521 lines
72 KiB
Plaintext
521 lines
72 KiB
Plaintext
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Deep Residual Learning for Image Recognition
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Kaiming He Xiangyu Zhang Shaoqing Ren Jian Sun
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Microsoft Research
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fkahe, v-xiangz, v-shren, jiansung@microsoft.com
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arXiv:1512.03385v1 [cs.CV] 10 Dec 2015 Abstract 20 20
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training error (%) Deeper neural networks are more difficult to train. We
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test error (%) 56-layer
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present a residual learning framework to ease the training 20-layer 10 10
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56-layer of networks that are substantially deeper than those used
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previously. We explicitly reformulate the layers as learn- 20-layer
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ing residual functions with reference to the layer inputs, in- 0 0 01 2
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iter. (1e4) 3 4 5 6 0 1 2 iter. (1e4) 3 4 5 6
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stead of learning unreferenced functions. We provide com- Figure 1. Training error (left) and test error (right) on CIFAR-10
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prehensive empirical evidence showing that these residual with 20-layer and 56-layer “plain” networks. The deeper network
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networks are easier to optimize, and can gain accuracy from has higher training error, and thus test error. Similar phenomena
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considerably increased depth. On the ImageNet dataset we on ImageNet is presented in Fig.4.
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evaluate residual nets with a depth of up to 152 layers—8
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deeper than VGG nets [41] but still having lower complex- greatly benefited from very deep models.
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ity. An ensemble of these residual nets achieves 3.57% error Driven by the significance of depth, a question arises:Is
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on the ImageNettestset. This result won the 1st place on the learning better networks as easy as stacking more layers?
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ILSVRC 2015 classification task. We also present analysis An obstacle to answering this question was the notorious
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on CIFAR-10 with 100 and 1000 layers. problem of vanishing/exploding gradients [1,9], which
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The depth of representations is of central importance hamper convergence from the beginning. This problem,
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for many visual recognition tasks. Solely due to our ex- however, has been largely addressed by normalized initial-
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tremely deep representations, we obtain a 28% relative im- ization [23,9,37,13] and intermediate normalization layers
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provement on the COCO object detection dataset. Deep [16], which enable networks with tens of layers to start con-
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residual nets are foundations of our submissions to ILSVRC verging for stochastic gradient descent (SGD) with back-
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& COCO 2015 competitions 1 , where we also won the 1st propagation [22].
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places on the tasks of ImageNet detection, ImageNet local- When deeper networks are able to start converging, a
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ization, COCO detection, and COCO segmentation. degradationproblem has been exposed: with the network
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depth increasing, accuracy gets saturated (which might be
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1. Introduction unsurprising) and then degrades rapidly. Unexpectedly,
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such degradation isnot caused by overfitting, and adding
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Deep convolutional neural networks [22,21] have led more layers to a suitably deep model leads tohigher train-
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to a series of breakthroughs for image classification [21, ing error, as reported in [11,42] and thoroughly verified by
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50,40]. Deep networks naturally integrate low/mid/high- our experiments. Fig.1shows a typical example.
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level features [50] and classifiers in an end-to-end multi- The degradation (of training accuracy) indicates that notlayer fashion, and the “levels” of features can be enriched all systems are similarly easy to optimize. Let us consider aby the number of stacked layers (depth). Recent evidence shallower architecture and its deeper counterpart that adds[41,44] reveals that network depth is of crucial importance, more layers onto it. There exists a solutionby constructionand the leading results [41,44,13,16] on the challenging to the deeper model: the added layers areidentitymapping,ImageNet dataset [36] all exploit “very deep” [41] models, and the other layers are copied from the learned shallowerwith a depth of sixteen [41] to thirty [16]. Many other non- model. The existence of this constructed solution indicatestrivial visual recognition tasks [8,12,7,32,27] have also that a deeper model should produce no higher training error
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than its shallower counterpart. But experiments show that 1 http://image-net.org/challenges/LSVRC/2015/ and
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http://mscoco.org/dataset/#detections-challenge2015. our current solvers on hand are unable to find solutions that
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1 x ImageNettestset, andwon the 1st place in the ILSVRC
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2015 classification competition. The extremely deep rep-
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weight layer resentations also have excellent generalization performance F(x) relu x on other recognition tasks, and lead us to furtherwin the
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weight layer identity 1st places on: ImageNet detection, ImageNet localization,
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COCO detection, and COCO segmentationin ILSVRC & F(x) + x relu COCO 2015 competitions. This strong evidence shows that
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Figure 2. Residual learning: a building block. the residual learning principle is generic, and we expect that
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it is applicable in other vision and non-vision problems.
