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MobileNets: Efficient Convolutional Neural Networks for Mobile Vision Applications 用于移动视觉应用的高效卷积神经网络
校正者：
布丁
中英文论文对照合集 https://aiqianji.com/blog/articles
Abstract
We present a class of efficient models called MobileNets for mobile and embedded vision applications. MobileNets are based on a streamlined architecture that uses depthwise separable convolutions to build light weight deep neural networks. We introduce two simple global hyper-parameters that efficiently trade off between latency and accuracy. These hyper-parameters allow the model builder to choose the right sized model for their application based on the constraints of the problem. We present extensive experiments on resource and accuracy tradeoffs and show strong performance compared to other popular models on ImageNet classification. We then demonstrate the effectiveness of MobileNets across a wide range of applications and use cases including object detection, finegrain classification, face attributes and large scale geo-localization.
摘要
本文针对嵌入式视觉应用领域，提出一个新颖的MobileNets网络，该网络使用了深度可分离卷积来构建轻量级深度神经网络。我们介绍了两个简单的全局超参数，使得模型可以在速度和准确度之间有效地进行折中。这些超参数允许模型构建器根据问题的约束，为其应用程序选择正确的大小模型。我们对资源和准确性权衡提供了广泛的实验，并与Imagenet分类的其他流行模型相比表现出优异的表现。然后，我们展示了Mobilenets跨各种应用程序的有效性和用例，包括物体检测，FineGrain分类，面部属性和大规模地理定位。
Introduction 简介
Convolutional neural networks have become ubiquitous in computer vision ever since AlexNet popularized deep convolutional neural networks by winning the ImageNet Challenge: ILSVRC 2012 . The general trend has been to make deeper and more complicated networks in order to achieve higher accuracy . However, these advances to improve accuracy are not necessarily making networks more efficient with respect to size and speed. In many real world applications such as robotics, self-driving car and augmented reality, the recognition tasks need to be carried out in a timely fashion on a computationally limited platform.
卷积神经网络在计算机视觉中普遍存在，自AlexNet通过赢得ImageNet挑战赢得了深度卷积神经网络：ILSVRC 2012。一般趋势一直是制造更深刻更复杂的网络，以实现更高的准确性。然而，这些提高准确性的进步不一定使网络在尺寸和速度方面更有效。在许多现实世界的应用程序中，如机器人，自驾驶汽车和增强现实，需要在计算有限的平台上以及时的方式进行识别任务。
This paper describes an efficient network architecture and a set of two hyper-parameters in order to build very small, low latency models that can be easily matched to the design requirements for mobile and embedded vision applications. Section prior reviews prior work in building small models. Section mobilenet describes the MobileNet architecture and two hyper-parameters width multiplier and resolution multiplier to define smaller and more efficient MobileNets. Section exp describes experiments on ImageNet as well a variety of different applications and use cases. Section conclusion closes with a summary and conclusion.
本文介绍了一种有效的网络架构和两个超参数，以便构建非常小的低延迟模型，可以轻松匹配移动和嵌入式视觉应用程序的设计要求。第一部分回顾了小模型建立的先前工作。 MobileNet部分描述了MobileNet架构和两个超参数：宽度乘法器和分辨率乘法器，以定义更小且更高效的移动单元。 exp章节描述了Imagenet的实验以及各种不同的应用和用例。最后是总结部分
图1： MobileNet模型可以应用于各种识别任务，以实现设备智能的高效。
Prior Work 相关工作
There has been rising interest in building small and efficient neural networks in the recent literature, e.g. . Many different approaches can be generally categorized into either compressing pretrained networks or training small networks directly. This paper proposes a class of network architectures that allows a model developer to specifically choose a small network that matches the resource restrictions (latency, size) for their application. MobileNets primarily focus on optimizing for latency but also yield small networks. Many papers on small networks focus only on size but do not consider speed.
