深度残差学习在图像识别中的应用

Posted 2021-04-07 视觉与机器学习实战

Abstract（摘要）

    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 [41] but still having lower complexity. An ensemble of these residual nets achieves 3.57% error ontheImageNet testset. This result won the 1st place on the ILSVRC 2015 classification task. We also present analysis on CIFAR-10 with 100 and 1000 layers.

    更深层次的神经网络更难训练。我们提出了一个残差学习框架，以简化对比以前使用的网络更深入的网络的训练。我们根据层输入显式地将层重新表示为学习残差函数（ learning residual functions），而不是学习未定义函数。我们提供了综合的经验证据，表明这些残差网络易于优化，并且可以从大幅度增加的深度中获得精度。在ImageNet数据集上，我们估计残差网络的深度可达152层--是vgg网络的8倍深[41]，但仍然具有较低的复杂性。这些残差网的集合在图像集上的误差达到了3.57%。这个结果获得了ILSVRC2015的分类任务第一名，我们还用CIFAR-10数据集分析了100层和1000层的网络。

    

    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 competitions 1 , where we also won the 1st places on the tasks of ImageNet detection, ImageNet localization, COCO detection, and COCO segmentation.

    表示的深度对于许多视觉识别任务是非常重要的。仅仅由于我们的表示非常深入，我们在coco对象检测数据集上得到了28%的相对改进。 深度残差网络是我们参加ILSVRC & COCO 2015 竞赛上所使用模型的基础，并且我们在ImageNet检测、ImageNet定位、COCO检测以及COCO分割上均获得了第一名的成绩。

 

1. Introduction(介绍)

    Deep convolutional neural networks [22, 21] have led to a series of breakthroughs for image classification [21,50, 40]. Deep networks naturally integrate low/mid/high-level features [50] and classifiers in an end-to-end multi-layer fashion, and the “levels” of features can be enriched by the number of stacked layers(depth). Recent evidence[41, 44] reveals that network depth is of crucial importance, and the leading results [41, 44, 13, 16] on the challenging ImageNet dataset [36] all exploit “very deep” [41] models, with a depth of sixteen [41] to thirty [16]. Many other nontrivial visual recognition tasks [8, 12, 7, 32, 27] have also greatly benefited from very deep models.

    深层卷积神经网络[22，21]导致了图像分类[21，50，40]的一系列突破。深层网络自然地将低/中/高层次特征[50]和分类器以端到端的多层方式集成在一起，而特征的“层次”可以通过堆叠层的数量（(深度）来丰富。最近的证据[41，44]表明，网络深度至关重要，在富有挑战性的ImageNet数据集[36]上的领先结果[41，44，13，16]都利用了“非常深”[41]模型，深度为16[41]至30[16]。许多其他非平凡（nontrivial）的视觉识别任务[8，12，7，32，27]也从非常深入的模型中获益良多。

 

    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 [1, 9], which hamper convergence from the beginning. This problem, however, has been largely addressed by normalized initialization [23, 9, 37, 13] and intermediate normalization layers [16], which enable networks with tens of layers to start converging for stochastic gradient descent (SGD) with backpropagation [22].

    在深度重要性的驱动下，出现了一个问题：学习更好的网络就像堆积更多的层一样容易吗？回答这个问题的一个障碍是臭名昭著的梯度消失/爆炸[1，9]的问题，它从一开始就阻碍了收敛（hamper convergence ）。然而，这个问题在很大程度上是通过标准化初始化[23，9，37，13]和中间归一化层[16]来解决的，这使得数十层的网络在反向传播的随机梯度下降（SGD）上能够收敛。

 

    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 [11, 42] 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，一个退化的问题就暴露出来了：随着网络深度的增加，精确度变得饱和(这可能不足为奇)，然后迅速退化。出乎意料的是，这种退化并不是由于过度拟合造成的，而且在适当深度的模型中增加更多的层会导致更高的训练误差，正如[11，42]中所报告的，并通过我们的实验进行了彻底验证。图1显示了一个典型的例子。

