Deep Residual Learning for Image Recognition
用于图像识别的深度残差学习
Abstract 抽象
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$\times$ deeper than VGG nets [41] 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 CIFAR10 with 100 and 1000 layers.
更深的神经网络更难训练。我们提出了一个残差学习框架，以简化比以前使用的要深入得多的网络训练。我们参考层输入显式地将层重新表述为学习残差函数，而不是学习未引用的函数。我们提供了全面的实证证据，表明这些残差网络更容易优化，并且可以从大大增加的深度中获得准确性。
在 ImageNet 数据集上，我们评估了深度高达 152 层的残差网络，比 VGG 网络 [41] $\times$ 深 8 层，但仍然具有较低的复杂性。这些残差网络的集合在 ImageNet 测试集上实现了 3.57% 的误差。这一结果在 ILSVRC 2015 分类任务中获得了第一名。我们还介绍了 100 层和 1000 层的 CIFAR10 分析。
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}^{1}1http://imagenet.org/challenges/LSVRC/2015/ and http://mscoco.org/dataset/#detectionschallenge2015.
http://imagenet.org/challenges/LSVRC/2015/ 和 http://mscoco.org/dataset/#detectionschallenge2015。
表示的深度对于许多视觉识别任务至关重要。仅仅由于我们极深入的表示，我们在 COCO 对象检测数据集上获得了 28% 的相对改进。深残网是我们向ILSVRC和COCO 2015比赛提交的基础1, where we also won the 1st places on the tasks of ImageNet detection, ImageNet localization, COCO detection, and COCO segmentation.
，我们还在 ImageNet 检测、ImageNet 定位、COCO 检测和 COCO 分割任务中获得了第一名。
1 Introduction 1 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/highlevel features [50] and classifiers in an endtoend multilayer 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.
深度卷积神经网络 [22， 21] 为图像分类带来了一系列突破 [21， 50， 40]。深度网络自然地以端到端的多层方式集成低/中/高级特征 [50] 和分类器，并且特征的“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，在具有挑战性的ImageNet数据集[36]上的主要结果[41,44,13,16]都利用了“非常深”的[41]模型，深度为16 [41]到30 [16]。许多其他非平凡的视觉识别任务 [8， 12， 7， 32， 27] 也从非常深的模型中受益匪浅。
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，一个问题出现了：学习更好的网络是否就像堆叠更多层一样容易？回答这个问题的一个障碍是臭名昭著的梯度消失/爆炸问题 [1， 9]，它从一开始就阻碍了收敛。然而，这个问题在很大程度上已经通过归一化初始化 [23， 9， 37， 13] 和中间归一化层 [16] 得到解决，它们使具有数十层的网络能够开始收敛以实现具有反向传播的随机梯度下降 （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 [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，就会暴露出一个劣化问题：随着网络深度的增加，准确性会达到饱和（这可能不足为奇），然后迅速下降。出乎意料的是，这种退化不是由过拟合引起的，并且向适当深度的模型添加更多层会导致更高的训练误差，如 [11， 42] 中所报告的那样，并通过我们的实验进行了彻底验证。无花果。1 显示了一个典型的示例。
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 comparably good or better than the constructed solution (or unable to do so in feasible time).
（训练精度的）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架构和在其上添加更多层的较深的对应结构。存在一个通过构建到更深模型的解决方案：添加的层是身份映射，而其他层是从学习的较浅模型复制的。这种构造解的存在表明，较深的模型不应产生比较浅的模型更高的训练误差。但实验表明，我们手头的求解器无法找到与构造的解决方案相当好或更好的解决方案（或者无法在可行的时间内做到这一点）。
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 $\mathcal{H}(\mathbf{x})$, we let the stacked nonlinear layers fit another mapping of $\mathcal{F}(\mathbf{x}):=\mathcal{H}(\mathbf{x})\mathbf{x}$. The original mapping is recast into $\mathcal{F}(\mathbf{x})+\mathbf{x}$.
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。我们不是希望每个几个堆叠层都直接拟合所需的底层映射，而是明确地让这些层拟合残差映射。形式上，将所需的底层映射表示为 $\mathcal{H}(\mathbf{x})$ ，我们让堆叠的非线性层拟合 的另一个 $\mathcal{F}(\mathbf{x}):=\mathcal{H}(\mathbf{x})\mathbf{x}$ 映射。原始映射将重新转换为 $\mathcal{F}(\mathbf{x})+\mathbf{x}$ 。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，如果恒等映射是最优的，那么将残差推到零比通过一堆非线性层拟合恒等映射要容易得多。
The formulation of $\mathcal{F}(\mathbf{x})+\mathbf{x}$ 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 endtoend by SGD with backpropagation, and can be easily implemented using common libraries (e.g., Caffe [19]) without modifying the solvers.
的公式 $\mathcal{F}(\mathbf{x})+\mathbf{x}$ 可以通过具有“捷径连接”的前馈神经网络来实现（图 D）。2）. 快捷连接 [2， 34， 49] 是跳过一个或多个图层的连接。在我们的例子中，快捷连接只执行身份映射，它们的输出被添加到堆叠层的输出中（图 D）。2）. 身份快捷方式连接既不会增加额外的参数，也不会增加计算复杂性。整个网络仍然可以通过具有反向传播的 SGD 进行端到端训练，并且可以使用公共库（例如 Caffe [19]）轻松实现，而无需修改求解器。
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]上进行了全面的实验，以展示退化问题并评估我们的方法。我们表明：1） 我们的极深残差网络很容易优化，但当深度增加时，对应的 “普通” 网络（简单地堆叠层）表现出更高的训练误差;2） 我们的深残差网可以轻松享受大幅增加的深度带来的精度增益，产生的结果比以前的网络要好得多。
Similar phenomena are also shown on the CIFAR10 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.