在最近的文献中构建小型高效的神经网络的兴趣正在增长，例如[ 16，34，12，36，22 ]。通常这些不同的方法归类为压缩预训练网络和直接训练小型网络。本文提出了一类网络体系结构，允许模型开发人员专门为其应用选择与资源限制（延迟，大小）相匹配的小型网络。MobileNets主要专注于优化速度，但也会产生小型网络。关于小型网络的许多论文只关注规模，却不考虑速度。
MobileNets are built primarily from depthwise separable convolutions initially introduced in and subsequently used in Inception models to reduce the computation in the first few layers. Flattened networks build a network out of fully factorized convolutions and showed the potential of extremely factorized networks. Independent of this current paper, Factorized Networks introduces a similar factorized convolution as well as the use of topological connections. Subsequently, the Xception network demonstrated how to scale up depthwise separable filters to out perform Inception V3 networks. Another small network is Squeezenet which uses a bottleneck approach to design a very small network. Other reduced computation networks include structured transform networks and deep fried convnets . A different approach for obtaining small networks is shrinking, factorizing or compressing pretrained networks. Compression based on product quantization , hashing , and pruning, vector quantization and Huffman coding have been proposed in the literature. Additionally various factorizations have been proposed to speed up pretrained networks . Another method for training small networks is distillation which uses a larger network to teach a smaller network. It is complementary to our approach and is covered in some of our use cases in section exp. Another emerging approach is low bit networks .
MobileNets主要是由[ 26 ]中最初引入并随后用于Inception模型[ 13 ]中的深度可分离卷积构建的，以减少前几层的计算量。 Flattened networks [ 16 ]由完全分解的卷积构建网络，并显示了高度分解的网络的潜力。独立于本文， Factorized Networks [ 34 ]引入了类似的分解卷积以及拓扑连接的使用。随后，Xception网络[ 3 ]演示了如何按比例放大深度可分离滤波器，以执行Inception V3网络。另一个小型网络是Squeezenet [ 12 ]，它使用瓶颈方法设计了一个非常小的网络。其他减少的计算网络包括结构化转换网络[ 28 ]和deep fried convnets[ 37 ]。
获得小型网络的另一种方法是收缩，分解或压缩预训练的网络。在文献中已经提出了基于乘积量化[ 36 ]，散列[ 2 ]以及修剪，矢量量化和霍夫曼编码[ 5 ]的压缩。此外各种因式分解已被提出以加快预训练网络[ 14，20 ]。训练小型网络的另一种方法是蒸馏[ 9 ]它使用较大的网络来教授较小的网络。它是对我们方法的补充，并且在第4节中的一些用例中进行了介绍。另一个新兴方法是低比特网络[ 4，22，11 ]。
MobileNet Architecture MOBILENET体系结构
In this section we first describe the core layers that MobileNet is built on which are depthwise separable filters. We then describe the MobileNet network structure and conclude with descriptions of the two model shrinking hyper-parameters width multiplier and resolution multiplier.
在本节中，我们首先描述了MobileNet构建的核心层，它是深度可分离的滤波器。然后，我们描述了MobileNet网络结构并结论，描述了两个模型缩小的超参数：宽度乘数和分辨率乘法器。
Depthwise Separable Convolution 深度可分离卷积
The MobileNet model is based on depthwise separable convolutions which is a form of factorized convolutions which factorize a standard convolution into a depthwise convolution and a $ 1 \times 1 $ convolution called a pointwise convolution.
MobileNet模型基于深度可分离卷积，该卷曲是一种分解卷积的形式，其将标准卷积分解为深度卷积和$ 1 \times 1 $卷积，称为点卷积。对于MobiLenets，深度卷积将单个过滤器应用于每个输入通道。然后，点卷积然后应用$ 1 \times 1 $卷积以组合输出的深度卷积。
For MobileNets the depthwise convolution applies a single filter to each input channel. The pointwise convolution then applies a $ 1 \times 1 $ convolution to combine the outputs the depthwise convolution. A standard convolution both filters and combines inputs into a new set of outputs in one step. The depthwise separable convolution splits this into two layers, a separate layer for filtering and a separate layer for combining. This factorization has the effect of drastically reducing computation and model size.Figure dw_conv shows how a standard convolution dw_conv_a is factorized into a depthwise convolution dw_conv_b and a $ 1 \times 1 $ pointwise convolution dw_conv_c.