图1、20层和56层“朴素”网络的CIFAR-10上的训练错误(左)和测试错误(右)。网络越深，训练误差越大，测试误差越大。图4中给出了ImageNet上的类似现象。

 

    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

   (训练精度的）退化表明，并非所有系统都同样容易优化。让我们考虑一种更浅的体系结构及其更深层次的架构，它增加了更多的层。对于更深的模型，这有一种通过构建的解决方案：恒等映射（identity mapping）来构建增加的层，而其它层直接从浅层模型中复制而来。该解的存在性表明，更深层次的模型不应比较浅的模型产生更高的训练误差。 但是实验表明，我们目前无法找到一个与这种构建的解决方案相当或者更好的方案（或者说无法在可行的时间内实现）。

 

   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（ a deep residual learning framework ）来解决退化问题。我们不是希望每个层叠层直接拟合所需的底层映射（desired underlying mapping），而是显式地让这些层拟合一个残差映射（residual mapping）。假设所需的底层映射为 H(x)H(x)，我们让堆叠的非线性层来拟合另一个映射：F(x):=H(x)−xF(x)：=H(x)−x。因此原来的映射转化为：F(x)+xF(x)+x。我们假设优化残差映射比优化原始的未参考的映射容易。在极端情况下，如果恒等映射是最优的，则将残差推至零比用一堆非线性层拟合恒等映射更容易。

 

    The formulation of F(x)+x can be realized by feedforward neural networks with “shortcut connections” (Fig. 2). Shortcut connections [2, 34, 49] 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.

    公式 F(x)+x 可以通过前馈神经网络（ feedforward neural networks ）的“快捷连接（shortcut connections）”来实现(图2)。捷径连接[2，34，49]是跳过一个或多个层的连接。在本例中，快捷连接只执行恒等映射，它们的输出被添加到叠加层的输出中(图2)。恒等捷径连接既不增加额外的参数，也不增加计算的复杂性。整个网络仍然可以使用反向传播的SGD进行端到端的训练，并且可以使用公共库(例如caffe[19])来实现，而无需修改求解器（ solvers）。

                                    图2、残差学习：一个积木块

   We present comprehensive experiments on ImageNet[36] 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[36]上进行了综合实验，以说明退化问题并对我们的方法进行评估。结果表明：1)我们的极深残差网络易于优化，但对应的“朴素”网(即简单的层叠层)随着深度的增加，训练误差较大；2)我们的深层残差网可以很容易地从深度的大幅度增加中获得精度增益，比以前的网络产生的结果要好得多。

    

     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.

     CIFAR-10数据集上也出现了类似的现象，这表明了我们提出的方法的优化难度和效果并不仅仅是对于一个特定数据集而言的。我们在这个数据集上展示了经过成功训练的100层以上的模型，并探索了1000层以上的模型。

 

    On the ImageNet classification dataset [36], 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 [41]. 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分类集[36]上，我们利用极深的残差网得到了很好的结果。我们的152层剩余网是迄今为止在ImageNet上出现的最深的网络，但其复杂度仍然低于vgg网[41]。我们的组合在ImageNet测试集上有3.57%的前5错误（ top-5 error），并在ILSVRC 2015分类竞赛中获得了第一名。他在其他识别任务上也有很好的泛化能力，使我们在ILSVRC中的图像网络检测、图像网络定位、coco检测和coco分割方面获得了第一名。这一强有力的证据表明，残差学习原理是通用的，我们期望它适用于其他视觉和非视觉问题。

 

2. Related Work（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, 48]. 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]是用残差向量对字典进行编码的表示，Fisher向量[30]可以表示为VLAD的概率版本[18]。两者都是图像检索和分类的有力表示法[4，48]。对于矢量量化，编码剩余向量[17]比编码原始矢量更有效。

 

   In low-level vision and computer graphics, for solving Partial Differential Equations (PDEs), the widely used Multigrid method [3] reformulates the system as subprob lems 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 [45, 46], which relies on variables that represent residual vectors between two scales. It has been shown [3,45,46] 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.