类似的现象也显示在 CIFAR10 集 [20] 上，这表明我们方法的优化难度和效果不仅仅是类似于特定的数据集。我们展示了此数据集上具有 100 多个层的成功训练模型，并探索了具有 1000 多个层的模型。
On the ImageNet classification dataset [36], we obtain excellent results by extremely deep residual nets.
Our 152layer residual net is the deepest network ever presented on ImageNet, while still having lower complexity than VGG nets [41]. Our ensemble has 3.57% top5 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 nonvision problems.
在 ImageNet 分类数据集 [36] 上，我们通过极深的残差网络获得了出色的结果。我们的 152 层残差网络是 ImageNet 上有史以来最深的网络，同时仍然比 VGG 网络复杂度低 [41]。我们的集成在 ImageNet 测试集上有 3.57% 的前 5 名误差，并在 ILSVRC 2015 分类竞赛中获得第一名。极深的表示在其他识别任务上也具有出色的泛化性能，并引导我们在以下方面进一步赢得了第一名：ImageNet检测、ImageNet定位、COCO检测和COCO分割在ILSVRC & COCO 2015比赛中。这一有力的证据表明，残差学习原则是通用的，我们预计它适用于其他视力和非视力问题。
2 Related Work 阿拉伯数字 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] 是一种由残差向量相对于字典进行编码的表示，Fisher Vector [30] 可以表述为 VLAD 的概率版本 [18]。它们都是用于图像检索和分类的强大浅层表示 [4， 48]。对于向量量化，编码残差向量 [17] 被证明比编码原始向量更有效。
In lowlevel 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 [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.
在低级视觉和计算机图形学中，为了求解偏微分方程 （PDE），广泛使用的 Multigrid 方法 [3] 将系统重构为多个尺度的子问题，其中每个子问题负责较粗尺度和较精细尺度之间的残差解。Multigrid 的另一种方法是分层基预处理 [45， 46]，它依赖于表示两个尺度之间残差向量的变量。已经表明 [3， 45， 46] 这些求解器的收敛速度比不知道解的残差性质的标准求解器快得多。这些方法表明，良好的重新配制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 multilayer 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.
Concurrent with our work, “highway networks” [42, 43] present shortcut connections with gating functions [15]. These gates are datadependent and have parameters, in contrast to our identity shortcuts that are parameterfree. When a gated shortcut is “closed” (approaching zero), the layers in highway networks represent nonresidual 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).
3 Deep Residual Learning
3.1 Residual Learning
Let us consider $\mathcal{H}(\mathbf{x})$ as an underlying mapping to be fit by a few stacked layers (not necessarily the entire net), with $\mathbf{x}$ denoting the inputs to the first of these layers. If one hypothesizes that multiple nonlinear layers can asymptotically approximate complicated functions^{2}^{2}2This hypothesis, however, is still an open question. See [28]., then it is equivalent to hypothesize that they can asymptotically approximate the residual functions, i.e., $\mathcal{H}(\mathbf{x})\mathbf{x}$ (assuming that the input and output are of the same dimensions). So rather than expect stacked layers to approximate $\mathcal{H}(\mathbf{x})$, we explicitly let these layers approximate a residual function $\mathcal{F}(\mathbf{x}):=\mathcal{H}(\mathbf{x})\mathbf{x}$. The original function thus becomes $\mathcal{F}(\mathbf{x})+\mathbf{x}$. Although both forms should be able to asymptotically approximate the desired functions (as hypothesized), the ease of learning might be different.
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.
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.
3.2 Identity Mapping by Shortcuts
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:
$\mathbf{y}=\mathcal{F}(\mathbf{x},\{W_{i}\})+\mathbf{x}.$  (1) 
Here $\mathbf{x}$ and $\mathbf{y}$ are the input and output vectors of the layers considered. The function $\mathcal{F}(\mathbf{x},\{W_{i}\})$ represents the residual mapping to be learned. For the example in Fig. 2 that has two layers, $\mathcal{F}=W_{2}\sigma(W_{1}\mathbf{x})$ in which $\sigma$ denotes ReLU [29] and the biases are omitted for simplifying notations. The operation $\mathcal{F}+\mathbf{x}$ is performed by a shortcut connection and elementwise addition. We adopt the second nonlinearity after the addition (i.e., $\sigma(\mathbf{y})$, see Fig. 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 elementwise addition).
The dimensions of $\mathbf{x}$ and $\mathcal{F}$ 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:
$\mathbf{y}=\mathcal{F}(\mathbf{x},\{W_{i}\})+W_{s}\mathbf{x}.$  (2) 
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.
The form of the residual function $\mathcal{F}$ is flexible. Experiments in this paper involve a function $\mathcal{F}$ that has two or three layers (Fig. 5), while more layers are possible. But if $\mathcal{F}$ has only a single layer, Eqn.(1) is similar to a linear layer: $\mathbf{y}=W_{1}\mathbf{x}+\mathbf{x}$, for which we have not observed advantages.
We also note that although the above notations are about fullyconnected layers for simplicity, they are applicable to convolutional layers. The function $\mathcal{F}(\mathbf{x},\{W_{i}\})$ can represent multiple convolutional layers. The elementwise addition is performed on two feature maps, channel by channel.
3.3 Network Architectures
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 [41] (Fig. 3, left). The convolutional layers mostly have 3$\times$3 filters and follow two simple design rules: (i) for the same output feature map size, the layers have the same number of filters; and (ii) if the feature map size is halved, the number of filters is doubled so as to preserve the time complexity per layer. We perform downsampling directly by convolutional layers that have a stride of 2. The network ends with a global average pooling layer and a 1000way fullyconnected layer with softmax. The total number of weighted layers is 34 in Fig. 3 (middle).
It is worth noticing that our model has fewer filters and lower complexity than VGG nets [41] (Fig. 3, left). Our 34layer baseline has 3.6 billion FLOPs (multiplyadds), which is only 18% of VGG19 (19.6 billion FLOPs).