标准卷积在一个步骤中，两个滤波器将输入组合成一组新的输出。深度可分离卷积将其分成两层，是用于独立的滤波器和独立的组合层。这种分解具有大幅减少计算和模型大小的效果。图2显示了如何将标准卷积2（a）分解为深度卷积2（b）和1×1个点向卷积2（c）。
A standard convolutional layer takes as input a $ D_F \times D_F \times M $ feature map $ F $ and produces a $ D_F \times D_F \times N $ feature map $ G $ where $ D_F $ is the spatial width and height of a square input feature map We assume that the output feature map has the same spatial dimensions as the input and both feature maps are square. Our model shrinking results generalize to feature maps with arbitrary sizes and aspect ratios. , $ M $ is the number of input channels (input depth), $ D_G $ is the spatial width and height of a square output feature map and $ N $ is the number of output channel (output depth). The standard convolutional layer is parameterized by convolution kernel $ K $ of size $ D_K \times D_K \times M \times N $ where $ D_K $ is the spatial dimension of the kernel assumed to be square and $ M $ is number of input channels and $ N $ is the number of output channels as defined previously. The output feature map for standard convolution assuming stride one and padding is computed as:
输入的特征映射$ F 尺寸为$ $ D_F \times D_F \times M $,输出的特征图$ G $ 尺寸为 $ D_F \times D_F \times N $ ，其中$ D_F $是正方形输入特征图的空间宽度和高度。（我们假设输出特征图具有与输入相同的空间尺寸，并且两个特征图均为正方形。我们的模型缩小结果可以概括为具有任意大小和纵横比的特征图。）$ M $是输入通道的数量（输入深度），$ D_G $是方形输出特征图的空间宽度和高度，$ N $是输出通道（输出深度）的数量。标准卷积层通过卷积核$ K $参数化$ D_K \times D_K \times M \times N $其中$ D_K $是假定为正方形的内核的空间尺寸，$ M $是输入通道的数量和$ N $是先前定义的输出通道数。
假设跨度为1和填充为标准卷积的输出特征图，计算公式为：
$$ G_{k,l,n} = \sum_{i,j,m} K_{i,j,m,n}\cdot F_{k+i-1,l+j-1,m} $$
Standard convolutions have the computational cost of: 标准卷积的计算成本为：
$$ D_K \cdot D_K \cdot M \cdot N \cdot D_F \cdot D_F $$
where the computational cost depends multiplicatively on the number of input channels $ M $ , the number of output channels $ N $ the kernel size $ D_k \times D_k $ and the feature map size $ D_F \times D_F $ . MobileNet models address each of these terms and their interactions. First it uses depthwise separable convolutions to break the interaction between the number of output channels and the size of the kernel. The standard convolution operation has the effect of filtering features based on the convolutional kernels and combining features in order to produce a new representation.
，其中计算成本差异依赖在输入通道$ M $的数量上，输出通道的数量$ N $内核大小$ D_k \times D_k $和特征映射大小$ D_F \times D_F $。 MobileNet模型解决了这些相互关系。首先，它使用深度可分离的卷积来破坏输出通道数与内核的大小之间的交互。标准卷积操作基于卷积核和组合特征的滤波功能效果，以产生新的表示。
The filtering and combination steps can be split into two steps via the use of factorized convolutions called depthwise separable convolutions for substantial reduction in computational cost. Depthwise separable convolution are made up of two layers: depthwise convolutions and pointwise convolutions. We use depthwise convolutions to apply a single filter per each input channel (input depth). Pointwise convolution, a simple $ 1 \times 1 $ convolution, is then used to create a linear combination of the output of the depthwise layer. MobileNets use both batchnorm and ReLU nonlinearities for both layers. Depthwise convolution with one filter per input channel (input depth) can be written as:
滤波和组合步骤可以通过使用称为深度可分离卷积的分解卷积分为两个步骤，以大幅降低计算成本。深度可分离卷积由两层组成：深度卷积和点卷积。我们使用深度卷积在每个输入通道（输入深度）上应用单个滤波器。点卷积，简单1×1个卷积，然后用于创建深度层输出的线性组合。MobileNets对这两个层都使用了batchnorm和ReLU非线性。
