【论文翻译】：Deep Residual Learning for Image Recognition
【论文来源】：Deep Residual Learning for Image Recognition
【翻译人】：莫墨莫陌

Deep Residual Learning for Image Recognition

基于深度残差学习的图像识别

2016 IEEE Conference on Computer Vision and Pattern Recognition 图像识别的深度残差学习2016 IEEE计算机视觉与模式识别会议 Kaiming He Xiangyu Zhang Shaoqing Ren Jian Sun Microsoft Research {kahe, v-xiangz, v-shren, jiansun}@microsoft.com

Abstract

Deeper neural networks are more difficult to train. We present a residual learning framework to ease the training of networks that are substantially deeper than those used previously. We explicitly reformulate the layers as learning residual functions with reference to the layer inputs, instead of learning unreferenced functions. We provide comprehensive empirical evidence showing that these residual networks are easier to optimize, and can gain accuracy from considerably increased depth. On the ImageNet dataset we evaluate residual nets with a depth of up to 152 layers—8× deeper than VGG nets [40] but still having lower complexity. An ensemble of these residual nets achieves 3.57% error on the ImageNet test set. This result won the 1st place on the ILSVRC 2015 classification task. We also present analysis on CIFAR-10 with 100 and 1000 layers.

The depth of representations is of central importance for many visual recognition tasks. Solely due to our extremely deep representations, we obtain a 28% relative improvement on the COCO object detection dataset. Deep residual nets are foundations of our submissions to ILSVRC & COCO 2015 competitions1, where we also won the 1st places on the tasks of ImageNet detection, ImageNet localization, COCO detection, and COCO segmentation.

摘要

更深的神经网络更难训练。我们提出了一个residual learning framework来简化网络的训练，这些网络比以前使用的要深得多。我们显式地将层重新表示为根据层输入学习residual function，而不是学习未引用的函数。我们提供了全面的经验证据表明，这些残差网络更容易优化，并可以获得准确性从相当大的深度。在ImageNet数据集上，我们评估的residual network深度可达152层，比VGG网络深8层，但仍然具有较低的复杂性。这些残余网的集合在ImageNet测试集上的误差达到3.57%，该结果在ILSVRC 2015分类任务中获得第一名。我们还对CIFAR-10进行了100层和1000层的分析。

对于许多视觉识别任务来说，表征的深度是至关重要的。仅仅由于我们非常深入的表示，我们在COCO对象检测数据集上获得了28%的相对改进。深残差网是我们提交给ILSVRC的基础。在2015年COCO竞赛中，我们在ImageNet检测、ImageNet定位、COCO检测、COCO分割任务上也获得了第一名。

1 Introduction

1 引言

Deep convolutional neural networks [22, 21] have led to a series of breakthroughs for image classification [21,49, 39]. Deep networks naturally integrate low/mid/highlevel features [49] and classifiers in an end-to-end multilayer fashion, and the “levels” of features can be enriched by the number of stacked layers (depth). Recent evidence [40, 43] reveals that network depth is of crucial importance, and the leading results [40, 43, 12, 16] on the challenging ImageNet dataset [35] all exploit “very deep” [40] models, with a depth of sixteen [40] to thirty [16]. Many other nontrivial visual recognition tasks [7, 11, 6, 32, 27] have also greatly benefited from very deep models.
深度卷积神经网络[22，21]在图像分类方面取得了一系列突破[21，49，39]。深度网络以端到端的多层方式自然地集成了低/中/高级功能[49]和分类器，并且特征的“层”可以通过堆叠的层数（深度）来丰富。最新证据[40，43]表明了网络深度至关重要，在具有挑战性的ImageNet数据集[35]上的领先结果[40，43，12，16]都采用了“非常深”的模型[40]，深度为十六[40]到三十[16]。许多其他重要的视觉识别任务[7，11，6，32，27]也有非常受益于非常深入的模型。

Driven by the significance of depth, a question arises: Is learning better networks as easy as stacking more layers? An obstacle to answering this question was the notorious problem of vanishing /exploding gradients [14, 1, 8], which hamper convergence from the beginning. This problem, however, has been largely addressed by normalized initialization [23, 8, 36, 12] and intermediate normalization layers [16], which enable networks with tens of layers to start converging for stochastic gradient descent (SGD) with backpropagation [22].
在深度意义的驱动下，出现了一个问题：学习更好的网络是否像堆叠更多的层一样容易？回答这个问题的障碍是众所周知的梯度消失/爆炸[14，1，8]，从一开始就阻碍了收敛。但是，此问题已通过归一化初始化[23，8，36，12]和中间归一化层[16]得到了很大解决，这使具有数十层的网络能够通过反向传播开始收敛用于随机梯度下降（SGD）[22]。

When deeper networks are able to start converging, a degradation problem has been exposed: with the network depth increasing, accuracy gets saturated (which might be unsurprising) and then degrades rapidly. Unexpectedly, such degradation is not caused by overfitting, and adding more layers to a suitably deep model leads to higher training error, as reported in [10, 41] and thoroughly verified by our experiments. Fig. 1 shows a typical example.
当更深的网络能够开始收敛时，就会暴露出一个退化问题：随着网络深度的增加，准确性达到饱和（这可能不足为奇），然后迅速退化。出乎意料的是，这种退化不是由过度拟合引起的，并且在[10，41]中报道，并由我们的实验充分验证了，将更多层添加到适当深度的模型中会导致更高的训练误差。图1显示了一个典型示例。

The degradation (of training accuracy) indicates that not all systems are similarly easy to optimize. Let us consider a shallower architecture and its deeper counterpart that adds more layers onto it. There exists a solution by construction to the deeper model: the added layers are identity mapping, and the other layers are copied from the learned shallower model. The existence of this constructed solution indicates that a deeper model should produce no higher training error than its shallower counterpart. But experiments show that our current solvers on hand are unable to find solutions that are compar- ably good or better than the constructed solution(or unable to do so in feasible time).
训练准确性的下降表明并非所有系统都同样容易优化。让我们考虑一个较浅的体系结构及其更深的对应结构，它会在其上添加更多层。通过构建更深层的模型，可以找到一种解决方案：添加的层是恒等映射，而其他层是从学习的浅层模型中复制的。该构造解决方案的存在表明，较深的模型不会产生比浅模型更高的训练误差。但是实验表明，我们现有的求解器无法找到解决方案比构造的解决方案好或更好（或在可行时间内无法做到）。