Residual Network. Based on the above plain network, we insert shortcut connections (Fig. 3, right) which turn the network into its counterpart residual version. The identity shortcuts (Eqn.(1)) can be directly used when the input and output are of the same dimensions (solid line shortcuts in Fig. 3). When the dimensions increase (dotted line shortcuts in Fig. 3), we consider two options: (A) The shortcut still performs identity mapping, with extra zero entries padded for increasing dimensions. This option introduces no extra parameter; (B) The projection shortcut in Eqn.(2) is used to match dimensions (done by 1$\times$1 convolutions). For both options, when the shortcuts go across feature maps of two sizes, they are performed with a stride of 2.
layer name  output size  18layer  34layer  50layer  101layer  152layer 
conv1  112$\times$112  7$\times$7, 64, stride 2  
conv2_x  56$\times$56  3$\times$3 max pool, stride 2  
$\left[\begin{array}[]{c}\text{3$\times$3, 64}\\[1.00006pt] \text{3$\times$3, 64}\end{array}\right]$$\times$2  $\left[\begin{array}[]{c}\text{3$\times$3, 64}\\[1.00006pt] \text{3$\times$3, 64}\end{array}\right]$$\times$3  $\left[\begin{array}[]{c}\text{1$\times$1, 64}\\[1.00006pt] \text{3$\times$3, 64}\\[1.00006pt] \text{1$\times$1, 256}\end{array}\right]$$\times$3  $\left[\begin{array}[]{c}\text{1$\times$1, 64}\\[1.00006pt] \text{3$\times$3, 64}\\[1.00006pt] \text{1$\times$1, 256}\end{array}\right]$$\times$3  $\left[\begin{array}[]{c}\text{1$\times$1, 64}\\[1.00006pt] \text{3$\times$3, 64}\\[1.00006pt] \text{1$\times$1, 256}\end{array}\right]$$\times$3  
conv3_x  28$\times$28  $\left[\begin{array}[]{c}\text{3$\times$3, 128}\\[1.00006pt] \text{3$\times$3, 128}\end{array}\right]$$\times$2  $\left[\begin{array}[]{c}\text{3$\times$3, 128}\\[1.00006pt] \text{3$\times$3, 128}\end{array}\right]$$\times$4  $\left[\begin{array}[]{c}\text{1$\times$1, 128}\\[1.00006pt] \text{3$\times$3, 128}\\[1.00006pt] \text{1$\times$1, 512}\end{array}\right]$$\times$4  $\left[\begin{array}[]{c}\text{1$\times$1, 128}\\[1.00006pt] \text{3$\times$3, 128}\\[1.00006pt] \text{1$\times$1, 512}\end{array}\right]$$\times$4  $\left[\begin{array}[]{c}\text{1$\times$1, 128}\\[1.00006pt] \text{3$\times$3, 128}\\[1.00006pt] \text{1$\times$1, 512}\end{array}\right]$$\times$8 
conv4_x  14$\times$14  $\left[\begin{array}[]{c}\text{3$\times$3, 256}\\[1.00006pt] \text{3$\times$3, 256}\end{array}\right]$$\times$2  $\left[\begin{array}[]{c}\text{3$\times$3, 256}\\[1.00006pt] \text{3$\times$3, 256}\end{array}\right]$$\times$6  $\left[\begin{array}[]{c}\text{1$\times$1, 256}\\[1.00006pt] \text{3$\times$3, 256}\\[1.00006pt] \text{1$\times$1, 1024}\end{array}\right]$$\times$6  $\left[\begin{array}[]{c}\text{1$\times$1, 256}\\[1.00006pt] \text{3$\times$3, 256}\\[1.00006pt] \text{1$\times$1, 1024}\end{array}\right]$$\times$23  $\left[\begin{array}[]{c}\text{1$\times$1, 256}\\[1.00006pt] \text{3$\times$3, 256}\\[1.00006pt] \text{1$\times$1, 1024}\end{array}\right]$$\times$36 
conv5_x  7$\times$7  $\left[\begin{array}[]{c}\text{3$\times$3, 512}\\[1.00006pt] \text{3$\times$3, 512}\end{array}\right]$$\times$2  $\left[\begin{array}[]{c}\text{3$\times$3, 512}\\[1.00006pt] \text{3$\times$3, 512}\end{array}\right]$$\times$3  $\left[\begin{array}[]{c}\text{1$\times$1, 512}\\[1.00006pt] \text{3$\times$3, 512}\\[1.00006pt] \text{1$\times$1, 2048}\end{array}\right]$$\times$3  $\left[\begin{array}[]{c}\text{1$\times$1, 512}\\[1.00006pt] \text{3$\times$3, 512}\\[1.00006pt] \text{1$\times$1, 2048}\end{array}\right]$$\times$3  $\left[\begin{array}[]{c}\text{1$\times$1, 512}\\[1.00006pt] \text{3$\times$3, 512}\\[1.00006pt] \text{1$\times$1, 2048}\end{array}\right]$$\times$3 
1$\times$1  average pool, 1000d fc, softmax  
FLOPs  1.8$\times 10^{9}$  3.6$\times 10^{9}$  3.8$\times 10^{9}$  7.6$\times 10^{9}$  11.3$\times 10^{9}$ 
3.4 Implementation
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$\times$224 crop is randomly sampled from an image or its horizontal flip, with the perpixel 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 minibatch 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 $60\times 10^{4}$ 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].
4 Experiments
4.1 ImageNet Classification
We evaluate our method on the ImageNet 2012 classification dataset [36] 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 top1 and top5 error rates.
Plain Networks. We first evaluate 18layer and 34layer plain nets. The 34layer plain net is in Fig. 3 (middle). The 18layer plain net is of a similar form. See Table 1 for detailed architectures.