每个输入通道（输入深度）带有一个滤波器的深度卷积可以写成
$$ \hat{G}{k,l,m} = \sum{i,j} \hat{K}{i,j,m} \cdot F{k+i-1,l+j-1,m} $$
where $ \hat{K} $ is the depthwise convolutional kernel of size $ D_K \times D_K \times M $ where the $ m_{th} $ filter in $ \hat{K} $ is applied to the $ m_{th} $ channel in $ F $ to produce the $ m_{th} $ channel of the filtered output feature map $ \hat{G} $ . Depthwise convolution has a computational cost of:
，其中$\hat{K} $是$ D_K \times D_K \times M $的深度卷积核，其中$中的$ m_{th} $滤波器T91_0 $应用于$ F $中的$ m_{th} $通道，以生成滤波输出功能映射$\hat{G} $的$ m_{th} $通道。深度卷积具有以下计算成本：
$$ D_K \cdot D_K \cdot M \cdot D_F \cdot D_F $$
Depthwise convolution is extremely efficient relative to standard convolution. However it only filters input channels, it does not combine them to create new features. So an additional layer that computes a linear combination of the output of depthwise convolution via $ 1 \times 1 $ convolution is needed in order to generate these new features. The combination of depthwise convolution and $ 1\times1 $ (pointwise) convolution is called depthwise separable convolution which was originally introduced in . Depthwise separable convolutions cost:
深度卷积相对于标准卷积非常有效。但是它只对输入通道进行滤波，它不会组合它们以创建新功能。因此，需要一种附加层，其通过$ 1 \times 1 $卷积需要计算深度卷积的输出的线性组合，以便生成这些新功能。
深度卷积和 1×1个（逐点）卷积称为“深度可分离卷积”，最初是在[ 26 ]中引入的。
深度可分离卷积代价：
$$ D_K \cdot D_K \cdot M \cdot D_F \cdot D_F + M \cdot N \cdot D_F \cdot D_F $$
which is the sum of the depthwise and $ 1 \times 1 $ pointwise convolutions. By expressing convolution as a two step process of filtering and combining we get a reduction in computation of: MobileNet uses $ 3 \times 3 $ depthwise separable convolutions which uses between 8 to 9 times less computation than standard convolutions at only a small reduction in accuracy as seen in Section exp.
，它是深度和$ 1 \times 1 $点卷积的总和。通过表达卷积作为过滤和组合的两个步骤过程，我们得到了计算的减少：MobileNet使用$ 3 \times 3 $深度可分离卷曲，其使用的计算比标准卷曲更小的准确性，所以计算得多。在exp节中看到。
Additional factorization in spatial dimension such as in does not save much additional computation as very little computation is spent in depthwise convolutions.
在空间维度附加因式分解，如在[ 16，31 ]不保存多少额外的计算，因为在深度卷积中花费了很少的计算。
Network Structure and Training 网络结构与训练
The MobileNet structure is built on depthwise separable convolutions as mentioned in the previous section except for the first layer which is a full convolution. By defining the network in such simple terms we are able to easily explore network topologies to find a good network. The MobileNet architecture is defined in Table 1. All layers are followed by a batchnorm [13] and ReLU nonlinearity with the exception of the final fully connected layer which has no nonlinearity and feeds into a softmax layer for classification. Figure 3 contrasts a layer with regular convolutions, batchnorm and ReLU nonlinearity to the factorized layer with depthwise convolution, 1×1 pointwise convolution as well as batchnorm and ReLU after each convolutional layer. Down sampling is handled with strided convolution in the depthwise convolutions as well as in the first layer. A final average pooling reduces the spatial resolution to 1 before the fully connected layer. Counting depthwise and pointwise convolutions as separate layers, MobileNet has 28 layers.