In this paper, we address the degradation problem by introducing a deep residual learning framework. Instead of hoping each few stacked layers directly fit a desired underlying mapping, we explicitly let these layers fit a residual mapping. Formally, denoting the desired underlying mapping as H(x), we let the stacked nonlinear layers fit another mapping of F(x) := H(x)−x. The original mapping is recast into F(x)+x. We hypothesize that it is easier to optimize the residual mapping than to optimize the original, unreferenced mapping. To the extreme, if an identity mapping were optimal, it would be easier to push the residual to zero than to fit an identity mapping by a stack of nonlinear layers.
在本文中，我们通过引入深度残差学习框架来解决退化问题。而不是希望每个堆叠的层都直接适合所需的基础映射，我们明确让这些层适合残差映射。形式上，将所需的基础映射表示为H(x)，我们让堆叠的非线性层适合另一映射F(x)：=H(x)-x。原始映射将重新转换为F(x)+x。我们假设优化残差映射比优化原始的、未引用的映射更容易。在极端情况下，如果恒等映射是最佳的，则将残差推到零比通过非线性层堆栈拟合恒等映射要容易。

The formulation of F(x)+x can be realized by feedforward neural networks with “shortcut connections” (Fig. 2). Shortcut connections [2, 33, 48] are those skipping one or more layers. In our case, the shortcut connections simply perform identity mapping, and their outputs are added to the outputs of the stacked layers (Fig. 2). Identity shortcut connections add neither extra parameter nor computational complexity. The entire network can still be trained end-to-end by SGD with backpropagation, and can be easily implemented using common libraries (e.g., Caffe [19]) without modifying the solvers.
F(x)+x的公式可通过具有“快捷连接”的前馈神经网络来实现（图2）。快捷连接[2、33、48]是跳过一层或多层的连接。在我们的例子中，快捷连接仅执行恒等映射，并将其输出添加到堆叠层的输出中（图2）。恒等快捷连接既不增加额外的参数，也不增加计算复杂度。整个网络仍然可以通过SGD反向传播进行端到端训练，并且可以使用通用库（例如Caffe [19]）轻松实现，而无需修改求解器。

We present comprehensive experiments on ImageNet [35] to show the degradation problem and evaluate our method. We show that: 1) Our extremely deep residual nets are easy to optimize, but the counterpart “plain” nets (that simply stack layers) exhibit higher training error when the depth increases; 2) Our deep residual nets can easily enjoy accuracy gains from greatly increased depth, producing results substantially better than previous networks.
我们在ImageNet [35]上进行了全面的实验，以显示退化问题并评估我们的方法。我们发现：1）我们极深的残差网络很容易优化，但是当深度增加时，对应的“普通”网络（简单地堆叠层）在深度增加时训练误差较大；2）我们的深层残差网络可以很容易地从深度的大幅增加中获得精度提升，从而产生比以前的网络更好的结果。

Similar phenomena are also shown on the CIFAR-10 set [20], suggesting that the optimization difficulties and the effects of our method are not just akin to a particular dataset. We present successfully trained models on this dataset with over 100 layers, and explore models with over 1000 layers.
在CIFAR-10集上也出现了类似的现象[20]，这表明我们的方法的优化困难和效果不仅仅类似于特定数据集。我们在这个数据集上成功地训练了超过100个层的模型，并探索了1000多个层的模型。

On the ImageNet classification dataset [35], we obtain excellent results by extremely deep residual nets. Our 152- layer residual net is the deepest network ever presented on ImageNet, while still having lower complexity than VGG nets [40]. Our ensemble has 3.57% top-5 error on the ImageNet test set, and won the 1st place in the ILSVRC 2015 classification competition. The extremely deep representations also have excellent generalization performance on other recognition tasks, and lead us to further win the 1st places on: ImageNet detection, ImageNet localization, COCO detection, and COCO segmentation in ILSVRC & COCO 2015 competitions. This strong evidence shows that the residual learning principle is generic, and we expect that it is applicable in other vision and non-vision problems.
在ImageNet分类数据集[35]上，我们通过极深的残差网得到了出色的结果。我们的152层残差网络是ImageNet上提出的最深的网络，同时其复杂度仍低于VGG网络[40]。在ImageNet测试集中，我们的集合有3.57％的top-5错误率，并在ILSVRC 2015分大赛中荣获第一名。极深的表征形式在其他识别任务上也具有出色的泛化性能，使我们在ILSVRC和COCO 2015竞赛中进一步赢得了第一名：ImageNet检测，ImageNet定位，COCO检测和COCO分割。这种强有力的证据表明，残留的学习原则是通用的，我们希望它是适用于其他视觉和非视觉问题。
退化问题：随着网络深度的增加，准确率达到饱和然后迅速退化。即网络达到一定层数后继续加深模型会导致模型表现下降。
意外的是，这种退化并不是由过拟合造成的，也不是由梯度消失和爆炸造成的，在一个合理的深度模型中增加更多的层却导致了更高的错误率。
解决思路：一是创造新的优化方法，二是化简现有的优化问题。而论文作者选择了第二种方法，通过让求解更深的神经网络模型变得更容易。

2 RelatedWork

2 相关工作

Residual Representations. In image recognition, VLAD [18] is a representation that encodes by the residual vectors with respect to a dictionary, and Fisher Vector [30] can be formulated as a probabilistic version [18] of VLAD. Both of them are powerful shallow representations for image retrieval and classification [4, 47]. For vector quantization, encoding residual vectors [17] is shown to be more effective than encoding original vectors.
残差表示。 在图像识别中，VLAD [18]是对字典的残差矢量进行编码的表示，Fisher Vector [30]可以表示为VLAD的概率版本[18]。它们都是用于图像检索和分类的有力的浅层表示[4，47]。对于矢量量化，残差矢量[17]进行编码被证明比原始矢量进行编码更有效。