The results in Table 2 show that the deeper 34layer plain net has higher validation error than the shallower 18layer 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 34layer plain net has higher training error throughout the whole training procedure, even though the solution space of the 18layer plain network is a subspace of that of the 34layer one.
plain  ResNet  

18 layers  27.94  27.88 
34 layers  28.54  25.03 
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 nonzero variances. We also verify that the backward propagated gradients exhibit healthy norms with BN. So neither forward nor backward signals vanish. In fact, the 34layer 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}^{3}3We have experimented with more training iterations (3$\times$) 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.
Residual Networks. Next we evaluate 18layer and 34layer 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$\times$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 zeropadding for increasing dimensions (option A). So they have no extra parameter compared to the plain counterparts.
We have three major observations from Table 2 and Fig. 4. First, the situation is reversed with residual learning – the 34layer ResNet is better than the 18layer ResNet (by 2.8%). More importantly, the 34layer 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.
Second, compared to its plain counterpart, the 34layer ResNet reduces the top1 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.
Last, we also note that the 18layer plain/residual nets are comparably accurate (Table 2), but the 18layer 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.
model  top1 err.  top5 err. 

VGG16 [41]  28.07  9.33 
GoogLeNet [44]    9.15 
PReLUnet [13]  24.27  7.38 
plain34  28.54  10.02 
ResNet34 A  25.03  7.76 
ResNet34 B  24.52  7.46 
ResNet34 C  24.19  7.40 
ResNet50  22.85  6.71 
ResNet101  21.75  6.05 
ResNet152  21.43  5.71 
Identity vs. Projection Shortcuts. We have shown that parameterfree, identity shortcuts help with training. Next we investigate projection shortcuts (Eqn.(2)). In Table 3 we compare three options: (A) zeropadding 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 (C) all shortcuts are projections.
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 zeropadded 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.
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}^{4}4Deeper nonbottleneck ResNets (e.g., Fig. 5 left) also gain accuracy from increased depth (as shown on CIFAR10), but are not as economical as the bottleneck ResNets. So the usage of bottleneck designs is mainly due to practical considerations. We further note that the degradation problem of plain nets is also witnessed for the bottleneck designs.. For each residual function $\mathcal{F}$, we use a stack of 3 layers instead of 2 (Fig. 5). The three layers are 1$\times$1, 3$\times$3, and 1$\times$1 convolutions, where the 1$\times$1 layers are responsible for reducing and then increasing (restoring) dimensions, leaving the 3$\times$3 layer a bottleneck with smaller input/output dimensions. Fig. 5 shows an example, where both designs have similar time complexity.
The parameterfree 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 highdimensional ends. So identity shortcuts lead to more efficient models for the bottleneck designs.
50layer ResNet: We replace each 2layer block in the 34layer net with this 3layer bottleneck block, resulting in a 50layer ResNet (Table 1). We use option B for increasing dimensions. This model has 3.8 billion FLOPs.
101layer and 152layer ResNets: We construct 101layer and 152layer ResNets by using more 3layer blocks (Table 1). Remarkably, although the depth is significantly increased, the 152layer ResNet (11.3 billion FLOPs) still has lower complexity than VGG16/19 nets (15.3/19.6 billion FLOPs).
The 50/101/152layer ResNets are more accurate than the 34layer ones by considerable margins (Table 3 and 5). 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 5).
Comparisons with Stateoftheart Methods. In Table 5 we compare with the previous best singlemodel results. Our baseline 34layer ResNets have achieved very competitive accuracy. Our 152layer ResNet has a singlemodel top5 validation error of 4.49%. This singlemodel result outperforms all previous ensemble results (Table 5). We combine six models of different depth to form an ensemble (only with two 152layer ones at the time of submitting). This leads to 3.57% top5 error on the test set (Table 5). This entry won the 1st place in ILSVRC 2015.
4.2 CIFAR10 and Analysis
We conducted more studies on the CIFAR10 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 stateoftheart results, so we intentionally use simple architectures as follows.
The plain/residual architectures follow the form in Fig. 3 (middle/right). The network inputs are 32$\times$32 images, with the perpixel mean subtracted. The first layer is 3$\times$3 convolutions. Then we use a stack of $6n$ layers with 3$\times$3 convolutions on the feature maps of sizes $\{32,16,8\}$ respectively, with 2$n$ 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 10way fullyconnected layer, and softmax. There are totally 6$n$+2 stacked weighted layers. The following table summarizes the architecture:
output map size  32$\times$32  16$\times$16  8$\times$8 

# layers  1+2$n$  2$n$  2$n$ 
# filters  16  32  64 
When shortcut connections are used, they are connected to the pairs of 3$\times$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.
method  error (%)  
Maxout [10]  9.38  
NIN [25]  8.81  
DSN [24]  8.22  
# layers  # params  
FitNet [35]  19  2.5M  8.39 
Highway [42, 43]  19  2.3M  7.54 (7.72$\pm$0.16) 
Highway [42, 43]  32  1.25M  8.80 
ResNet  20  0.27M  8.75 
ResNet  32  0.46M  7.51 
ResNet  44  0.66M  7.17 
ResNet  56  0.85M  6.97 
ResNet  110  1.7M  6.43 (6.61$\pm$0.16) 
ResNet  1202  19.4M  7.93 
We use a weight decay of 0.0001 and momentum of 0.9, and adopt the weight initialization in [13] and BN [16] but with no dropout. These models are trained with a minibatch size of 128 on two GPUs. We start with a learning rate of 0.1, divide it by 10 at 32k and 48k iterations, and terminate training at 64k iterations, which is determined on a 45k/5k train/val split. We follow the simple data augmentation in [24] for training: 4 pixels are padded on each side, and a 32$\times$32 crop is randomly sampled from the padded image or its horizontal flip. For testing, we only evaluate the single view of the original 32$\times$32 image.
We compare $n=\{3,5,7,9\}$, leading to 20, 32, 44, and 56layer 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.
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.