   在低水平视觉和计算机图形学中，对于求解偏微分方程(PDEs)，广泛使用的多重网格方法[3]在多尺度上将系统重新定义为子问题，其中每个子问题负责较粗和较细尺度之间的残差解（ residual solution ）。多重网格的另一种选择是分层基预处理（ hierarchical basis preconditioning）[45，46]，它依赖于在两个尺度之间表示残差向量的变量。[3，45，46]已证明这些求解器比不知道解的残差性质的标准求解器收敛得快得多。这些方法表明，一个好的配方或预处理可以简化优化。

 

    Shortcut Connections. Practices and theories that lead to shortcut connections [2, 34, 49] 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 [34, 49]. In [44, 24], a few intermediate layers are directly connected to auxiliary classifiers for addressing vanishing/exploding gradients. The papers of [39, 38, 31, 47] propose methods for centering layer responses, gradients, and propagated errors, implemented by shortcut connections. In [44], an “inception” layer is composed of a shortcut branch and a few deeper branches.

    捷径连接。捷径连接[2, 34, 49] 已经经过了很长的一段实践和理论研究过程。一个训练多层感知器(MLPs)的早期实践是添加一个线性层，从网络输入连接到输出[34，49]。在[44，24]中，一些中间层直接连接到辅助分类器，用于解决消失/爆炸梯度（的问题）。[39，38，31，47]的论文提出了用捷径连接实现集中层响应、梯度和传播误差的方法。在[44]中，“Inception”层是由一个捷径分支和几个更深的分支组成的。

 

     Concurrent with our work, “highway networks” [42, 43] 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).

     与此同时，“ 高速网“（”highway networks”）[42,43]将捷径连接与门控函数[15]结合起来。这些门依赖于数据，并且有参数，而我们的恒等快捷连接（ identity shortcuts ）是无参数的。当门控捷径“关闭”(接近于零)时，公路网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；我们的恒等快捷连接永远不会关闭，所有信息都会被传递出去，而附加的残差函数将被学习。此外，高速网络在深度极深(例如，超过100层)的情况下，没有表现出精确性的提高。

 

3. Deep Residual Learning（深度残差学习）

3.1. Residual Learning（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 functions 2 , 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.

    让我们把H(x)看作是由几个层叠层(不一定是整个网)组成的底层映射，用x表示这些层中的第一个层的输入。如果假设多个非线性层可以渐近逼近复杂函数【2--This hypothesis, however, is still an open question. See [28].】，则等于假设它们可以渐近逼近残差函数，即H(X)−x(假设输入和输出具有相同的维度)。因此，与其期望叠加层近似H(X)，我们不如显式地让这些层近似一个残差函数F(x)：=h(x)−x。原来的函数因此变成F(x)+x。虽然这两种形式都应该能够渐近地近似于所期望的函数(如假设)，但学习的容易程度可能是不同的。

   

    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.

    此重新表示（ reformulation）是由有关退化问题的反直觉现象所驱动的(图1，左)。正如我们在介绍中所讨论的，如果可以将添加的层构造为恒等映射，则更深层次的模型应该具有不大于其浅层结构的训练错误。退化问题表明求解者很难用多个非线性层逼近恒等映射。利用残差学习重构，如果恒等映射是最优的，则求解者可以简单地将多个非线性层的权值推向零，以逼近恒等映射。

     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 thel earned 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优的，但是我们的重新表达对于这个问题的预处理是有帮助的。如果最优函数更接近于恒等映射而不是零映射，则求解者应该更容易找到与恒等映射有关的扰动（perturbations），而不是将其作为新的扰动来学习。我们通过实验(图7)证明了学习的残差函数一般都有较小的响应，说明恒等映射提供了合理的预条件。

 

3.2. Identity Mapping by Shortcuts（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:

    我们对每几个层叠的层次采用残差学习。图2中展示出了一个积木块（building block ）。形式上，在本文中，我们考虑了一个积木块被定义为：

 

      Here x and y are the input and output vectors of the layers considered. The function F(x,{W i }) represents the residual mapping to be learned. For the example in Fig. 2 that has two layers, F = W 2 σ(W 1 x) 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).