In low-level vision and computer graphics, for solving Partial Differential Equations (PDEs), the widely used Multigrid method [3] reformulates the system as subproblems at multiple scales, where each subproblem is responsible for the residual solution between a coarser and a finer scale. An alternative to Multigrid is hierarchical basis preconditioning [44, 45], which relies on variables that represent residual vectors between two scales. It has been shown [3, 44, 45] that these solvers converge much faster than standard solvers that are unaware of the residual nature of the solutions. These methods suggest that a good reformulation or preconditioning can simplify the optimization.
在低级视觉和计算机图形学中，为了求解偏微分方程（PDEs），广泛使用的多网格方法[3]将系统重新形成为多个尺度的子问题，其中每个子问题负责粗尺度和细尺度之间的残差解。多网格的替代方法是分层基础预处理[44，45]，它依赖于表示两个尺度之间残差矢量的变量。已经证明[3，44，45]，这些求解器的收敛速度比不知道解决方案残差性质的标准求解器要快得多。这些方法表明，良好的重构或预处理可以简化优化过程。

Shortcut Connections. Practices and theories that lead to shortcut connections [2, 33, 48] have been studied for a long time. An early practice of training multi-layer perceptrons (MLPs) is to add a linear layer connected from the network input to the output [33, 48]. In [43, 24], a few intermediate layers are directly connected to auxiliary classifiers for addressing vanishing/exploding gradients. The papers of [38, 37, 31, 46] propose methods for centering layer responses, gradients, and propagated errors, implemented by shortcut connections. In [43], an “inception” layer is composed of a shortcut branch and a few deeper branches.
快捷连接。 导快捷连接[2、33、48]的实践和理论已经研究了很长时间。训练多层感知器（MLPs）的早期实践是添加从网络输入连接到输出的线性层[33，48]。在[43，24]中，一些中间层直接连接到辅助分类器，以解决梯度消失/爆炸。[38，37，31，46]的论文提出了通过捷径连接实现居中层响应、梯度和传播误差的方法。在[43]中，“起始”层由快捷分支和一些更深的分支组成。

Concurrent with our work, “highway networks” [41, 42] present shortcut connections with gating functions [15]. These gates are data-dependent and have parameters, in contrast to our identity shortcuts that are parameter-free. When a gated shortcut is “closed” (approaching zero), the layers in highway networks represent non-residual functions. On the contrary, our formulation always learns residual functions; our identity shortcuts are never closed, and all information is always passed through, with additional residual functions to be learned. In addition, highway networks have not demonstrated accuracy gains with extremely increased depth (e.g., over 100 layers).
与我们的工作同时，“高速公路网络”[41，42]提供了与门功能[15]的快捷连接。与我们的不带参数的标识快捷方式相反，这些门取决于数据并具有参数。当封闭的快捷方式“关闭”（接近零）时，高速公路网络中的层表示非残差函数。相反，我们的公式总是学习残差函数。我们的标识快捷键永远不会关闭，所有信息始终都会被传递，还需要学习其他残余函数。另外，“高速公路网络”还没有证明深度会大大增加（例如，超过100层）会提高准确性。

3 Deep Residual Learning

3.1 Residual Learning

3.1 残差学习

Let us consider H(x) as an underlying mapping to be fit by a few stacked layers (not necessarily the entire net), with x denoting the inputs to the first of these layers. If one hypothesizes that multiple nonlinear layers can asymptotically approximate complicated functions2, then it is equivalent to hypothesize that they can asymptotically approximate the residual functions, i.e., H(x) − x (assuming that the input and output are of the same dimensions). So rather than expect stacked layers to approximate H(x), we explicitly let these layers approximate a residual function F(x) := H(x) − x. The original function thus becomes F(x)+x. Although both forms should be able to asymptotically approximate the desired functions (as hypothesized), the ease of learning might be different.
让我们将H(x)视为由一些堆叠层（不一定是整个网络）拟合的基础映射，其中x表示这些层中第一层的输入。如果假设多个非线性层可以渐近地逼近复杂函数2，则等效于假设它们可以渐近地近似残差函数，即H(x)-x（假设输入和输出的维数相同）。因此，不是让堆叠的层逼近H(x)，而是明确让这些层逼近残差函数F(x)：=H(x)-x。因此，原始函数变为F(x)+x。尽管两种形式都应能够渐近地逼近所需的函数（如假设），但学习的难易程度可能有所不同。

This reformulation is motivated by the counterintuitive phenomena about the degradation problem (Fig. 1, left). As we discussed in the introduction, if the added layers can be constructed as identity mappings, a deeper model should have training error no greater than its shallower counterpart. The degradation problem suggests that the solvers might have difficulties in approximating identity mappings by multiple nonlinear layers. With the residual learning reformulation, if identity mappings are optimal, the solvers may simply drive the weights of the multiple nonlinear layers toward zero to approach identity mappings.
关于退化问题的反直觉现象促使这种重新构造（图1，左）。正如我们在引言中所讨论的，如果可以将添加的层构造为标识映射，则较深的模型应具有的训练误差不大于其较浅的模型的训练误差。退化问题表明，求解器在用多个非线性层逼近恒等映射时可能存在困难。通过残差学习的重构，如果恒等映射是最佳的，则求解器可以简单地将多个非线性层的权重趋近于零来逼近恒等映射。

In real cases, it is unlikely that identity mappings are optimal, but our reformulation may help to precondition the problem. If the optimal function is closer to an identity mapping than to a zero mapping, it should be easier for the solver to find the perturbations with reference to an identity mapping, than to learn the function as a new one. We show by experiments (Fig. 7) that the learned residual functions in general have small responses, suggesting that identity mappings provide reasonable preconditioning.
在实际情况下，恒等映射不太可能是最佳的，但是我们的重新构造可能有助于为这个问题提供先决条件。如果最优函数比零映射更接近恒等映射，则求解器参考恒等映射来查找扰动，应该比学习新函数更容易。我们通过实验（图7）表明，所学习的残差函数通常具有较小的响应，这表明恒等映射提供了合理的预处理。