We further explore $n=18$ that leads to a 110layer ResNet. In this case, we find that the initial learning rate of 0.1 is slightly too large to start converging^{5}^{5}5With an initial learning rate of 0.1, it starts converging ($<$90% error) after several epochs, but still reaches similar accuracy.. So we use 0.01 to warm up the training until the training error is below 80% (about 400 iterations), and then go back to 0.1 and continue training. The rest of the learning schedule is as done previously. This 110layer network converges well (Fig. 6, middle). It has fewer parameters than other deep and thin networks such as FitNet [35] and Highway [42] (Table 6), yet is among the stateoftheart results (6.43%, Table 6).
Analysis of Layer Responses. Fig. 7 shows the standard deviations (std) of the layer responses. The responses are the outputs of each 3$\times$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 nonresidual functions. We also notice that the deeper ResNet has smaller magnitudes of responses, as evidenced by the comparisons among ResNet20, 56, and 110 in Fig. 7. When there are more layers, an individual layer of ResNets tends to modify the signal less.
Exploring Over 1000 layers. We explore an aggressively deep model of over 1000 layers. We set $n=200$ that leads to a 1202layer 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).
But there are still open problems on such aggressively deep models. The testing result of this 1202layer network is worse than that of our 110layer network, although both have similar training error. We argue that this is because of overfitting. The 1202layer 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 optimization. But combining with stronger regularization may improve results, which we will study in the future.
4.3 Object Detection on PASCAL and MS COCO
training data  07+12  07++12 

test data  VOC 07 test  VOC 12 test 
VGG16  73.2  70.4 
ResNet101  76.4  73.8 
metric  mAP@.5  mAP@[.5, .95] 

VGG16  41.5  21.2 
ResNet101  48.4  27.2 
Our method has good generalization performance on other recognition tasks. Table 8 and 8 show the object detection baseline results on PASCAL VOC 2007 and 2012 [5] and COCO [26]. We adopt Faster RCNN [32] as the detection method. Here we are interested in the improvements of replacing VGG16 [41] with ResNet101. 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.
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.
References
 [1] Y. Bengio, P. Simard, and P. Frasconi. Learning longterm dependencies with gradient descent is difficult. IEEE Transactions on Neural Networks, 5(2):157–166, 1994.
 [2] C. M. Bishop. Neural networks for pattern recognition. Oxford university press, 1995.
 [3] W. L. Briggs, S. F. McCormick, et al. A Multigrid Tutorial. Siam, 2000.
 [4] K. Chatfield, V. Lempitsky, A. Vedaldi, and A. Zisserman. The devil is in the details: an evaluation of recent feature encoding methods. In BMVC, 2011.
 [5] M. Everingham, L. Van Gool, C. K. Williams, J. Winn, and A. Zisserman. The Pascal Visual Object Classes (VOC) Challenge. IJCV, pages 303–338, 2010.
 [6] S. Gidaris and N. Komodakis. Object detection via a multiregion & semantic segmentationaware cnn model. In ICCV, 2015.
 [7] R. Girshick. Fast RCNN. In ICCV, 2015.
 [8] R. Girshick, J. Donahue, T. Darrell, and J. Malik. Rich feature hierarchies for accurate object detection and semantic segmentation. In CVPR, 2014.
 [9] X. Glorot and Y. Bengio. Understanding the difficulty of training deep feedforward neural networks. In AISTATS, 2010.
 [10] I. J. Goodfellow, D. WardeFarley, M. Mirza, A. Courville, and Y. Bengio. Maxout networks. arXiv:1302.4389, 2013.
 [11] K. He and J. Sun. Convolutional neural networks at constrained time cost. In CVPR, 2015.
 [12] K. He, X. Zhang, S. Ren, and J. Sun. Spatial pyramid pooling in deep convolutional networks for visual recognition. In ECCV, 2014.
 [13] K. He, X. Zhang, S. Ren, and J. Sun. Delving deep into rectifiers: Surpassing humanlevel performance on imagenet classification. In ICCV, 2015.
 [14] G. E. Hinton, N. Srivastava, A. Krizhevsky, I. Sutskever, and R. R. Salakhutdinov. Improving neural networks by preventing coadaptation of feature detectors. arXiv:1207.0580, 2012.
 [15] S. Hochreiter and J. Schmidhuber. Long shortterm memory. Neural computation, 9(8):1735–1780, 1997.
 [16] S. Ioffe and C. Szegedy. Batch normalization: Accelerating deep network training by reducing internal covariate shift. In ICML, 2015.
 [17] H. Jegou, M. Douze, and C. Schmid. Product quantization for nearest neighbor search. TPAMI, 33, 2011.
 [18] H. Jegou, F. Perronnin, M. Douze, J. Sanchez, P. Perez, and C. Schmid. Aggregating local image descriptors into compact codes. TPAMI, 2012.
 [19] Y. Jia, E. Shelhamer, J. Donahue, S. Karayev, J. Long, R. Girshick, S. Guadarrama, and T. Darrell. Caffe: Convolutional architecture for fast feature embedding. arXiv:1408.5093, 2014.
 [20] A. Krizhevsky. Learning multiple layers of features from tiny images. Tech Report, 2009.
 [21] A. Krizhevsky, I. Sutskever, and G. Hinton. Imagenet classification with deep convolutional neural networks. In NIPS, 2012.
 [22] Y. LeCun, B. Boser, J. S. Denker, D. Henderson, R. E. Howard, W. Hubbard, and L. D. Jackel. Backpropagation applied to handwritten zip code recognition. Neural computation, 1989.
 [23] Y. LeCun, L. Bottou, G. B. Orr, and K.R. Müller. Efficient backprop. In Neural Networks: Tricks of the Trade, pages 9–50. Springer, 1998.
 [24] C.Y. Lee, S. Xie, P. Gallagher, Z. Zhang, and Z. Tu. Deeplysupervised nets. arXiv:1409.5185, 2014.
 [25] M. Lin, Q. Chen, and S. Yan. Network in network. arXiv:1312.4400, 2013.
 [26] T.Y. Lin, M. Maire, S. Belongie, J. Hays, P. Perona, D. Ramanan, P. Dollár, and C. L. Zitnick. Microsoft COCO: Common objects in context. In ECCV. 2014.