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are comparably good or better than the constructed solution
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(or unable to do so in feasible time). 2. Related Work
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In this paper, we address the degradation problem by
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introducing adeep residual learningframework. In- Residual Representations.In image recognition, VLAD
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stead of hoping each few stacked layers directly fit a [18] is a representation that encodes by the residual vectors
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desired underlying mapping, we explicitly let these lay- with respect to a dictionary, and Fisher Vector [30] can be
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ers fit a residual mapping. Formally, denoting the desired formulated as a probabilistic version [18] of VLAD. Both
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underlying mapping asH(x), we let the stacked nonlinear of them are powerful shallow representations for image re-
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layers fit another mapping ofF(x) :=H(x) x. The orig- trieval and classification [4,48]. For vector quantization,
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inal mapping is recast intoF(x)+x. We hypothesize that it encoding residual vectors [17] is shown to be more effec-
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is easier to optimize the residual mapping than to optimize tive than encoding original vectors.
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the original, unreferenced mapping. To the extreme, if an In low-level vision and computer graphics, for solv-
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identity mapping were optimal, it would be easier to push ing Partial Differential Equations (PDEs), the widely used
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the residual to zero than to fit an identity mapping by a stack Multigrid method [3] reformulates the system as subprob-
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of nonlinear layers. lems at multiple scales, where each subproblem is respon-
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The formulation ofF(x)+xcan be realized by feedfor- sible for the residual solution between a coarser and a finer
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ward neural networks with “shortcut connections” (Fig.2). scale. An alternative to Multigrid is hierarchical basis pre-
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Shortcut connections [2,34,49] are those skipping one or conditioning [45,46], which relies on variables that repre-
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more layers. In our case, the shortcut connections simply sent residual vectors between two scales. It has been shown
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performidentitymapping, and their outputs are added to [3,45,46] that these solvers converge much faster than stan-
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the outputs of the stacked layers (Fig.2). Identity short- dard solvers that are unaware of the residual nature of the
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cut connections add neither extra parameter nor computa- solutions. These methods suggest that a good reformulation
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tional complexity. The entire network can still be trained or preconditioning can simplify the optimization.
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end-to-end by SGD with backpropagation, and can be eas- Shortcut Connections.Practices and theories that lead toily implemented using common libraries (e.g., Caffe [19]) shortcut connections [2,34,49] have been studied for a longwithout modifying the solvers. time. An early practice of training multi-layer perceptrons
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We present comprehensive experiments on ImageNet (MLPs) is to add a linear layer connected from the network
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[36] to show the degradation problem and evaluate our input to the output [34,49]. In [44,24], a few interme-
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method. We show that: 1) Our extremely deep residual nets diate layers are directly connected to auxiliary classifiers
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are easy to optimize, but the counterpart “plain” nets (that for addressing vanishing/exploding gradients. The papers
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simply stack layers) exhibit higher training error when the of [39,38,31,47] propose methods for centering layer re-
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depth increases; 2) Our deep residual nets can easily enjoy sponses, gradients, and propagated errors, implemented by
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accuracy gains from greatly increased depth, producing re- shortcut connections. In [44], an “inception” layer is com-
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sults substantially better than previous networks. posed of a shortcut branch and a few deeper branches.