3.2 Identity Mapping by Shortcuts

3.2 通过快捷方式进行恒等映射

We adopt residual learning to every few stacked layers. A building block is shown in Fig. 2. Formally, in this paper we consider a building block defined as:

y = F(x, {Wi}) + x. (1) Here x and y are the input and output vectors of the layers considered. The function F(x, {Wi}) represents the residual mapping to be learned. For the example in Fig. 2 that has two layers, F = W2σ(W1x) in which σ denotes ReLU [29] and the biases are omitted for simplifying notations. The operation F + x is performed by a shortcut connection and element-wise addition. We adopt the second nonlinearity after the addition (i.e., σ(y), see Fig. 2). 我们对每几个堆叠的层采用残差学习。构建块如图2所示。在形式上，在本文中，我们考虑定义为： y = F(x, {Wi}) + x. (1) 这里的x和y是所考虑层的输入和输出向量。函数F(x，{Wi})表示要学习的残差映射。对于图2中具有两层的示例，F =W2σ(W1x)，其中σ表示为简化符号，省略了ReLU [29]和偏差。F+x操作通过快捷连接和逐元素加法执行。在加法之后我们采用第二个非线性度(即σ(y)，见图2)。

The shortcut connections in Eqn.(1) introduce neither extra parameter nor computation complexity. This is not only attractive in practice but also important in our comparisons between plain and residual networks. We can fairly compare plain/residual networks that simultaneously have the same number of parameters, depth, width, and computational cost (except for the negligible element-wise addition).
公式(1)中，快捷连接既没有引入额外的参数，也没有引入计算复杂性。这不仅在实践中具有吸引力，而且在我们比较普通网络和残差网络时也很重要。我们可以公平地比较同时具有相同数量的参数、深度、宽度和计算成本（除了可以忽略的逐元素加法）的普通/残差网络。

The dimensions of x and F must be equal in Eqn.(1). If this is not the case (e.g., when changing the input/output channels), we can perform a linear projection Ws by the shortcut connections to match the dimensions:

y = F(x, {Wi}) +Wsx. (2) 在等式(1)中，x和F的维数必须相等。如果不是这种情况（例如，在更改输入/输出通道时），我们可以通过快捷方式连接执行线性投影Ws以匹配维度： y = F(x, {Wi}) +Wsx. (2)

We can also use a square matrixWs in Eqn.(1). But we will show by experiments that the identity mapping is sufficient for addressing the degradation problem and is economical, and thus Ws is only used when matching dimensions.
在等式(1)中，我们还可以使用方阵Ws。但是我们将通过实验证明，恒等映射足以解决退化问题并且经济，因此Ws仅在匹配维度时使用。

The form of the residual function F is flexible. Experiments in this paper involve a function F that has two or three layers (Fig. 5), while more layers are possible. But if F has only a single layer, Eqn.(1) is similar to a linear layer: y = W1x+x, for which we have not observed advantages.
残差函数F的形式是灵活的。本文中的实验涉及一个具有两层或三层的函数F（图5），而更多的层是可能的。但是，如果F仅具有一层，则等式(1)类似于线性层：y =W1x + x，对此我们没有观察到优势。

We also note that although the above notations are about fully-connected layers for simplicity, they are applicable to convolutional layers. The function F(x, {Wi}) can represent multiple convolutional layers. The element-wise addition is performed on two feature maps, channel by channel.
我们还注意到，尽管为简化起见，上述符号是关于全连接层的，但它们也适用于卷积层。函数F(x，{Wi})可以表示多个卷积层。在两个特征映射上逐个通道执行逐元素加法。

3.3 Network Architectures

3.3 网络体系结构

We have tested various plain/residual nets, and have observed consistent phenomena. To provide instances for discussion, we describe two models for ImageNet as follows.
Plain Network. Our plain baselines (Fig. 3, middle) are mainly inspired by the philosophy of VGG nets [40] (Fig. 3,left). The convolutional layers mostly have 3×3 filters and follow two simple design rules: (i) for the same output feature map size, the layers have the same number of filters; and (ii) if the feature map size is halved, the number of filters is doubled so as to preserve the time complexity per layer. We perform downsampling directly by convolutional layers that have a stride of 2. The network ends with a global average pooling layer and a 1000-way fully-connected layer with softmax. The total number of weighted layers is 34 in Fig. 3 (middle).
我们已经测试了各种平原/残差网络，并观察到了一致的现象。为了提供讨论实例，我们描述了ImageNet的两个模型，如下所示。
普通网络。 我们简单的基线（图3，中间）主要受到VGG网络原理的启发[40]（图3，左）。卷积层通常具有3×3的过滤器，并遵循两个简单的设计规则：(1)对于相同的输出要素图大小，这些层具有相同的过滤器数；(2)如果特征图的大小减半，则过滤器的数量将增加一倍，以保持每层的时间复杂度。我们直接通过步长为2的卷积层执行下采样。网络以全局平均池化层和带有softmax的1000路全连接层结束。图3中的加重层总数为34（中）。