如前一节所述，MobileNet结构建立在深度可分离卷积之上，第一层是完整卷积。通过以这种简单的术语定义网络，我们可以轻松地探索网络拓扑以找到一个好的网络。表1中定义了MobileNet体系结构。除了最后的完全连接的层（没有非线性，并馈入softmax层进行分类）外，所有层都遵循batchnorm [ 13 ]和ReLU非线性。图3将具有规则卷积，batchnorm和ReLU非线性的层与具有深度卷积的分解层进行了对比，1个×1个每个卷积层之后的逐点卷积以及batchnorm和ReLU。下采样是在深度卷积以及第一层中通过跨步卷积来处理的。最终平均池在完全连接的层之前将空间分辨率降低为1。将深度卷积和点积卷积计为单独的层，MobileNet有28层。
It is not enough to simply define networks in terms of a small number of Mult-Adds. It is also important to make sure these operations can be efficiently implementable. For instance unstructured sparse matrix operations are not typically faster than dense matrix operations until a very high level of sparsity. Our model structure puts nearly all of the computation into dense 1×1 convolutions. This can be implemented with highly optimized general matrix multiply (GEMM) functions. Often convolutions are implemented by a GEMM but require an initial reordering in memory called im2col in order to map it to a GEMM. For instance, this approach is used in the popular Caffe package [15]. 1×1 convolutions do not require this reordering in memory and can be implemented directly with GEMM which is one of the most optimized numerical linear algebra algorithms. MobileNet spends 95% of it’s computation time in 1×1 convolutions which also has 75% of the parameters as can be seen in Table 2. Nearly all of the additional parameters are in the fully connected layer.
仅用少量的Mult-Adds定义网络是不够的。确保这些操作可以有效实施也很重要。例如，直到非常高的稀疏性，非结构化稀疏矩阵运算通常不比密集矩阵运算快。我们的模型结构使几乎所有计算都变得密集1个×1个卷积。这可以通过高度优化的通用矩阵乘法（GEMM）函数来实现。卷积通常由GEMM实现，但需要在内存中进行名为im2col的初始重新排序，才能将其映射到GEMM。例如，这种方法在流行的Caffe包中使用[ 15 ]。1个×1个卷积不需要在内存中进行这种重新排序，可以直接使用GEMM进行实现，GEMM是最优化的数值线性代数算法之一。MobileNet支出95％ 它的计算时间 1个×1个 卷积也有 75％表2中可以看到这些参数。几乎所有其他参数都在完全连接的层中。
MobileNet models were trained in TensorFlow [1] using RMSprop [33] with asynchronous gradient descent similar to Inception V3 [31]. However, contrary to training large models we use less regularization and data augmentation techniques because small models have less trouble with overfitting. When training MobileNets we do not use side heads or label smoothing and additionally reduce the amount image of distortions by limiting the size of small crops that are used in large Inception training [31]. Additionally, we found that it was important to put very little or no weight decay (l2 regularization) on the depthwise filters since their are so few parameters in them. For the ImageNet benchmarks in the next section all models were trained with same training parameters regardless of the size of the model.
MobileNet模型在TensorFlow [ 1 ]中使用RMSprop [ 33 ]的异步梯度下降来训练，类似于Inception V3 [ 31 ]。但是，与训练大型模型相反，我们使用较少的正则化和数据增强技术，因为小型模型的过拟合麻烦较小。在训练MobileNets时，我们不使用侧边或标签平滑处理，并且通过限制在大型Inception训练中使用的小农作物的大小来减少失真的图像量[ 31 ]。此外，我们发现，对深度过滤器进行很少或没有权重衰减（l 2正则化）是很重要的，因为它们中的参数太少了。对于下一部分中的ImageNet基准，无论模型的大小如何，所有模型都使用相同的训练参数进行训练。
| Type / Stride | Filter Shape | Input Size |
|---|---|---|
| Conv / s2 | 3×3×3×32 | 224×224×3 |
| Conv dw / s1 | 3×3×32 dw | 112×112×32 |
| Conv / s1 | 1×1×32×64 | 112×112×32 |
| Conv dw / s2 | 3×3×64 dw | 112×112×64 |
| Conv / s1 | 1×1×64×128 | 56×56×64 |
| Conv dw / s1 | 3×3×128 dw | 56×56×128 |
| Conv / s1 | 1×1×128×128 | 56×56×128 |
| Conv dw / s2 | 3×3×128 dw | 56×56×128 |
| Conv / s1 | 1×1×128×256 | 28×28×128 |
| Conv dw / s1 | 3×3×256 dw | 28×28×256 |
| Conv / s1 | 1×1×256×256 | 28×28×256 |
| Conv dw / s2 | 3×3×256 dw | 28×28×256 |
| Conv / s1 | 1×1×256×512 | 14×14×256 |
| 5× Conv dw / s1 | 3×3×512 dw | 14×14×512 |
| Conv / s1 | 1×1×512×512 | 14×14×512 |
| Conv dw / s2 | 3×3×512 dw | 14×14×512 |
| Conv / s1 | 1×1×512×1024 | 7×7×512 |
| Conv dw / s2 | 3×3×1024 dw | 7×7×1024 |
| Conv / s1 | 1×1×1024×1024 | 7×7×1024 |
| Avg Pool / s1 | Pool 7×7 | 7×7×1024 |
| FC / s1 | 1024×1000 | 1×1×1024 |
| Softmax / s1 | Classifier | 1×1×1000 |
Table 1: MobileNet Body Architecture
表1： MobileNet主体架构
Figure 3: Left: Standard convolutional layer with batchnorm and ReLU. Right: Depthwise Separable convolutions with Depthwise and Pointwise layers followed by batchnorm and ReLU.