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Similar phenomena are also shown on the CIFAR-10 set Concurrent with our work, “highway networks” [42,43]
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[20], suggesting that the optimization difficulties and the present shortcut connections with gating functions [15].
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effects of our method are not just akin to a particular dataset. These gates are data-dependent and have parameters, in
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We present successfully trained models on this dataset with contrast to our identity shortcuts that are parameter-free.
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over 100 layers, and explore models with over 1000 layers. When a gated shortcut is “closed” (approaching zero), the
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On the ImageNet classification dataset [36], we obtain layers in highway networks representnon-residualfunc-
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excellent results by extremely deep residual nets. Our 152- tions. On the contrary, our formulation always learns
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layer residual net is the deepest network ever presented on residual functions; our identity shortcuts are never closed,
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ImageNet, while still having lower complexity than VGG and all information is always passed through, with addi-
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nets [41]. Our ensemble has3.57%top-5 error on the tional residual functions to be learned. In addition, high-
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2 way networks have not demonstrated accuracy gains with ReLU [29] and the biases are omitted for simplifying no-
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extremely increased depth (e.g., over 100 layers). tations. The operationF+xis performed by a shortcut
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connection and element-wise addition. We adopt the sec-
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3. Deep Residual Learning ond nonlinearity after the addition (i.e., (y), see Fig.2).
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The shortcut connections in Eqn.(1) introduce neither ex- 3.1. Residual Learning tra parameter nor computation complexity. This is not only
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Let us considerH(x)as an underlying mapping to be attractive in practice but also important in our comparisons
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fit by a few stacked layers (not necessarily the entire net), between plain and residual networks. We can fairly com-
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withxdenoting the inputs to the first of these layers. If one pare plain/residual networks that simultaneously have the
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hypothesizes that multiple nonlinear layers can asymptoti- same number of parameters, depth, width, and computa-
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cally approximate complicated functions 2 , then it is equiv- tional cost (except for the negligible element-wise addition).
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alent to hypothesize that they can asymptotically approxi- The dimensions ofxandFmust be equal in Eqn.(1).
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mate the residual functions,i.e.,H(x) x(assuming that If this is not the case (e.g., when changing the input/output
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the input and output are of the same dimensions). So channels), we can perform a linear projectionWs by the
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rather than expect stacked layers to approximateH(x), we shortcut connections to match the dimensions:
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explicitly let these layers approximate a residual function
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F(x) :=H(x) x. The original function thus becomes y=F(x;fWi g) +Ws x: (2)
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F(x)+x. Although both forms should be able to asymptot-
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ically approximate the desired functions (as hypothesized), We can also use a square matrixWs in Eqn.(1). But we will
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the ease of learning might be different. show by experiments that the identity mapping is sufficient
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This reformulation is motivated by the counterintuitive for addressing the degradation problem and is economical,
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phenomena about the degradation problem (Fig.1, left). As and thusWs is only used when matching dimensions.
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we discussed in the introduction, if the added layers can The form of the residual functionFis flexible. Exper-
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be constructed as identity mappings, a deeper model should iments in this paper involve a functionFthat has two or
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have training error no greater than its shallower counter- three layers (Fig.5), while more layers are possible. But if
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part. The degradation problem suggests that the solvers Fhas only a single layer, Eqn.(1) is similar to a linear layer:
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might have difficulties in approximating identity mappings y=W1 x+x, for which we have not observed advantages.
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by multiple nonlinear layers. With the residual learning re- We also note that although the above notations are about
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formulation, if identity mappings are optimal, the solvers fully-connected layers for simplicity, they are applicable to
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may simply drive the weights of the multiple nonlinear lay- convolutional layers. The functionF(x;fWi g)can repre-
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ers toward zero to approach identity mappings. sent multiple convolutional layers. The element-wise addi-
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In real cases, it is unlikely that identity mappings are op- tion is performed on two feature maps, channel by channel.