It is worth noticing that our model has fewer filters and lower complexity than VGG nets [40] (Fig. 3, left). Our 34- layer baseline has 3.6 billion FLOPs (multiply-adds), which is only 18% of VGG-19 (19.6 billion FLOPs).
Residual Network. Based on the above plain network, we insert shortcut connections (Fig. 3, right) which turn the network into its counterpart residual version. The identity shortcuts (Eqn.(1)) can be directly used when the input and output are of the same dimensions (solid line shortcuts in Fig. 3). When the dimensions increase (dotted line shortcuts in Fig. 3), we consider two options: (A) The shortcut still performs identity mapping, with extra zero entries padded for increasing dimensions. This option introduces no extra parameter; (B) The projection shortcut in Eqn.(2) is used to match dimensions (done by 1×1 convolutions). For both options, when the shortcuts go across feature maps of two sizes, they are performed with a stride of 2.
值得注意的是，我们的模型比VGG网络[40]具有更少的过滤器和更低的复杂性（图3，左）。我们的34层基准具有36亿个FLOP（乘加），仅占VGG-19（196亿个FLOP）的18％。
残留网络。 在上面的普通网络的基础上，我们插入快捷方式连接（图3，右），将网络变成其对应的残差版本。当输入和输出的尺寸相同时，可以直接使用标识快捷方式（等式（1））（图3中的实线快捷方式）。当维度增加时（图3中的虚线快捷方式），我们考虑两个选项：（A）快捷方式仍然执行恒等映射，并为增加维度填充了额外的零项填充。此选项不引入任何额外的参数。（B）等式（2）中的投影快捷方式用于匹配维度（按1×1卷积完成）。对于这两个选项，当快捷方式遍历两种维度的特征图时，步幅为2。

3.4 Implementation

3.4 实施

Our implementation for ImageNet follows the practice in [21, 40]. The image is resized with its shorter side randomly sampled in [256, 480] for scale augmentation [40]. A 224×224 crop is randomly sampled from an image or its horizontal flip, with the per-pixel mean subtracted [21]. The standard color augmentation in [21] is used. We adopt batch normalization (BN) [16] right after each convolution and before activation, following [16]. We initialize the weights as in [12] and train all plain/residual nets from scratch. We use SGD with a mini-batch size of 256. The learning rate starts from 0.1 and is divided by 10 when the error plateaus, and the models are trained for up to 60×104 iterations. We use a weight decay of 0.0001 and a momentum of 0.9. We do not use dropout [13], following the practice in [16].
我们对ImageNet的实现遵循[21，40]中的做法。调整图像大小，并在[256，480]中随机采样其较短的一面，以进行比例增强[40]。从图像或其水平翻转中随机采样224×224作物，并减去每像素均值[21]。使用[21]中的标准色彩增强。在每次卷积之后和激活之前，紧接着[16]，我们采用批归一化(BN)[16]。我们按照[12]中的方法初始化权重，并从头开始训练所有普通/残差网络。我们使用最小批量为256的SGD。学习率从0.1开始，当误差平稳时除以10，并且对模型进行了多达60×104迭代的训练。我们使用0.0001的权重衰减和0.9的动量。我们不遵循[16]中的做法使用dropout[13]。

In testing, for comparison studies we adopt the standard 10-crop testing [21]. For best results, we adopt the fullyconvolutional form as in [40, 12], and average the scores at multiple scales (images are resized such that the shorter side is in {224, 256, 384, 480, 640}).
在测试中，为了进行比较研究，我们采用了标准的10种作物测试方法[21]。为了获得最佳结果，我们采用[40，12]中的完全卷积形式，并在多个尺度上对分数取平均（图像被调整大小，使得较短的边在{224，256，384，480，640}中）。

4 Experiments

4 实验

4.1 ImageNet Classification

4.1 ImageNet分类

We evaluate our method on the ImageNet 2012 classification dataset [35] that consists of 1000 classes. The models are trained on the 1.28 million training images, and evaluated on the 50k validation images. We also obtain a final result on the 100k test images, reported by the test server. We evaluate both top-1 and top-5 error rates.
Plain Networks. We first evaluate 18-layer and 34-layer plain nets. The 34-layer plain net is in Fig. 3 (middle). The 18-layer plain net is of a similar form. See Table 1 for detailed architectures.
我们在ImageNet 2012分类数据集[35]上评估了我们的方法，该数据集包含1000个类。在128万张训练图像上训练模型，并在50k验证图像上进行评估。我们还将在测试服务器报告的10万张测试图像上获得最终结果。我们评估了top-1和top-5的错误率。
普通网络。 我们首先评估18层和34层普通网络。34层普通网络在图3中（中）。18层普通网络具有类似的形式。有关详细架构，请参见表1。

The results in Table 2 show that the deeper 34-layer plain net has higher validation error than the shallower 18-layer plain net. To reveal the reasons, in Fig. 4 (left) we compare their training/validation errors during the training procedure. We have observed the degradation problem - the 34-layer plain net has higher training error throughout the whole training procedure, even though the solution space of the 18-layer plain network is a subspace of that of the 34-layer one.
表2中的结果表明，较深的34层普通网络比较浅的18层普通网络具有更高的验证误差。为了揭示原因，在图4（左）中，我们比较了他们在训练过程中的训练/验证错误。我们已经观察到了退化问题，即使18层普通网络的解空间是34层普通网络的子空间，在整个训练过程中34层普通网络具有较高的训练误差。

We argue that this optimization difficulty is unlikely to be caused by vanishing gradients. These plain networks are trained with BN [16], which ensures forward propagated signals to have non-zero variances. We also verify that the backward propagated gradients exhibit healthy norms with BN. So neither forward nor backward signals vanish. In fact, the 34-layer plain net is still able to achieve competitive accuracy (Table 3), suggesting that the solver works to some extent. We conjecture that the deep plain nets may have exponentially low convergence rates, which impact the reducing of the training error3. The reason for such optimization difficulties will be studied in the future.
我们认为，这种优化困难不太可能是由消失的梯度引起的。这些普通网络使用BN [16]进行训练，可确保前向传播信号具有非零方差。我们还验证了向后传播的梯度具有BN的健康规范。因此，前进或后退信号都不会消失。实际上，34层普通网络仍然可以达到竞争精度（表3），这表明求解器在某种程度上可以工作。我们推测深层的普通网络的收敛速度可能呈指数级降低，这会影响到减少训练误差。将来将研究这种优化困难的原因。

Residual Networks. Next we evaluate 18-layer and 34-layer residual nets (ResNets). The baseline architectures are the same as the above plain nets, expect that a shortcut connection is added to each pair of 3×3 filters as in Fig. 3 (right). In the first comparison (Table 2 and Fig. 4 right), we use identity mapping for all shortcuts and zero-padding for increasing dimensions (option A). So they have no extra parameter compared to the plain counterparts.
残差网络。 接下来，我们评估18层和34层残差网络（ResNets）。基线架构与上述普通网络相同，希望将快捷连接添加到图3（右）中的每对3×3过滤器中。在第一个比较中（表2和图4），我们将恒等映射用于所有短链接，将零填充用于增加维度（选项A）。因此，与普通网络相比，它们没有额外的参数。

