用的特性是可以根据数组的索引自动处理边界条件，不需要对特殊边缘进行处理即可完成数组内元素操作，从而防止线程中分支的产生。 - - -### 硬件加速器的计算单元 -:label:`compute-unit-title` - -为了支持不同的神经网络模型，加速器会提供以下几种计算单元，不同的网络层可以根据需要选择使用合适的计算单元，如 :numref:`compute-unit`所示 - -- **标量计算单元**：与标准的精简指令运算集（Reduced Instruction Set Computer，RISC）相似，一次计算一个标量元素。 - -- **一维向量计算单元**：一次可以完成多个元素的计算，与传统的CPU和GPU架构中单指令多数据（SIMD）相似，已广泛应用于高性能计算（High Performance Computing，HPC）和信号处理中。 - -- **二维向量计算单元**：一次运算可以完成一个矩阵与向量的内积，或向量的外积。利用数据重复使用这一特性，降低数据通信成本与存储空间，更高效的提高矩阵乘法性能。 - -- **三维向量计算单元**：一次完成一个矩阵的乘法，专为神经网络应用设计的计算单元，更充分利用数据重复特性，隐藏数据通信带宽与数据计算的差距。 - - -:width:`800px` -:label:`compute-unit` - -GPU计算单元主要由标量计算单元和三维向量计算单元组成。如 :numref:`SM`所示,对于每个SM，其中64个32位浮点运算单元、64个32位整数运算单元、32个64位浮点运算单元均为标量计算单元。而8个张量计算核心则是专为神经网络应用设计的三维向量计算单元。 - - -:width:`800px` -:label:`SM` - -张量计算核心每个时钟周期完成一次$4\times4$的矩阵乘累加计算,如 :numref:`tensorcore`所示： - -```cpp - D = A * B + C -``` - - -:width:`800px` -:label:`tensorcore` - -其中A,B,C和D都是$4\times4$的矩阵，矩阵乘累加的输入矩阵A和B是FP16的矩阵，累加矩阵C和D可以是FP16也可以是FP32。 V100的张量计算核心是可编程的矩阵乘法和累加计算单元，可以提供多达125 Tensor TFLOPS(Tera Floating-point Operations Per Second)的训练和推理应用。相比于普通的FP32计算单元可以提速10倍以上。 - -### DSA芯片架构 - -为了满足飞速发展的深度神经网络对芯片算力的需求，业界也纷纷推出了特定领域架构DSA芯片设计。以华为公司昇腾系列AI处理器为例，本质上是一个片上系统（System on Chip，SoC），主要应用在图像、视频、语音、文字处理相关的场景。主要的架构组成部件包括特制的计算单元、大容量的存储单元和相应的控制单元。该芯片由以下几个部分构成：芯片系统控制CPU（Control CPU）、AI计算引擎（包括AI Core和AI CPU）、多层级的片上系统缓存（Cache）或缓冲区（Buffer）、数字视觉预处理模块（Digital Vision Pre-Processing，DVPP）等。 - -昇腾AI芯片的计算核心主要由AI Core构成，负责执行标量、向量和张量相关的计算密集型算子。AI Core采用了达芬奇架构 :cite:`2021Ascend`，基本结构如 :numref:`davinci_architecture`所示，从控制上可以看成是一个相对简化的现代微处理器基本架构。它包括了三种基础计算单元：矩阵计算单元（Cube Unit）、向量计算单元（Vector Unit）和标量计算单元（Scalar Unit）。这三种计算单元分别对应了张量、向量和标量三种常见的计算模式，在实际的计算过程中各司其职，形成了三条独立的执行流水线，在系统软件的统一调度下互相配合达到优化计算效率的目的。 -同GPU类似，在矩阵乘加速设计上，在AICore中也提供了矩阵计算单元作为昇腾AI芯片的核心计算模块，意图高效解决矩阵计算的瓶颈问题。矩阵计算单元提供强大的并行乘加计算能力，可以用一条指令完成两个$16\times16$矩阵的相乘运算，等同于在极短时间内进行了$16\times16\times16=4096$个乘加运算，并且可以实现FP16的运算精度。 - - -:width:`800px` -:label:`davinci_architecture` - diff --git a/zh_chapters/chapter_accelerator/accelerator_introduction.md b/zh_chapters/chapter_accelerator/accelerator_introduction.md deleted file mode 100644 index c242642..0000000 --- a/zh_chapters/chapter_accelerator/accelerator_introduction.md +++ /dev/null @@ -1,17 +0,0 @@ -## 概述 - -### 硬件加速器设计的意义 - -未来人工智能发展的三大核心要素是数据、算法和算力。目前，人工智能系统算力大都构建在CPU和GPU之上且主体多是GPU。随着神经网络的层增多，模型体量增大，算法趋于复杂，CPU和GPU很难再满足新型网络对于算力的需求。例如，2015年谷歌的AlphaGo用了1202个CPU和176个GPU打败了人类职业选手，每盘棋需要消耗上千美元的电费，而与之对应的是人类选手的功耗仅为20瓦。 - -虽然GPU在面向向量、矩阵以及张量的计算上，引入许多新颖的优化设计，但由于GPU需要支持的计算类型复杂，芯片规模大、能耗高，人们开始将更多的精力转移到深度学习硬件加速器的设计上来。和传统CPU和GPU芯片相比，深度学习硬件加速器有更高的性能和更低的能耗。未来随着人们真正进入智能时代，智能应用的普及会越来越广泛，到那时每台服务器、每台智能手机和每个智能摄像头，都需要使用深度学习加速器。 - - -### 硬件加速器设计的思路 -:label:`accelerator-design-title` - -近些年来，计算机体系结构的研究热点之一是深度学习硬件加速器的设计。在体系结构的研究中，能效和通用性是两个重要的衡量指标。其中能效关注单位能耗下基本计算的次数，通用性主要指芯片能够覆盖的任务种类。以两类特殊的芯片为例：一种是较为通用的通用处理器(如CPU)，该类芯片理论上可以完成各种计算任务，但是其能效较低大约只有0.1TOPS/W。另一种是专用集成电路(Application Specific Integrated Circuit, ASIC)，其能效更高，但是支持的任务相对而言就比较单一。对于通用的处理器而言，为了提升能效，在芯片设计上引入了许多加速技术，例如：超标量技术、单指令多数据（Single Instruction Multiple Data，SIMD）技术以及单指令多线程（Single Instruction Multiple Threads，SIMT）技术等。 - -对于不同的加速器设计方向，业界也有不同的硬件实现。针对架构的通用性，NVIDIA持续在GPU芯片上发力，先后推出了Volta、 Turing、 Ampere等架构，并推出用于加速矩阵计算的张量计算核心（Tensor Core），以满足深度学习海量算力的需求。 - -对于偏定制化的硬件架构，面向深度学习计算任务，业界提出了特定领域架构(Domain Specific Architecture， DSA)。Google公司推出了TPU芯片，专门用于加速深度学习计算任务，其使用脉动阵列(Systolic Array)来优化矩阵乘法和卷积运算，可以充分地利用数据局部性，降低对内存的访问次数。华为也推出了自研昇腾AI处理器，旨在为用户提供更高能效的算力和易用的开发、部署体验，其中的CUBE运算单元，就用于加速矩阵乘法的计算。 diff --git a/zh_chapters/chapter_accelerator/accelerator_practise.md b/zh_chapters/chapter_accelerator/accelerator_practise.md deleted file mode 100644 index b7ea306..0000000 --- a/zh_chapters/chapter_accelerator/accelerator_practise.md +++ /dev/null @@ -1,290 +0,0 @@ -## 加速器实践 - -在本节中会通过具体的CUDA代码向读者介绍如何编写一个并行计算的广义矩阵乘法程序，通过提高计算强度、使用共享内存、优化内存读取流水线等方法最终取得接近硬件加速器性能峰值的实现。虽然在以上章节介绍了张量计算核心相关的内容，但由于篇幅限制，在本节中不使用此硬件结构。而是通过使用更为基本的CUDA代码实现FP32的广义矩阵乘法，来讲解若干实用优化策略。 - -### 环境 - -本节的实践有以下的软件环境依赖： - -* Eigen：Eigen是一个线性代数C++模板库，用户可以只使用几条语句完成多线程线性代数运算。 -* OpenMP（可选）：OpenMP是用于共享内存并行系统的多处理器程序设计的一套指导性编译处理方案，可以使用OpenMP对Eigen的计算进行加速。 -* CUDA Toolkit：CUDA Toolkit是英伟达发布的CUDA工具包，其包含了CUDA编译器（NVCC），CUDA线性代数库（cuBLAS）等组件。 -本节的实践都是在CPU Intex Xeon E5-2650 v3，GPU Nvidia Geforce RTX 3080；系统Ubuntu 18.04版本，CUDA Toolkit 11.1进行的。 - -安装相关依赖如下： - -* Eigen：Eigen的安装可以通过使用包管理器安装（如使用指令`apt install libeigen3-dev`），也可以从[官网](https://eigen.tuxfamily.org/index.php?title=Main_Page)下载。 -* OpenMP（可选）：通常会被大多数编译器默认支持，如果没有被支持的话可以使用包管理器安装（如使用指令`apt install libomp-dev`）。 -* CUDA Toolkit：CUDA Toolkit的安装建议按照[官方的提示](https://developer.nvidia.com/cuda-downloads)安装，也可以通过使用包管理器安装（如使用指令`apt install cuda`）。 - -### 广义矩阵乘法的朴素实现 - -:label:`sec-accelerator-naive` - -依照算法如 :numref:`gemm-algorith`所示，编写CPU代码如下所示： -```c++ -float A[M][K]; -float B[K][N]; -float C[M][N]; -float alpha, beta; - -for (unsigned m = 0; m < M; ++m) { - for (unsigned n = 0; n < N; ++n) { - float c = 0; - for (unsigned k = 0; k < K; ++k) { - c += A[m][k] * B[k][n]; - } - C[m][n] = alpha * c + beta * C[m][n]; - } -} -``` - -可以看到，矩阵$C$ 中各个元素的计算是独立的。可以利用GPU的大量线程去分别计算矩阵$C$ 中相应的元素，以达到并行计算的目的，GPU核函数将如下所示： - -```c++ -__global__ void gemmKernel(const float * A, - const float * B, float * C, - float alpha, float beta, unsigned M, unsigned N, - unsigned K) { - unsigned int m = threadIdx.x + blockDim.x * blockIdx.x; - unsigned int n = threadIdx.y + blockDim.y * blockIdx.y; - if (m >= M || n >= N) - return; - float c = 0; - for (unsigned k = 0; k < K; ++k) { - c += A[m * K + k] * B[k * N + n]; - } - c = c * alpha; - float result = c; - if (beta != 0) { - result = result + C[m * N + n] * beta; - } - C[m * N + n] = result; -} -``` - -其可视化结构如 :numref:`cuda_naive_gemm`所示，矩阵$C$中每一个元素由一个线程计算，在GPU Kernel的第5和6行计算该线程对应矩阵$C$中的元素行号$m$及列号$n$，然后在第9到11行该线程利用行号与列号读取矩阵$A$和矩阵$B$中相应的行列向量元素并计算向量内积，最后在第17行将结果写回$C$矩阵。 - - -:width:` 800px` -:label:`cuda_naive_gemm` - -使用以下代码启动核函数： - -```c++ -void gemmNaive(const float *A, const float *B, float *C, - float alpha, float beta, unsigned M, - unsigned N, unsigned K) { - dim3 block(16, 16); - dim3 grid((M - 1) / block.x + 1, (N - 1) / block.y + 1); - - gemmKernel<<
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