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timal, but our reformulation may help to precondition the 3.3. Network Architectures problem. If the optimal function is closer to an identity
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mapping than to a zero mapping, it should be easier for the We have tested various plain/residual nets, and have ob-
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solver to find the perturbations with reference to an identity served consistent phenomena. To provide instances for dis-
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mapping, than to learn the function as a new one. We show cussion, we describe two models for ImageNet as follows.
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by experiments (Fig.7) that the learned residual functions in Plain Network. Our plain baselines (Fig.3, middle) aregeneral have small responses, suggesting that identity map- mainly inspired by the philosophy of VGG nets [41] (Fig.3,pings provide reasonable preconditioning. left). The convolutional layers mostly have 3 3 filters and
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3.2. Identity Mapping by Shortcuts follow two simple design rules: (i) for the same output
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feature map size, the layers have the same number of fil-We adopt residual learning to every few stacked layers. ters; and (ii) if the feature map size is halved, the num-A building block is shown in Fig.2. Formally, in this paper ber of filters is doubled so as to preserve the time com-we consider a building block defined as: plexity per layer. We perform downsampling directly by
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convolutional layers that have a stride of 2. The networky=F(x;fWi g) +x: (1) ends with a global average pooling layer and a 1000-way
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fully-connected layer with softmax. The total number ofHerexandyare the input and output vectors of the lay- weighted layers is 34 in Fig.3(middle).ers considered. The functionF(x;fWi g)represents the It is worth noticing that our model hasfewerfilters andresidual mapping to be learned. For the example in Fig.2 lowercomplexity than VGG nets [41] (Fig.3, left). Our 34-that has two layers,F=W2 (W1 x)in which denotes layer baseline has 3.6 billion FLOPs (multiply-adds), which
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2 This hypothesis, however, is still an open question. See [28]. is only 18% of VGG-19 (19.6 billion FLOPs).
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3 VGG-19 34-layer plain 34-layer residual Residual Network.Based on the above plain network, we
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insert shortcut connections (Fig.3, right) which turn the image image image
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output network into its counterpart residual version. The identity 3x3 conv, 64size: 224 shortcuts (Eqn.(1)) can be directly used when the input and 3x3 conv, 64 output are of the same dimensions (solid line shortcuts in pool, /2output Fig.3). When the dimensions increase (dotted line shortcuts size: 112 3x3 conv, 128 in Fig.3), we consider two options: (A) The shortcut still
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3x3 conv, 128 7x7 conv, 64, /2 7x7 conv, 64, /2 performs identity mapping, with extra zero entries padded
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pool, /2 pool, /2 pool, /2output for increasing dimensions. This option introduces no extra size: 56 3x3 conv, 256 3x3 conv, 64 3x3 conv, 64 parameter; (B) The projection shortcut in Eqn.(2) is used to
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3x3 conv, 256 3x3 conv, 64 3x3 conv, 64 match dimensions (done by 1 1 convolutions). For both
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3x3 conv, 256 3x3 conv, 64 3x3 conv, 64 options, when the shortcuts go across feature maps of two
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3x3 conv, 256 3x3 conv, 64 3x3 conv, 64 sizes, they are performed with a stride of 2.
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3x3 conv, 64 3x3 conv, 64 3.4. Implementation 3x3 conv, 64 3x3 conv, 64
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pool, /2 3x3 conv, 128, /2 3x3 conv, 128, /2 Our implementation for ImageNet follows the practice output
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size: 28 3x3 conv, 512 3x3 conv, 128 3x3 conv, 128 in [21,41]. The image is resized with its shorter side ran-
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3x3 conv, 512 3x3 conv, 128 3x3 conv, 128 domly sampled in[256;480]for scale augmentation [41].