图3：左：具有batchnorm和ReLU的标准卷积层。右：Depthwise可拆分卷积，其中Depthwise和Pointwise层紧随其后是batchnorm和ReLU。
| Type | Mult-Adds | Parameters |
|---|---|---|
| Conv 1×1 | 94.86% | 74.59% |
| Conv DW 3×3 | 3.06% | 1.06% |
| Conv 3×3 | 1.19% | 0.02% |
| Fully Connected | 0.18% | 24.33% |
Table 2: Resource Per Layer Type 表2：每种层类型的资源
Width Multiplier: Thinner Models 宽度乘数：更薄的模型
Although the base MobileNet architecture is already small and low latency, many times a specific use case or application may require the model to be smaller and faster. In order to construct these smaller and less computationally expensive models we introduce a very simple parameter $ \alpha $ called width multiplier. The role of the width multiplier $ \alpha $ is to thin a network uniformly at each layer. For a given layer and width multiplier $ \alpha $ , the number of input channels $ M $ becomes $ \alpha M $ and the number of output channels $ N $ becomes $ \alpha N $ . The computational cost of a depthwise separable convolution with width multiplier $ \alpha $ is:
尽管基本的MobileNet体系结构已经很小并且延迟很短，但是很多时候，特定的用例或应用程序可能要求模型更小，更快。为了构造这些较小且计算量较小的模型，我们引入了一个非常简单的参数$\alpha $称为宽度乘法器。宽度乘法器$\alpha $的作用是在每层均匀地缩小网络。对于给定的层和宽度乘法器$\alpha $，输入通道$ M $的数量变为$\alpha M $和输出通道$ N $的数量变为$\alpha N $。具有宽度乘法器$\alpha $的深度可分离卷积的计算成本是：
$$ D_K \cdot D_K \cdot\alpha M \cdot D_F \cdot D_F + \alpha M \cdot\alpha N \cdot D_F \cdot D_F $$
where $ \alpha\in(0,1] $ with typical settings of 1, 0.75, 0.5 and 0.25. $ \alpha=1 $ is the baseline MobileNet and $ \alpha<1 $ are reduced MobileNets. Width multiplier has the effect of reducing computational cost and the number of parameters quadratically by roughly $ \alpha^2 $ . Width multiplier can be applied to any model structure to define a new smaller model with a reasonable accuracy, latency and size trade off. It is used to define a new reduced structure that needs to be trained from scratch.