     这里x和y是考虑的层的输入和输出向量。函数

表示要学习的残差映射。 图2中的例子包含两层，

，其中σσ代表ReLU，为了简化省略了偏置项。F+xF+x操作由一个快捷连接和元素级（element-wise）的加法来表示。在加法之后我们再执行另一个非线性操作(例如, σ(y)σ(y)，如图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).

      Eq.1中的shortcut连接没有增加额外的参数和计算复杂度。这不仅在实践中很有吸引力，而且在我们比较普通网络和残差网络时也很重要。我们可以在参数、深度、宽度以及计算成本都相同的基础上对两个网络进行公平的比较（除了可以忽略不计的元素级的加法）。

  

    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 W s by the shortcut connections to match the dimensions:

    在eqn.（1）中，x和F的维数必须相等。如果情况并非如此(例如，在更改输入/输出通道时)，我们可以通过快捷连接执行线性投影W s ，以匹配维度:

  

      We can also use a square matrix W s 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 W s is only used when matching dimensions.

     我们还可以在eqn(1)中使用方阵Ws。但是，我们将通过实验证明，恒等映射对于解决退化问题是足够的，而且是经济的，因此只有在匹配维数时才使用Ws。

 

     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 = W 1 x+x, for which we have not observed advantages.

     残差函数F的形式是灵活的。本文的实验涉及一个函数F，它有两个或三个层(图5)，然而它可能有更多的层。但如果F只有一个单层，则eqn.(1)类似于线性层：y=w1x+x，对此我们没有发现任何优势。

    

    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,{W i }) can represent multiple convolutional layers. The element-wise addition is performed on two feature maps, channel by channel.

    我们还注意到，虽然为了简单起见，上述表示法是关于全连通层的，但它们适用于卷积层。函数F(x，{wi})可以表示多个卷积层.元素级加法是在两个特征映射上相应通道上执行的。.

 

3.3. Network Architectures（网络结构）

    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.

    我们测试了各种普通/残差网络，并观察到一致的现象。为了提供讨论的实例，我们对ImageNet的两个模型进行了如下描述。

    

    Plain Network. Our plain baselines (Fig. 3, middle) are mainly inspired by the philosophy of VGG nets [41] (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).

    Plain网络。我们的plain网络结构(图3，中)主要受VGG网络 (图.3，左)的启发。卷积层主要为3*3的滤波器，并遵循以下两点要求：(i) 输出特征映射尺寸相同的层含有相同数量的滤波器；(ii) 如果特征尺寸减半，则滤波器的数量增加一倍来保证每层的时间复杂度相同。我们直接用步长为2的卷积层进行下采样。网络以一个全局平均池层和一个带有Softmax的1000路全连接层结束。在图3(中)，有权值的层的总数为34 。

 

   It is worth noticing that our model has fewer filters and lower complexity than VGG nets [41] (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).

   值得注意的是，与vgg网[41]（图3，左）相比，我们的模型具有更少的滤波器和更低的复杂度。我们的34层基线（baseline）有36亿FLOPs乘加)，仅为VGG-19(196亿FLOPs)的18%。

        图3 对应于ImageNet的网络框架举例。 左：VGG-19模型 （196亿个FLOPs）作为参考。中：plain网络，含有34个参数层（36 亿个FLOPs）。右：残差网络，含有34个参数层（36亿个FLOPs）。虚线表示的shortcuts增加了维度。Table 1展示了更多细节和其它变体。 

 

   表1. 对应于ImageNet的结构框架。括号中为构建块的参数(同样见Fig.5)，数个构建块进行堆叠。下采样由stride为2的conv3_1、conv4_1和conv5_1 来实现。

 

      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.