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3x3 conv, 512 3x3 conv, 128 3x3 conv, 128 A 224 224 crop is randomly sampled from an image or its
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horizontal flip, with the per-pixel mean subtracted [21]. The 3x3 conv, 512 3x3 conv, 128 3x3 conv, 128
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standard color augmentation in [21] is used. We adopt batch 3x3 conv, 128 3x3 conv, 128
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normalization (BN) [16] right after each convolution and 3x3 conv, 128 3x3 conv, 128
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before activation, following [16]. We initialize the weights 3x3 conv, 128 3x3 conv, 128 as in [13] and train all plain/residual nets from scratch. We output pool, /2 3x3 conv, 256, /2 3x3 conv, 256, /2size: 14 use SGD with a mini-batch size of 256. The learning rate 3x3 conv, 512 3x3 conv, 256 3x3 conv, 256 starts from 0.1 and is divided by 10 when the error plateaus, 3x3 conv, 512 3x3 conv, 256 3x3 conv, 256 and the models are trained for up to60 10 4 iterations. We
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3x3 conv, 512 3x3 conv, 256 3x3 conv, 256 use a weight decay of 0.0001 and a momentum of 0.9. We
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3x3 conv, 512 3x3 conv, 256 3x3 conv, 256 do not use dropout [14], following the practice in [16].
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3x3 conv, 256 3x3 conv, 256 In testing, for comparison studies we adopt the standard
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3x3 conv, 256 3x3 conv, 256 10-crop testing [21]. For best results, we adopt the fully-
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3x3 conv, 256 3x3 conv, 256 convolutional form as in [41,13], and average the scores
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3x3 conv, 256 3x3 conv, 256 at multiple scales (images are resized such that the shorter
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3x3 conv, 256 3x3 conv, 256 side is inf224;256;384;480;640g).
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3x3 conv, 256 3x3 conv, 256
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4. Experiments 3x3 conv, 256 3x3 conv, 256
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output pool, /2 3x3 conv, 512, /2 3x3 conv, 512, /2size: 7 4.1. ImageNet Classification
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3x3 conv, 512 3x3 conv, 512
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We evaluate our method on the ImageNet 2012 classifi- 3x3 conv, 512 3x3 conv, 512
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cation dataset [36] that consists of 1000 classes. The models 3x3 conv, 512 3x3 conv, 512 are trained on the 1.28 million training images, and evalu- 3x3 conv, 512 3x3 conv, 512 ated on the 50k validation images. We also obtain a final 3x3 conv, 512 3x3 conv, 512 result on the 100k test images, reported by the test server. output fc 4096 avg pool avg poolsize: 1 We evaluate both top-1 and top-5 error rates.
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fc 4096 fc 1000 fc 1000
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fc 1000 Plain Networks. We first evaluate 18-layer and 34-layer
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plain nets. The 34-layer plain net is in Fig.3(middle). The
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Figure 3. Example network architectures for ImageNet.Left: the 18-layer plain net is of a similar form. See Table1for de-
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VGG-19 model [41] (19.6 billion FLOPs) as a reference.Mid- tailed architectures.