其中$\alpha\in(0,1] $ 通常设置为1、0.75、0.5和0.25。 $\alpha=1 $是基线MOBILENET和$\alpha<1 $减少了MOBILENETS。宽度乘数通过大致$\alpha^2 $逐步降低计算成本和参数数量的效果。宽度乘法器可以应用于任何模型结构，以定义具有合理精度，延迟和尺寸折衷的新的较小模型。它用于定义需要从头开始训练的新的精简结构。
在哪里 α∈（0，1个] 通常设置为1、0.75、0.5和0.25。 α=1个 是baseline MobileNet 和 α<1个 reduced MobileNets。宽度乘数的作用是将计算量和参数数量大约减少了两倍α2个。宽度乘数可以应用于任何模型结构，以合理的精度，等待时间和尺寸折衷来定义新的较小模型。它用于定义新的精简结构，需要从头开始进行培训。
Resolution Multiplier: Reduced Representation 分辨率乘数：减少表达
The second hyper-parameter to reduce the computational cost of a neural network is a resolution multiplier $ \rho $ . We apply this to the input image and the internal representation of every layer is subsequently reduced by the same multiplier. In practice we implicitly set $ \rho $ by setting the input resolution. We can now express the computational cost for the core layers of our network as depthwise separable convolutions with width multiplier $ \alpha $ and resolution multiplier $ \rho $ :
减少神经网络计算成本的第二个超参数是分辨率乘数 ρ。我们将其应用于输入图像，然后通过相同的乘数来减少每一层的内部表示。在实践中，我们 通过设置输入分辨率隐式设置ρ。
现在，我们可以将网络核心层的计算成本表示为具有宽度乘数的深度可分离卷积 α 和分辨率乘数 ρ：
$$ D_K \cdot D_K \cdot\alpha M \cdot\rho D_F \cdot\rho D_F + \alpha M \cdot\alpha N \cdot\rho D_F \cdot\rho D_F $$
where $ \rho\in(0,1] $ which is typically set implicitly so that the input resolution of the network is 224, 192, 160 or 128. $ \rho=1 $ is the baseline MobileNet and $ \rho<1 $ are reduced computation MobileNets. Resolution multiplier has the effect of reducing computational cost by $ \rho^2 $ . As an example we can look at a typical layer in MobileNet and see how depthwise separable convolutions, width multiplier and resolution multiplier reduce the cost and parameters. Table layer_resource shows the computation and number of parameters for a layer as architecture shrinking methods are sequentially applied to the layer. The first row shows the Mult-Adds and parameters for a full convolutional layer with an input feature map of size $ 14 \times 14 \times 512 $ with a kernel $ K $ of size $ 3 \times 3 \times 512 \times 512 $ . We will look in detail in the next section at the trade offs between resources and accuracy.
其中$\rho\in(0,1] $通常隐含地设置，以便网络的输入分辨率为224,192,160或128. $\rho=1 $是baseline MobileNet 和$\rho<1 $ reduced MobileNets。分辨率乘数具有通过$\rho^2 $降低计算成本的效果。作为一个例子，我们可以看一下MobileNet的典型层，看看如何通过深度可分离卷积，宽度乘法器和分辨率乘数降低成本和参数。表3显示了将体系结构收缩方法依次应用于该层时该层的参数的计算和数量。第一行显示完整卷积层的Mult-Adds和参数，输入特征图的大小为14×14×512 带有内核 ķ 大小 3×3×512×512。我们将在下一部分中详细讨论资源与准确性之间的权衡。
| Layer/Modification | Million Mult-Adds | Million Parameters |
|---|---|---|
| Convolution | 462 | 2.36 |
| Depthwise Separable Conv | 52.3 | 0.27 |
| α=0.75 | 29.6 | 0.15 |
| ρ=0.714 | 15.1 | 0.15 |
Table 3: Resource usage for modifications to standard convolution. Note that each row is a cumulative effect adding on top of the previous row. This example is for an internal MobileNet layer with DK=3, M=512, N=512, DF=14.
表3：用于标准卷积修改的资源使用情况。请注意，每一行都是在前一行之上添加的累积效果。此示例适用于具有以下内容的内部MobileNet层：DK=3, M=512, N=512, DF=14.
Experiments 实验
In this section we first investigate the effects of depthwise convolutions as well as the choice of shrinking by reducing the width of the network rather than the number of layers. We then show the trade offs of reducing the network based on the two hyper-parameters: width multiplier and resolution multiplier and compare results to a number of popular models. We then investigate MobileNets applied to a number of different applications.
在本节中，我们首先研究深度卷积的影响以及通过减小网络的宽度而不是层数来选择收缩的方法。然后，我们基于两个超参数（宽度乘数和分辨率乘数）显示减少网络的权衡取舍，并将结果与许多流行的模型进行比较。然后，我们研究MobileNets应用于许多不同的应用程序。
Model Choices 模型选择
First we show results for MobileNet with depthwise separable convolutions compared to a model built with full convolutions. In Table dm_ful