      残差网络。基于上述plain网络，我们插入快捷连接(图3,右)将网络转换为对应的残差版本。当输入和输出尺寸相同时(图3中的实线快捷连接)，可以直接使用恒等快捷键(eqn.1)。当维度增加时（Fig.3中的虚线部分），考虑两个选项： (A) shortcut仍然使用恒等映射，在增加的维度上使用0来填充，这样做不会增加额外的参数； (B) 使用Eq.2的映射shortcut来使维度保持一致（通过1*1的卷积）。  对于这两个选项，当shortcut跨越两种尺寸的特征图时，均使用stride为2的卷积。

 

3.4. Implementation（实现）

   Our implementation for ImageNet follows the practice in [21, 41]. The image is resized with its shorter side randomly sampled in [256,480] for scale augmentation [41]. 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 [13] 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 60×10 4 iterations. We use a weight decay of 0.0001 and a momentum of 0.9. We do not use dropout [14], following the practice in [16].

   我们对ImageNet的实现遵循了[21，41]中的做法。调整图像的大小使它的短边长度随机的从[256,480] 中采样来进行尺寸扩展（ scale augmentation）[41]。 从图像或其水平翻转中随机抽取224×224 crop，并减去每个像素平均（the per-pixel mean）[21]。使用了[21]中的标准颜色增强。我们遵循[16]，在每次卷积之后，在激活之前采用批归一化(BN)[16]。我们像[13]一样初始化权重，从零开始训练所有plain/残差网。我们使用小批量大小为256的SGD。学习速率从0.1开始，当误差稳定时除以10，并且 整个模型进行60∗10^4次迭代训练。我们使用的权重衰减为0.0001，动量为0.9。我们不使用Dropout[14]，按照[16]的做法。

   

   In testing, for comparison studies we adopt the standard 10-crop testing [21]. For best results, we adopt the fully-convolutional form as in [41, 13], 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，我们采取标准的10-crop测试。 为了取得最好的效果，我们采用了[41，13]中的全卷积形式，并且在多尺度上平均分数(图像被调整大小，使较短的一面为{224，256，386，480，640})。

 

4. Experiments(实验）

4.1. ImageNet Classification（ImageNet分类）

    We evaluate our method on the ImageNet 2012 classificationdataset[36]thatconsistsof1000classes. Themodels 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.

    我们在ImageNet 2012分类数据集[36]上评估了我们的方法，该数据集包含1000个类。模型在128万张训练图像上进行了巽寮，在50k验证图像上进行了评估。我们还获得了测试服务器报告的100 k张测试图像的最终结果。我们评估了前1位和前5位的错误率（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

   普通的网络。我们首先评估18层和34层普通网。34层普通网在图3(中)。18层普通网具有类似的形式.详细的体系结构见表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的结果表明，较深的34层普通网比较浅的18层普通网具有更高的验证误差。为了揭示原因。在图4(左)中，我们在训练过程中比较他们的训练/验证错误。我们在整个训练过程中观察到了34层普通网的退化问题---它在整个训练过程中训练误差较大，尽管18层普通网的解空间（ solution space）是34层普通网的子空间。

  图4、关于ImageNet的训练。细曲线表示训练误差，粗体曲线表示中心crop的验证误差。左：18层和34层的普通网络。右：18层和34层残差网络。在此图中，与普通网络相比，残差网络没有（增加）额外的参数。

 

表2、ImageNet验证上的Top-1错误(%，10-crop 测试)。在这里，与普通的对等网相比，残差网没有额外的参数。图4展示了培训过程。

 

   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 error【3-- We have experimented with more training iterations (3×) and still observed the degradation problem, suggesting that this problem cannot be feasibly addressed by simply using more iterations.】】. 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梯度消失引起的。这些简单的网络使用BN[16]进行训练，从而确保前向传播的信号具有非零方差。我们还验证了使用BN的向后传播梯度具有健康的行为（norms）。所以无论向前还是向后信号都不会消失。事实上，34层普通网仍然能够达到具有竞争力的精度(表3)，这表明求解器在某种程度上可以工作。我们推测深普通网可能具有指数级别的低收敛速度，从而影响训练误差的减小【3--我们已经试验了更多的训练迭代(3×)，并仍然观察到退化问题，这表明这个问题不可能通过简单地使用更多的迭代来解决】。这种优化困难的原因将在今后进行研究。