We have three major observations from Table 2 and Fig. 4. First, the situation is reversed with residual learning – the 34-layer ResNet is better than the 18-layer ResNet (by 2.8%). More importantly, the 34-layer ResNet exhibits considerably lower training error and is generalizable to the validation data. This indicates that the degradation problem is well addressed in this setting and we manage to obtain accuracy gains from increased depth.
我们从表2和图4中获得了三个主要观察结果。首先，这种情况通过残差学习得以逆转34层ResNet优于18层ResNet（降低了2.8％）。更重要的是，34层ResNet表现出较低的训练误差，并且可以推广到验证数据。这表明在这种情况下可以很好地解决退化问题，并且我们设法从增加的深度中获得准确性的提高。

Second, compared to its plain counterpart, the 34-layer ResNet reduces the top-1 error by 3.5% (Table 2), resulting from the successfully reduced training error (Fig. 4 right vs. left). This comparison verifies the effectiveness of residual learning on extremely deep systems.
其次，与普通的34层相比ResNet将top-1错误减少了3.5％（表2），这是由于成功减少了训练错误（图4右与左）。这项比较验证了残留学习在极深系统上的有效性。

Last, we also note that the 18-layer plain/residual nets are comparably accurate (Table 2), but the 18-layer ResNet converges faster (Fig. 4 right vs. left). When the net is “not overly deep” (18 layers here), the current SGD solver is still able to find good solutions to the plain net. In this case, the ResNet eases the optimization by providing faster convergence at the early stage.
最后，我们还注意到18层普通/残差网络比较准确（表2），但18层ResNet收敛更快（图4右vs左）。当网络“不是太深”（此处为18层）时，当前的SGD求解器仍然能够为普通找到良好的解决方案。在这种情况下，ResNet通过在早期提供更快的收敛来简化优化。

Identity vs. Projection Shortcuts. We have shown that parameter-free, identity shortcuts help with training. Next we investigate projection shortcuts (Eqn.(2)). In Table 3 we compare three options: (A) zero-padding shortcuts are used for increasing dimensions, and all shortcuts are parameterfree (the same as Table 2 and Fig. 4 right); (B) projection shortcuts are used for increasing dimensions, and other shortcuts are identity; and © all shortcuts are projections.
恒等与投影短链接。 我们已经证明无参数的恒等快捷方式有助于训练。接下来，我们研究投影短链接（等式（2））。在表3中，我们比较了三个选项：（A）零填充短链接用于增加维度，并且所有短链接都是无参数的（与表2和右图4相同）；（B）投影短链接用于增加维度，其他短链接是恒等的。（C）所有短链接都是投影。

Table 3 shows that all three options are considerably better than the plain counterpart. B is slightly better than A.We argue that this is because the zero-padded dimensions in A indeed have no residual learning. C is marginally better than B, and we attribute this to the extra parameters introduced by many (thirteen) projection shortcuts. But the small differences among A/B/C indicate that projection shortcuts are not essential for addressing the degradation problem. So we do not use option C in the rest of this paper, to reduce memory/time complexity and model sizes. Identity shortcuts are particularly important for not increasing the complexity of the bottleneck architectures that are introduced below.
表3显示，所有三个选项都比普通选项好得多。B比A稍好。我们认为这是因为A中的零填充维度确实没有残留学习。C比B好一点，我们将其归因于许多（十三）投影快捷方式引入的额外参数。但是，A/B/C之间的细微差异表明，投影捷径对于解决退化问题并不是必不可少的。因此，在本文的其余部分中，我们不会使用选项C来减少内存/时间的复杂性和模型大小。恒等快捷方式对于不增加下面介绍的瓶颈架构的复杂性特别重要。

Deeper Bottleneck Architectures. Next we describe our deeper nets for ImageNet. Because of concerns on the training time that we can afford, we modify the building block as a bottleneck design4. For each residual function F, we use a stack of 3 layers instead of 2 (Fig. 5). The three layers are 1×1, 3×3, and 1×1 convolutions, where the 1×1 layers are responsible for reducing and then increasing (restoring) dimensions, leaving the 3×3 layer a bottleneck with smaller input/output dimensions. Fig. 5 shows an example, where both designs have similar time complexity.
更深的瓶颈架构。 接下来，我们将介绍ImageNet的更深层网络。由于担心我们可以负担得起的培训时间，因此我们将构建模块修改为瓶颈设计4。对于每个残差函数F，我们使用3层而不是2层的堆栈（图5）。这三个层分别是1×1、3×3和1×1卷积，其中1×1层负责减小然后增加（还原）尺寸，从而使3×3层成为输入/输出尺寸较小的瓶颈。图5显示了一个示例，其中两种设计都具有相似的时间复杂度。

The parameter-free identity shortcuts are particularly important for the bottleneck architectures. If the identity shortcut in Fig. 5 (right) is replaced with projection, one can show that the time complexity and model size are doubled, as the shortcut is connected to the two high-dimensional ends. So identity shortcuts lead to more efficient models for the bottleneck designs.
无参数标识短链接对于瓶颈体系结构特别重要。如果将图5（右）中的恒等短链接替换为投影，则可以显示时间复杂度和模型大小增加了一倍，因为短链接连接到两个高维端。因此，恒等短链接可以为瓶颈设计提供更有效的模型。

50-layer ResNet: We replace each 2-layer block in the 34-layer net with this 3-layer bottleneck block, resulting in a 50-layer ResNet (Table 1). We use option B for increasing dimensions. This model has 3.8 billion FLOPs.
50层ResNet： 我们替换了具有3层瓶颈块的34层网，形成了50层ResNet（表1）。我们使用选项B来增加尺寸。该模型具有38亿个FLOP。