 [27] J. Long, E. Shelhamer, and T. Darrell. Fully convolutional networks for semantic segmentation. In CVPR, 2015.
 [28] G. Montúfar, R. Pascanu, K. Cho, and Y. Bengio. On the number of linear regions of deep neural networks. In NIPS, 2014.
 [29] V. Nair and G. E. Hinton. Rectified linear units improve restricted boltzmann machines. In ICML, 2010.
 [30] F. Perronnin and C. Dance. Fisher kernels on visual vocabularies for image categorization. In CVPR, 2007.
 [31] T. Raiko, H. Valpola, and Y. LeCun. Deep learning made easier by linear transformations in perceptrons. In AISTATS, 2012.
 [32] S. Ren, K. He, R. Girshick, and J. Sun. Faster RCNN: Towards realtime object detection with region proposal networks. In NIPS, 2015.
 [33] S. Ren, K. He, R. Girshick, X. Zhang, and J. Sun. Object detection networks on convolutional feature maps. arXiv:1504.06066, 2015.
 [34] B. D. Ripley. Pattern recognition and neural networks. Cambridge university press, 1996.
 [35] A. Romero, N. Ballas, S. E. Kahou, A. Chassang, C. Gatta, and Y. Bengio. Fitnets: Hints for thin deep nets. In ICLR, 2015.
 [36] O. Russakovsky, J. Deng, H. Su, J. Krause, S. Satheesh, S. Ma, Z. Huang, A. Karpathy, A. Khosla, M. Bernstein, et al. Imagenet large scale visual recognition challenge. arXiv:1409.0575, 2014.
 [37] A. M. Saxe, J. L. McClelland, and S. Ganguli. Exact solutions to the nonlinear dynamics of learning in deep linear neural networks. arXiv:1312.6120, 2013.
 [38] N. N. Schraudolph. Accelerated gradient descent by factorcentering decomposition. Technical report, 1998.
 [39] N. N. Schraudolph. Centering neural network gradient factors. In Neural Networks: Tricks of the Trade, pages 207–226. Springer, 1998.
 [40] P. Sermanet, D. Eigen, X. Zhang, M. Mathieu, R. Fergus, and Y. LeCun. Overfeat: Integrated recognition, localization and detection using convolutional networks. In ICLR, 2014.
 [41] K. Simonyan and A. Zisserman. Very deep convolutional networks for largescale image recognition. In ICLR, 2015.
 [42] R. K. Srivastava, K. Greff, and J. Schmidhuber. Highway networks. arXiv:1505.00387, 2015.
 [43] R. K. Srivastava, K. Greff, and J. Schmidhuber. Training very deep networks. 1507.06228, 2015.
 [44] C. Szegedy, W. Liu, Y. Jia, P. Sermanet, S. Reed, D. Anguelov, D. Erhan, V. Vanhoucke, and A. Rabinovich. Going deeper with convolutions. In CVPR, 2015.
 [45] R. Szeliski. Fast surface interpolation using hierarchical basis functions. TPAMI, 1990.
 [46] R. Szeliski. Locally adapted hierarchical basis preconditioning. In SIGGRAPH, 2006.
 [47] T. Vatanen, T. Raiko, H. Valpola, and Y. LeCun. Pushing stochastic gradient towards secondorder methods–backpropagation learning with transformations in nonlinearities. In Neural Information Processing, 2013.
 [48] A. Vedaldi and B. Fulkerson. VLFeat: An open and portable library of computer vision algorithms, 2008.
 [49] W. Venables and B. Ripley. Modern applied statistics with splus. 1999.
 [50] M. D. Zeiler and R. Fergus. Visualizing and understanding convolutional neural networks. In ECCV, 2014.
Appendix A Object Detection Baselines
In this section we introduce our detection method based on the baseline Faster RCNN [32] system. The models are initialized by the ImageNet classification models, and then finetuned on the object detection data. We have experimented with ResNet50/101 at the time of the ILSVRC & COCO 2015 detection competitions.
Unlike VGG16 used in [32], our ResNet has no hidden fc layers. We adopt the idea of “Networks on Conv feature maps” (NoC) [33] to address this issue. We compute the fullimage shared conv feature maps using those layers whose strides on the image are no greater than 16 pixels (i.e., conv1, conv2_ x, conv3_x, and conv4_x, totally 91 conv layers in ResNet101; Table 1). We consider these layers as analogous to the 13 conv layers in VGG16, and by doing so, both ResNet and VGG16 have conv feature maps of the same total stride (16 pixels). These layers are shared by a region proposal network (RPN, generating 300 proposals) [32] and a Fast RCNN detection network [7]. RoI pooling [7] is performed before conv5_1. On this RoIpooled feature, all layers of conv5_x and up are adopted for each region, playing the roles of VGG16’s fc layers. The final classification layer is replaced by two sibling layers (classification and box regression [7]).
For the usage of BN layers, after pretraining, we compute the BN statistics (means and variances) for each layer on the ImageNet training set. Then the BN layers are fixed during finetuning for object detection. As such, the BN layers become linear activations with constant offsets and scales, and BN statistics are not updated by finetuning. We fix the BN layers mainly for reducing memory consumption in Faster RCNN training.
PASCAL VOC
Following [7, 32], for the PASCAL VOC 2007 test set, we use the 5k trainval images in VOC 2007 and 16k trainval images in VOC 2012 for training (“07+12”). For the PASCAL VOC 2012 test set, we use the 10k trainval+test images in VOC 2007 and 16k trainval images in VOC 2012 for training (“07++12”). The hyperparameters for training Faster RCNN are the same as in [32]. Table 8 shows the results. ResNet101 improves the mAP by $>$3% over VGG16. This gain is solely because of the improved features learned by ResNet.