 

   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(ResNet).基线结构与上述普通网相同，只是要求在每对3×3过滤器中添加一个快捷连接，如图3(右）所示。在第一个比较中(表2和图4右)，我们使用所有快捷方式为恒等映射，以及使用零填充增加维度(选项A)。因此，与普通的对应网络相比，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中有三个主要的观察结果。首先，使用残差学习的情况与之前（普通网）相反----34层ResNet优于18层 ResNet(2.8%).更重要的是，34层ResNet的训练误差要小得多，并且可以推广到验证数据.这表明，在这种情况下，退化问题得到了很好的解决，并且我们设法从增加的深度中获得了精度增益。

   

   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.

   第二，与普通的对应网络相比，34层ResNet使Top-1误差减少了3.5%(表2)，这是成功地减少了训练误差(图2)的结果（图4右 VS 左)）。这一比较验证了残差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/残差网具有大致相等的精确率(表2)，但18层ResNet的收敛速度更快(图4右 VS 左)。当网络“不太深”(比如这里的18层)时，当前的SGD解决程序仍然能够为普通网络找到好的解决方案。在这种情况下，ResNet通过在早期阶段提供更快的收敛速度来简化优化。

 

    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 parameter- free (the same as Table 2 and Fig. 4 right); (B) projection shortcuts are used for increasing dimensions, and other shortcuts are identity; and (C) all shortcuts are projections.

    恒等快捷键 VS 投影快捷键（ Projection Shortcuts）。我们已经证明，无参数的恒等快捷键有助于培训。接下来我们研究投影快捷键(eqn.(2)。在表3中，我们比较了三个选项：(A)零填充快捷键用于增加维度，所有快捷方式都是无参数的(与表2和图4右相同)；(B)投影快捷键用于增加尺寸，而其他快捷键是恒等快捷键；(C)所有快捷键都是投影快捷键。

  表3、对ImageNet验证的错误率(%，10-crop测试)。vgg-16是基于我们的测试。ResNet-50/101/152属于方案B ，它只对增加的维度使用投影（快捷键）。

 

   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 indeedhavenoresiduallearning. Cismarginallybetterthan 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，所有这三个选项都比普通的对应方案要好得多。B比A稍好。我们认为，这是因为A中零填充的维度实际上并没有（使用）残差学习。C比b略好，我们把这归因于许多(13个)投影快捷键引入的额外参数。但是a/b/c之间的小差异表明，投影快捷键对于解决退化问题并不重要。因此，在本文的其余部分中，我们不使用选项c以降低计算/时间复杂度和模型大小。恒等快捷键对于不增加下面介绍的瓶颈架构（bottleneck architectures）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 design 4 . 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.

   更深层次的瓶颈架构。接下来，我们将描述我们针对ImageNet的更深层次的网络。由于考虑到我们负担得起的训练时间，我们将积木块（building block）修改为瓶颈设计（bottleneck design）。对于每个残差函数F，我们使用一个由3层组成的堆栈，而不是2层(图5)。这三层分别是1×1、3×3和1×1卷积，其中1×1层负责减小然后增加(恢复)维数，使3×3层成为输入/输出维数较小的瓶颈。图5给出了一个例子，其中两种设计都具有相似的时间复杂度。

图5、ImageNet的一个更深层次的残差函数F。左图：如图3所示的用于ResNet-34的一个及积木块(在56×56特征图上)。右：ResNet-50/101/152的“瓶颈”积木块。

 

   The parameter-free identity shortcuts are particularly important forthe bottleneck architectures. Ifthe 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.