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dle: a plain network with 34 parameter layers (3.6 billion FLOPs). The results in Table2show that the deeper 34-layer plain
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Right: a residual network with 34 parameter layers (3.6 billion net has higher validation error than the shallower 18-layer FLOPs). The dotted shortcuts increase dimensions.Table1shows plain net. To reveal the reasons, in Fig.4(left) we com- more details and other variants. pare their training/validation errors during the training pro-
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cedure. We have observed the degradation problem - the
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4 layer nameoutput size 18-layer 34-layer 50-layer 101-layer 152-layer
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conv1 112 112 7 7, 64, stride 2
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3 3 max pool, stride 22 3 2 3 2 3 1 1, 64 1 1, 64 1 1, 64conv2x 56 56 3 3, 64 3 3, 64 2 3 43 3, 645 3 43 3, 645 3 43 3, 645 33 3, 64 3 3, 64 1 1, 256 1 1, 256 1 1, 2562 3 2 3 2 3 1 1, 128 1 1, 128 1 1, 1283 3, 128 3 3, 128conv3x 28 28 2 4 43 3, 1285 4 43 3, 1285 4 43 3, 1285 83 3, 128 3 3, 128 1 1, 512 1 1, 512 1 1, 5122 3 2 3 2 3 1 1, 256 1 1, 256 1 1, 2563 3, 256 3 3, 256conv4x 14 14 2 643 3, 2565 643 3, 2565 2343 3, 2565 363 3, 256 3 3, 256 1 1, 1024 1 1, 1024 1 1, 10242 3 2 3 2 3 1 1, 512 1 1, 512 1 1, 5123 3, 512 3 3, 512conv5x 7 7 2 343 3, 5125 3 43 3, 5125 3 43 3, 5125 33 3, 512 3 3, 512 1 1, 2048 1 1, 2048 1 1, 2048
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1 1 average pool, 1000-d fc, softmax
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FLOPs 1.8 10 9 3.6 10 9 3.8 10 9 7.6 10 9 11.3 10 9
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Table 1. Architectures for ImageNet. Building blocks are shown in brackets (see also Fig.5), with the numbers of blocks stacked. Down-
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sampling is performed by conv3 1, conv41, and conv51 with a stride of 2.
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60 60
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50 50
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error (%) error (%)40 40
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34-layer 18-layer
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30 30 18-layer plain-18 ResNet-18
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plain-34 ResNet-34 34-layer 200 2010 20 30 40 50 0 10 20 30 40 50
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iter. (1e4) iter. (1e4)
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Figure 4. Training onImageNet. Thin curves denote training error, and bold curves denote validation error of the center crops. Left: plain
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networks of 18 and 34 layers. Right: ResNets of 18 and 34 layers. In this plot, the residual networks have no extra parameter compared to
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their plain counterparts.
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plain ResNet reducing of the training error 3 . The reason for such opti-
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18 layers 27.94 27.88 mization difficulties will be studied in the future.
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34 layers 28.54 25.03 Residual Networks. Next we evaluate 18-layer and 34-
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Table 2. Top-1 error (%, 10-crop testing) on ImageNet validation. layer residual nets (ResNets). The baseline architectures Here the ResNets have no extra parameter compared to their plain are the same as the above plain nets, expect that a shortcut counterparts. Fig.4shows the training procedures. connection is added to each pair of 3 3 filters as in Fig.3
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(right). In the first comparison (Table2and Fig.4right),
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we use identity mapping for all shortcuts and zero-padding34-layer plain net has highertrainingerror throughout the for increasing dimensions (option A). So they haveno extrawhole training procedure, even though the solution space parametercompared to the plain counterparts.of the 18-layer plain network is a subspace of that of the We have three major observations from Table2and34-layer one. Fig.4. First, the situation is reversed with residual learn-
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We argue that this optimization difficulty isunlikelyto ing – the 34-layer ResNet is better than the 18-layer ResNet
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be caused by vanishing gradients. These plain networks are (by 2.8%). More importantly, the 34-layer ResNet exhibits
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trained with BN [16], which ensures forward propagated considerably lower training error and is generalizable to the
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signals to have non-zero variances. We also verify that the validation data. This indicates that the degradation problem
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backward propagated gradients exhibit healthy norms with is well addressed in this setting and we manage to obtain
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BN. So neither forward nor backward signals vanish. In accuracy gains from increased depth.
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fact, the 34-layer plain net is still able to achieve compet- Second, compared to its plain counterpart, the 34-layer
|
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itive accuracy (Table3), suggesting that the solver works 3 We have experimented with more training iterations (3 ) and still ob- to some extent. We conjecture that the deep plain nets may served the degradation problem, suggesting that this problem cannot be have exponentially low convergence rates, which impact the feasibly addressed by simply using more iterations.