MS COCO
The MS COCO dataset [26] involves 80 object categories. We evaluate the PASCAL VOC metric (mAP @ IoU = 0.5) and the standard COCO metric (mAP @ IoU = .5:.05:.95). We use the 80k images on the train set for training and the 40k images on the val set for evaluation. Our detection system for COCO is similar to that for PASCAL VOC. We train the COCO models with an 8GPU implementation, and thus the RPN step has a minibatch size of 8 images (i.e., 1 per GPU) and the Fast RCNN step has a minibatch size of 16 images. The RPN step and Fast RCNN step are both trained for 240k iterations with a learning rate of 0.001 and then for 80k iterations with 0.0001.
Table 8 shows the results on the MS COCO validation set. ResNet101 has a 6% increase of mAP@[.5, .95] over VGG16, which is a 28% relative improvement, solely contributed by the features learned by the better network. Remarkably, the mAP@[.5, .95]’s absolute increase (6.0%) is nearly as big as mAP@.5’s (6.9%). This suggests that a deeper network can improve both recognition and localization.
Appendix B Object Detection Improvements
For completeness, we report the improvements made for the competitions. These improvements are based on deep features and thus should benefit from residual learning.
training data  COCO train  COCO trainval  

test data  COCO val  COCO testdev  
mAP  @.5  @[.5, .95]  @.5  @[.5, .95] 
baseline Faster RCNN (VGG16)  41.5  21.2  
baseline Faster RCNN (ResNet101)  48.4  27.2  
+box refinement  49.9  29.9  
+context  51.1  30.0  53.3  32.2 
+multiscale testing  53.8  32.5  55.7  34.9 
ensemble  59.0  37.4 
system  net  data  mAP  areo  bike  bird  boat  bottle  bus  car  cat  chair  cow  table  dog  horse  mbike  person  plant  sheep  sofa  train  tv 

baseline  VGG16  07+12  73.2  76.5  79.0  70.9  65.5  52.1  83.1  84.7  86.4  52.0  81.9  65.7  84.8  84.6  77.5  76.7  38.8  73.6  73.9  83.0  72.6 
baseline  ResNet101  07+12  76.4  79.8  80.7  76.2  68.3  55.9  85.1  85.3  89.8  56.7  87.8  69.4  88.3  88.9  80.9  78.4  41.7  78.6  79.8  85.3  72.0 
baseline+++  ResNet101  COCO+07+12  85.6  90.0  89.6  87.8  80.8  76.1  89.9  89.9  89.6  75.5  90.0  80.7  89.6  90.3  89.1  88.7  65.4  88.1  85.6  89.0  86.8 
system  net  data  mAP  areo  bike  bird  boat  bottle  bus  car  cat  chair  cow  table  dog  horse  mbike  person  plant  sheep  sofa  train  tv 

baseline  VGG16  07++12  70.4  84.9  79.8  74.3  53.9  49.8  77.5  75.9  88.5  45.6  77.1  55.3  86.9  81.7  80.9  79.6  40.1  72.6  60.9  81.2  61.5 
baseline  ResNet101  07++12  73.8  86.5  81.6  77.2  58.0  51.0  78.6  76.6  93.2  48.6  80.4  59.0  92.1  85.3  84.8  80.7  48.1  77.3  66.5  84.7  65.6 
baseline+++  ResNet101  COCO+07++12  83.8  92.1  88.4  84.8  75.9  71.4  86.3  87.8  94.2  66.8  89.4  69.2  93.9  91.9  90.9  89.6  67.9  88.2  76.8  90.3  80.0 
MS COCO
Box refinement. Our box refinement partially follows the iterative localization in [6]. In Faster RCNN, the final output is a regressed box that is different from its proposal box. So for inference, we pool a new feature from the regressed box and obtain a new classification score and a new regressed box. We combine these 300 new predictions with the original 300 predictions. Nonmaximum suppression (NMS) is applied on the union set of predicted boxes using an IoU threshold of 0.3 [8], followed by box voting [6]. Box refinement improves mAP by about 2 points (Table 9).
Global context. We combine global context in the Fast RCNN step. Given the fullimage conv feature map, we pool a feature by global Spatial Pyramid Pooling [12] (with a “singlelevel” pyramid) which can be implemented as “RoI” pooling using the entire image’s bounding box as the RoI. This pooled feature is fed into the postRoI layers to obtain a global context feature. This global feature is concatenated with the original perregion feature, followed by the sibling classification and box regression layers. This new structure is trained endtoend. Global context improves mAP@.5 by about 1 point (Table 9).
Multiscale testing. In the above, all results are obtained by singlescale training/testing as in [32], where the image’s shorter side is $s=600$ pixels. Multiscale training/testing has been developed in [12, 7] by selecting a scale from a feature pyramid, and in [33] by using maxout layers. In our current implementation, we have performed multiscale testing following [33]; we have not performed multiscale training because of limited time. In addition, we have performed multiscale testing only for the Fast RCNN step (but not yet for the RPN step). With a trained model, we compute conv feature maps on an image pyramid, where the image’s shorter sides are $s\in\{200,400,600,800,1000\}$. We select two adjacent scales from the pyramid following [33]. RoI pooling and subsequent layers are performed on the feature maps of these two scales [33], which are merged by maxout as in [33]. Multiscale testing improves the mAP by over 2 points (Table 9).
Using validation data. Next we use the 80k+40k trainval set for training and the 20k testdev set for evaluation. The testdev set has no publicly available ground truth and the result is reported by the evaluation server. Under this setting, the results are an mAP@.5 of 55.7% and an mAP@[.5, .95] of 34.9% (Table 9). This is our singlemodel result.
Ensemble. In Faster RCNN, the system is designed to learn region proposals and also object classifiers, so an ensemble can be used to boost both tasks. We use an ensemble for proposing regions, and the union set of proposals are processed by an ensemble of perregion classifiers. Table 9 shows our result based on an ensemble of 3 networks. The mAP is 59.0% and 37.4% on the testdev set. This result won the 1st place in the detection task in COCO 2015.