  无参数的恒等快捷键对于瓶颈架构尤其重要。如果是图5（右）中的同恒等快捷键用投影快捷键代替，可以看出时间复杂度和模型大小加倍，因为快捷方式连接到两个高维端点。因此，恒等快捷键为瓶颈设计提供了更有效的模型。

 

     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：我们将34层网络中的每个2层块替换为这个3层瓶颈块，从而形成一个50层ResNet(表1).我们使用选项B来增加维度。这种模式有38亿次FLOPs。

    

    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：我们使用更多的三层块来构造101层和152层的ResNet(表1).值得注意的是，虽然深度明显增加，但152层 ResNet((113亿次 FLOPs)的复杂性仍然低于vgg-16/19网(153/196亿次 FLOPs)。

 

   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层网有相当大程度的准确率提升(表3和表4)。我们没有观察到退化的问题，因此，我们可以享受从大大增加的深度中获得的显著的精确性。所有评价指标都能看到深度的好处(表3和表4)。

    表4、ImageNet验证集上单模型结果的错误率(%)(除了†报告了测试集)。

 

       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.

       和最先进的方法比较。在表4中，我们将与之前最好的单模型结果进行比较。我们的基线34层ResNet已经达到了非常竞争的准确性。我们的152层 ResNet的单模型Top-5验证误差为4.49%。这个单一模型的结果优于所有以前的集成结果(表5)。我们将六个不同深度的模型组合成一个整体(在提交时只有两个152层网络)。这将得到了测试集上3.57%的Top-5错误(表5).这一项目获得了2015年ILSVRC的第一名。

表5、组合的错误率(%)。在ImageNet的测试集上的top-5错误，并由测试服务器报告。

 

4.2. CIFAR-10 and Analysis（CIFAR-10和分析）

     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.

     我们在CIFAR-10数据集[20]进行了更多的研究，该数据集包括50个训练图像和10个类别的10k测试图像。我们在训练集上进行了实验训练，并在测试集上进行了评估。我们的重点是极深网络的行为，而不是推进最先进的结果，所以我们故意使用简单的架构如下。

 

     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 filtersare{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, andsoftmax. There are totally 6n+2 stacked weighted layers. The following table summarizes the architecture:

     普通/残差结构遵循图3(中/右)中的形式。网络输入32×32图像，每像素被减去每像素平均（ with the per-pixel mean subtracted）。第一层为3×3卷积层。然后，我们在尺寸为{32，16，8}的特征映射上分别使用3×3卷积的共6n层叠加，每个特征地图大小都有2n层。滤波数分别为{16，32，64}。下采样是以2的步长的卷积来执行的。。网络以全局平均池、10路全连接层和softmax为结束。共有6n+2层加权层。下表概述了该体系结构：

     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.

    当使用快捷连接时，它们被连接到3×3层的对上(总共3n条捷径)。在这个数据集中，我们在所有情况下都使用恒等快捷键(即选项A)，因此，我们的残差模型的深度、宽度和参数与对应的普通模型完全相同。

 

    We use a weight decay of 0.0001 and momentum of 0.9, and adopt the weight initialization in [13] and BN [16] but with no dropout. These models are trained with a mini-batch 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.

    我们使用权重衰减为0.0001，动量为0.9，采用了在[13]中的权值初始化在[13]和bn[16]，但没有使用Dropout。这些模型是在两个GPU上训练的，小批量大小为128。我们的学习速度为0.1，在第32K和48K次迭代时除以10，在64k迭代时终止训练，这是由45k/5k训练/验证的分割决定。我们按照[24]中的简单数据增强进行训练：每边填充4个像素，从填充图像或水平翻转中随机抽取32×32帧。对于测试，我们只评估原始32×32图像的单一图像。

    

    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 [42]), suggesting that such an optimization difficulty is a fundamental problem.

    我们比较n={3，5，7，9}，从而形成的20，32，44和56层网络。图6(左)显示了普通网的行为。深普通网随着深度增大，深度训练误差较大。这个现象类似于ImageNet(图4左）和mnist(见[42])上的现象，这表明这种优化困难是一个基本问题。

 

     Fig. 6 (middle) shows the behaviors of ResNets. Also similar to the ImageNet cases (Fig. 4, right), our ResNets manage to overcome the optimization difficulty and demonstrate accuracy gains when the depth increases.