101-layer and 152-layer ResNets: We construct 101-layer and 152-layer ResNets by using more 3-layer blocks (Table 1). Remarkably, although the depth is significantly increased, the 152-layer ResNet (11.3 billion FLOPs) still has lower complexity than VGG-16/19 nets (15.3/19.6 billion FLOPs).
101层和152层ResNet： 我们通过使用更多的3层块来构建101层和152层ResNet（表1）。值得注意的是，尽管深度显着增加，但152层ResNet（113亿个FLOP）的复杂度仍低于VGG-16/19网（153.96亿个FLOP）。

The 50/101/152-layer ResNets are more accurate than the 34-layer ones by considerable margins (Table 3 and 4). We do not observe the degradation problem and thus enjoy significant accuracy gains from considerably increased depth. The benefits of depth are witnessed for all evaluation metrics (Table 3 and 4).
50/101/152层ResNet比34层ResNet准确度高（表3和表4）。我们没有观察到退化问题，因此深度的增加大大提高了精度。所有评估指标都证明了深度的好处（表3和表4）。

Comparisons with State-of-the-art Methods. In Table 4 we compare with the previous best single-model results. Our baseline 34-layer ResNets have achieved very competitive accuracy. Our 152-layer ResNet has a single-model top-5 validation error of 4.49%. This single-model result outperforms all previous ensemble results (Table 5). We combine six models of different depth to form an ensemble (only with two 152-layer ones at the time of submitting). This leads to 3.57% top-5 error on the test set (Table 5). This entry won the 1st place in ILSVRC 2015.
与最新方法的比较。 在表4中，我们与以前的最佳单模型的结果进行了比较。我们的基准34层ResNet获得了非常具有竞争力的准确性。我们的152层ResNet的单模型top-5验证错误为4.49％。该单模型的结果优于所有之前的整体结果（表5）。我们将六个不同深度的模型组合在一起，形成一个整体（提交时只有两个152层模型）。这导致测试集上3.5-5的top-5错误（表5）。该作品在ILSVRC 2015中获得第一名。

4.2 CIFAR-10 and Analysis

4.2 CIFAR-10与分析

We conducted more studies on the CIFAR-10 dataset [20], which consists of 50k training images and 10k testing images in 10 classes. We present experiments trained on the training set and evaluated on the test set. Our focus is on the behaviors of extremely deep networks, but not on pushing the state-of-the-art results, so we intentionally use simple architectures as follows.
我们对CIFAR-10数据集[20]进行了更多研究，该数据集包含10个类别的50k训练图像和10k测试图像。我们介绍在训练集上训练的实验，并在测试集上进行评估。我们的重点是极度深度的网络的行为，而不是推动最先进的结果，因此我们有意使用了如下的简单架构。

The plain/residual architectures follow the form in Fig. 3 (middle/right). The network inputs are 32×32 images, with the per-pixel mean subtracted. The first layer is 3×3 convolutions. Then we use a stack of 6n layers with 3×3 convolutions on the feature maps of sizes {32, 16, 8} respectively, with 2n layers for each feature map size. The numbers of filters are {16, 32, 64} respectively. The subsampling is performed by convolutions with a stride of 2. The network ends with a global average pooling, a 10-way fully-connected layer, and softmax. There are totally 6n+2 stacked weighted layers. The following table summarizes the architecture:
普通/残留体系结构遵循图3中的形式（中间/右侧）。网络输入为32×32图像，每像素均值被减去。第一层是3×3卷积。然后，我们分别在大小为{32,16,8}的特征图上使用具有3×3卷积的6n层堆栈，每个特征图尺寸为2n层。过滤器的数量分别为{16,32,64}。二次采样通过步幅为2的卷积执行。网络以全局平均池，10路全连接层和softmax结尾。总共有6n +2个堆叠的加权层。下表总结了体系结构：

When shortcut connections are used, they are connected to the pairs of 3×3 layers (totally 3n shortcuts). On this dataset we use identity shortcuts in all cases (i.e., option A), so our residual models have exactly the same depth, width, and number of parameters as the plain counterparts.
使用快捷方式连接时，它们连接到成对的3×3层对（总共3n个快捷方式）。在此数据集上，我们在所有情况下都使用身份快捷方式（即选项A），因此我们的残差模型的深度，宽度和参数数量与普通模型完全相同。

We use a weight decay of 0.0001 and momentum of 0.9,and adopt the weight initialization in [12] and BN [16] but with no dropout. These models are trained with a minibatch size of 128 on two GPUs. We start with a learning rate of 0.1, divide it by 10 at 32k and 48k iterations, and terminate training at 64k iterations, which is determined on a 45k/5k train/val split. We follow the simple data augmentation in [24] for training: 4 pixels are padded on each side, and a 32×32 crop is randomly sampled from the padded image or its horizontal flip. For testing, we only evaluate the single view of the original 32×32 image.
我们使用0.0001的权重衰减和0.9的动量，并在[12]和BN [16]中采用权重初始化，但是没有丢失。这些模型在两个GPU上以最小批量为128进行训练。我们从0.1的学习率开始，在32k和48k迭代中将其除以10，然后在64k迭代中终止训练，这是由45k/5k的火车/ val分配决定的。我们按照[24]中的简单数据增强进行训练：在每侧填充4个像素，从填充的图像或其水平翻转中随机抽取3 2×32的农作物。为了进行测试，我们仅评估原始32×32图像的单个视图。

We compare n = {3, 5, 7, 9}, leading to 20, 32, 44, and 56-layer networks. Fig. 6 (left) shows the behaviors of the plain nets. The deep plain nets suffer from increased depth, and exhibit higher training error when going deeper. This phenomenon is similar to that on ImageNet (Fig. 4, left) and on MNIST (see [41]), suggesting that such an optimization difficulty is a fundamental problem.
我们比较n={3,5,7,9}，得出20、32、44和56层网络。图6（左）显示了普通网络的行为。较深的平原网会增加深度，并且在深入时会表现出较高的训练误差。这种现象类似于ImageNet（图4，左）和MNIST（参见[41]）上的现象，表明这种优化困难是一个基本问题。