PASCAL VOC
We revisit the PASCAL VOC dataset based on the above model. With the single model on the COCO dataset (55.7% mAP@.5 in Table 9), we finetune this model on the PASCAL VOC sets. The improvements of box refinement, context, and multiscale testing are also adopted. By doing so we achieve 85.6% mAP on PASCAL VOC 2007 (Table 11) and 83.8% on PASCAL VOC 2012 (Table 11)^{6}^{6}6http://host.robots.ox.ac.uk:8080/anonymous/3OJ4OJ.html, submitted on 20151126.. The result on PASCAL VOC 2012 is 10 points higher than the previous stateoftheart result [6].
ImageNet Detection
val2  test  

GoogLeNet [44] (ILSVRC’14)    43.9 
our single model (ILSVRC’15)  60.5  58.8 
our ensemble (ILSVRC’15)  63.6  62.1 
The ImageNet Detection (DET) task involves 200 object categories. The accuracy is evaluated by mAP@.5. Our object detection algorithm for ImageNet DET is the same as that for MS COCO in Table 9. The networks are pretrained on the 1000class ImageNet classification set, and are finetuned on the DET data. We split the validation set into two parts (val1/val2) following [8]. We finetune the detection models using the DET training set and the val1 set. The val2 set is used for validation. We do not use other ILSVRC 2015 data. Our single model with ResNet101 has 58.8% mAP and our ensemble of 3 models has 62.1% mAP on the DET test set (Table 12). This result won the 1st place in the ImageNet detection task in ILSVRC 2015, surpassing the second place by 8.5 points (absolute).
Appendix C ImageNet Localization


testing 





VGG’s [41]  VGG16  1crop  33.1 [41]  
RPN  ResNet101  1crop  13.3  
RPN  ResNet101  dense  11.7  
RPN  ResNet101  dense  ResNet101  14.4  
RPN+RCNN  ResNet101  dense  ResNet101  10.6  
RPN+RCNN  ensemble  dense  ensemble  8.9 
The ImageNet Localization (LOC) task [36] requires to classify and localize the objects. Following [40, 41], we assume that the imagelevel classifiers are first adopted for predicting the class labels of an image, and the localization algorithm only accounts for predicting bounding boxes based on the predicted classes. We adopt the “perclass regression” (PCR) strategy [40, 41], learning a bounding box regressor for each class. We pretrain the networks for ImageNet classification and then finetune them for localization. We train networks on the provided 1000class ImageNet training set.
Our localization algorithm is based on the RPN framework of [32] with a few modifications. Unlike the way in [32] that is categoryagnostic, our RPN for localization is designed in a perclass form. This RPN ends with two sibling 1$\times$1 convolutional layers for binary classification (cls) and box regression (reg), as in [32]. The cls and reg layers are both in a perclass from, in contrast to [32]. Specifically, the cls layer has a 1000d output, and each dimension is binary logistic regression for predicting being or not being an object class; the reg layer has a 1000$\times$4d output consisting of box regressors for 1000 classes. As in [32], our bounding box regression is with reference to multiple translationinvariant “anchor” boxes at each position.
As in our ImageNet classification training (Sec. 3.4), we randomly sample 224$\times$224 crops for data augmentation. We use a minibatch size of 256 images for finetuning. To avoid negative samples being dominate, 8 anchors are randomly sampled for each image, where the sampled positive and negative anchors have a ratio of 1:1 [32]. For testing, the network is applied on the image fullyconvolutionally.
method  top5 localization err  

val  test  
OverFeat [40] (ILSVRC’13)  30.0  29.9 
GoogLeNet [44] (ILSVRC’14)    26.7 
VGG [41] (ILSVRC’14)  26.9  25.3 
ours (ILSVRC’15)  8.9  9.0 
Table 13 compares the localization results. Following [41], we first perform “oracle” testing using the ground truth class as the classification prediction. VGG’s paper [41] reports a centercrop error of 33.1% (Table 13) using ground truth classes. Under the same setting, our RPN method using ResNet101 net significantly reduces the centercrop error to 13.3%. This comparison demonstrates the excellent performance of our framework. With dense (fully convolutional) and multiscale testing, our ResNet101 has an error of 11.7% using ground truth classes. Using ResNet101 for predicting classes (4.6% top5 classification error, Table 5), the top5 localization error is 14.4%.
The above results are only based on the proposal network (RPN) in Faster RCNN [32]. One may use the detection network (Fast RCNN [7]) in Faster RCNN to improve the results. But we notice that on this dataset, one image usually contains a single dominate object, and the proposal regions highly overlap with each other and thus have very similar RoIpooled features. As a result, the imagecentric training of Fast RCNN [7] generates samples of small variations, which may not be desired for stochastic training. Motivated by this, in our current experiment we use the original RCNN [8] that is RoIcentric, in place of Fast RCNN.
Our RCNN implementation is as follows. We apply the perclass RPN trained as above on the training images to predict bounding boxes for the ground truth class. These predicted boxes play a role of classdependent proposals. For each training image, the highest scored 200 proposals are extracted as training samples to train an RCNN classifier. The image region is cropped from a proposal, warped to 224$\times$224 pixels, and fed into the classification network as in RCNN [8]. The outputs of this network consist of two sibling fc layers for cls and reg, also in a perclass form. This RCNN network is finetuned on the training set using a minibatch size of 256 in the RoIcentric fashion. For testing, the RPN generates the highest scored 200 proposals for each predicted class, and the RCNN network is used to update these proposals’ scores and box positions.
This method reduces the top5 localization error to 10.6% (Table 13). This is our singlemodel result on the validation set. Using an ensemble of networks for both classification and localization, we achieve a top5 localization error of 9.0% on the test set. This number significantly outperforms the ILSVRC 14 results (Table 14), showing a 64% relative reduction of error. This result won the 1st place in the ImageNet localization task in ILSVRC 2015.