     图6(中间)显示了残差网的行为。类似于ImageNet的案例(图4，右)，当深度增加时，我们的残差网也设法克服了优化的困难，并提高了精度。

 

     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 converging 5 . 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

     我们进一步探索了当n=18时获得的110层ResNet。在这种情况下，我们发现初始学习速率0.1太大，以致无法开始收敛。因此，我们使用0.01的学习速率为训练热身，直到训练误差小于80%(约400次迭代)，然后将学习速率改为0.1继续训练。学习计划的其余部分和以前一样。这个110层网络能够很好地收敛(图6， 中)。它的参数比 FitNet[35]和 Highway[42](表6)等其他深而瘦的网络少，但却是最先进的结果之一(6.43%，表6)。

图6、在CIFAR-10上的训练。虚线表示训练错误，粗体线表示测试错误。左：普通网络。普通-110的误差大于60%，不显示。中间：残差网。右：有110层和1202层的残差网。

表6、CIFAR-10测试集的分类错误。所有方式都有数据增强。对于ResNet-110，我们运行5次，显示“最佳(平均±STD)”，如[43]中。

    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 analy-sis 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显示层响应的标准差(std)。响应为每个3×3层的输出，它在BN之后，在其它非线性(relu/加法)之前。对于ResNet，本分析揭示了残差函数的响应强度。图7表明残差网的响应一般比普通网的小。这些结果支持了我们的基本动机(第3.1节)，即残差函数一般比非残差函数更接近于零。我们还注意到，较深的ResNet的响应幅度较小，如图7中ResNet-20、56和110之间的比较所示。当有更多的层时，单个的一层残差网倾向于对信号进行较少的修改。

图7、CIFAR-10层响应的标准差(STD)。响应是每个3×3层的输出，在BN之后，在非线性之前。顶部：各层按原来的顺序显示。底部：响应按降序排列。

 

    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 10 3 -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（的网络）。我们探索了一个超过1000层的深度模型。我们设置n=200得到1202层网络，该网络就像上面所描述的那样被训练。我们的方法不存在优化困难，该1000层网络的训练误差小于0.1%(图6，右)。它的测试误差仍然相当好(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 [10] or dropout [14] is applied to obtain the best results ([10, 25, 24, 35]) 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 optimiza-

tion. But combining with stronger regularization may improve results, which we will study in the future.

    但在这些激进的深层次模型上，仍存在一些有待解决的问题。这个1202层网络的测试结果比我们的110层网络差，尽管两者都有相似的训练误差。我们认为这是因为过拟合。对于这个小数据集，1202层网络可能不必要地大(19.4M)。在此数据集使用强正则化，如maxout[10]或dropout[14]，可以获得最佳结果([10，25，24，35]。但在本文中，我们使用的是无 maxout/无漏的方法，只需通过深而瘦的结构设计来实现正则化，而不分散对优化的困难的关注。但是，与更强的正则化相结合可以提高结果，这是我们今后研究的方向。

 

4.3. Object Detection on PASCAL and MS COCO（在PASCAL和MS COCO上的目标检测）

   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 [41] 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.

   该方法对其它识别任务具有较好的泛化性能。表7和表8显示了PASCAL VOC     2007 and 2012[5]和COCO[26]的目标检测基线结果。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[41]的改进感兴趣。使用这两种模型的检测实现(见附录)是相同的，因此收益只能归功于更好的网络。最值得注意的是，在具有挑战性的coco数据集上，我们得到了coco标准度量的6.0%的增长(map@[.5，.95])，，这是一个28%的相对改进。这一收益完全归功于所学习的表述（learned representations）。

表7、在Pascal voc 2007/2012测试集上使用基线Faster R-CNN的目标检测 mAP(%)。更好的结果见10和11。

表8、在coco验证集上 使用基线Faster R-CNN的目标检测mAP(%)。另见表9，以获得更好的结果。

 

    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.

    基于深度剩余网，我们在ILSVRC的几个项目中获得了第一名：Imagenet检测，ImageNet定位，coco检测和coco分割。详情见附录。