We further explore n = 18 that leads to a 110-layer ResNet. In this case, we find that the initial learning rate of 0.1 is slightly too large to start converging5. So we use 0.01 to warm up the training until the training error is below 80% (about 400 iterations), and then go back to 0.1 and continue training. The rest of the learning schedule is as done previously. This 110-layer network converges well (Fig. 6, middle). It has fewer parameters than other deep and thin networks such as FitNet [34] and Highway [41] (Table 6),yet is among the state-of-the-art results (6.43%, Table 6).
我们进一步探索n=18导致110层ResNet。在这种情况下，我们发现初始学习速率0.1太大，无法开始收敛5。因此，我们使用0.01来预热训练，直到训练误差低于80％（约400次迭代），然后返回0.1并继续训练。其余的学习时间表与之前一样。这个110层的网络可以很好地融合（图6，中间）。它的参数比其他任何参数都少网络，例如FitNet [34]和Highway [41]（表6），但仍处于最新结果之中（6.43％，表6）。

Analysis of Layer Responses. Fig. 7 shows the standard deviations (std) of the layer responses. The responses are the outputs of each 3×3 layer, after BN and before other nonlinearity (ReLU/addition). For ResNets, this analysis reveals the response strength of the residual functions. Fig. 7 shows that ResNets have generally smaller responses than their plain counterparts. These results support our basic motivation (Sec.3.1) that the residual functions might be generally closer to zero than the non-residual functions. We also notice that the deeper ResNet has smaller magnitudes of responses, as evidenced by the comparisons among ResNet-20, 56, and 110 in Fig. 7. When there are more layers, an individual layer of ResNets tends to modify the signal less.
层响应分析。 图7显示了层响应的标准偏差（std）。响应是BN之后以及其他非线性（ReLU /加法）之前每个3×3层的输出。对于ResNet，此分析揭示了残差函数的响应强度。图7显示ResNet的响应通常比普通响应小。这些结果支持我们的基本动机（第3.1节），即与非残差函数相比，残差函数通常可能更接近于零。我们还注意到，较深的ResNet具有较小的响应幅度，如图7中ResNet-20、56和110之间的比较所证明的。当有更多层时，ResNets的单个层往往会修改信号较少。

Exploring Over 1000 layers. We explore an aggressively deep model of over 1000 layers. We set n = 200 that leads to a 1202-layer network, which is trained as described above. Our method shows no optimization difficulty, and this 103-layer network is able to achieve training error <0.1% (Fig. 6, right). Its test error is still fairly good (7.93%, Table 6).
探索超过1000层。 我们探索了一个超过1000层的深度模型。我们将n设置为200，这将导致1202层网络的运行，如上所述。我们的方法没有优化困难，该103层网络能够实现训练误差<0.1％（图6，右）。其测试误差仍然相当不错（7.93％，表6）。

But there are still open problems on such aggressively deep models. The testing result of this 1202-layer network is worse than that of our 110-layer network, although both have similar training error. We argue that this is because of overfitting. The 1202-layer network may be unnecessarily large (19.4M) for this small dataset. Strong regularization such as maxout [9] or dropout [13] is applied to obtain the best results ([9, 25, 24, 34]) on this dataset. In this paper, we use no maxout/dropout and just simply impose regularization via deep and thin architectures by design, without distracting from the focus on the difficulties of optimization. But combining with stronger regularization may improve results, which we will study in the future.
但是，在如此积极的深度模型上仍然存在未解决的问题。尽管这1202层网络的测试结果都比我们110层网络的测试结果差有类似的训练错误。我们认为这是由于过度拟合。对于这个小的数据集，1202层网络可能会不必要地大（19.4M）。使用强正则化(例如maxout [9]或dropout [13])可以在此数据集上获得最佳结果([9，25，24，34])。在本文中，我们不使用maxout/dropout，而只是通过设计通过深度和精简架构强加正则化，而不会分散对优化困难的关注。但是，结合更强的正则化可能会改善结果，我们将在以后进行研究。

4.3 Object Detection on PASCAL and MS COCO

4.3 基于PASCAL和MS-COCO的目标检测

Our method has good generalization performance on other recognition tasks. Table 7 and 8 show the object detection baseline results on PASCAL VOC 2007 and 2012 [5] and COCO [26]. We adopt Faster R-CNN [32] as the detection method. Here we are interested in the improvements of replacing VGG-16 [40] with ResNet-101. The detection implementation (see appendix) of using both models is the same, so the gains can only be attributed to better networks. Most remarkably, on the challenging COCO dataset we obtain a 6.0% increase in COCO’s standard metric (mAP@[.5,.95]), which is a 28% relative improvement. This gain is solely due to the learned representations.
我们的方法在其他识别任务上具有良好的泛化性能。表7和8显示了PASCAL VOC 2007和2012 [5]和COCO [26]上的对象检测基线结果。我们采用Faster R-CNN [32]作为检测方法。在这里，我们对用ResNet-101替换VGG-16 [40]的改进感兴趣。使用这两种模型的检测实现方式（请参阅附录）是相同的，因此只能将收益归因于更好的网络。最值得注意的是，在具有挑战性的COCO数据集上，我们的COCO标准指标（mAP @ [.5，.95]）增加了6.0％，相对提高了28％。该收益完全归因于所学的表示。

Based on deep residual nets, we won the 1st places in several tracks in ILSVRC & COCO 2015 competitions: ImageNet detection, ImageNet localization, COCO detection, and COCO segmentation. The details are in the appendix.
基于深层残差网络，我们在ILSVRC和COCO 2015竞赛的多个赛道上均获得了第一名：ImageNet检测，ImageNet本地化，COCO检测和COCO分割。详细信息在附录中。

残差网络事实上是由多个浅的网络融合而成,它没有在根本上解决消失的梯度问题,只是避免了消失的梯度问题,因为它是由多个浅的网络融合而成，浅的网络在训练时不会出现消失的梯度问题,所以它能够加速网络的收敛.