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5 model top-1 err. top-5 err. 64-d 256-d
|
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VGG-16 [41] 28.07 9.33 3x3, 64 1x1, 64
|
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relu GoogLeNet [44] - 9.15 relu 3x3, 64
|
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PReLU-net [13] 24.27 7.38 3x3, 64 relu
|
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1x1, 256
|
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plain-34 28.54 10.02
|
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ResNet-34 A 25.03 7.76 relu relu
|
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ResNet-34 B 24.52 7.46 Figure 5. A deeper residual functionFfor ImageNet. Left: a ResNet-34 C 24.19 7.40 building block (on 56 56 feature maps) as in Fig.3for ResNet- ResNet-50 22.85 6.71 34. Right: a “bottleneck” building block for ResNet-50/101/152. ResNet-101 21.75 6.05
|
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ResNet-152 21.43 5.71 parameter-free, identity shortcuts help with training. Next Table 3. Error rates (%,10-croptesting) on ImageNet validation. we investigate projection shortcuts (Eqn.(2)). In Table3we VGG-16 is based on our test. ResNet-50/101/152 are of option B compare three options: (A) zero-padding shortcuts are used that only uses projections for increasing dimensions. for increasing dimensions, and all shortcuts are parameter-
|
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method top-1 err. top-5 err. free (the same as Table2and Fig.4right); (B) projec-
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VGG [41] (ILSVRC’14) - 8.43 y tion shortcuts are used for increasing dimensions, and other
|
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GoogLeNet [44] (ILSVRC’14) - 7.89 shortcuts are identity; and (C) all shortcuts are projections.
|
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VGG [41] Table3shows that all three options are considerably bet- (v5) 24.4 7.1
|
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PReLU-net [13] 21.59 5.71 ter than the plain counterpart. B is slightly better than A. We
|
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BN-inception [16] 21.99 5.81 argue that this is because the zero-padded dimensions in A
|
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ResNet-34 B 21.84 5.71 indeed have no residual learning. C is marginally better than
|
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ResNet-34 C 21.53 5.60 B, and we attribute this to the extra parameters introduced
|
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by many (thirteen) projection shortcuts. But the small dif- ResNet-50 20.74 5.25 ferences among A/B/C indicate that projection shortcuts are ResNet-101 19.87 4.60 not essential for addressing the degradation problem. So we ResNet-152 19.38 4.49 do not use option C in the rest of this paper, to reduce mem-
|
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Table 4. Error rates (%) ofsingle-modelresults on the ImageNet ory/time complexity and model sizes. Identity shortcuts are validation set (except y reported on the test set). particularly important for not increasing the complexity of
|
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the bottleneck architectures that are introduced below. method top-5 err. (test)
|
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VGG [41] (ILSVRC’14) 7.32 Deeper Bottleneck Architectures.Next we describe our
|
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GoogLeNet [44] (ILSVRC’14) 6.66 deeper nets for ImageNet. Because of concerns on the train-
|
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VGG [41](v5) 6.8 ing time that we can afford, we modify the building block
|
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PReLU-net [13] 4.94 as abottleneckdesign 4 . For each residual functionF, we
|
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BN-inception [16] 4.82 use a stack of 3 layers instead of 2 (Fig.5). The three layers
|
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ResNet (ILSVRC’15) 3.57 are 1 1, 3 3, and 1 1 convolutions, where the 1 1 layers
|
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are responsible for reducing and then increasing (restoring) Table 5. Error rates (%) ofensembles. The top-5 error is on the dimensions, leaving the 3 3 layer a bottleneck with smaller test set of ImageNet and reported by the test server. input/output dimensions. Fig.5shows an example, where
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both designs have similar time complexity.
|
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ResNet reduces the top-1 error by 3.5% (Table2), resulting The parameter-free identity shortcuts are particularly im-
|
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from the successfully reduced training error (Fig.4rightvs. portant for the bottleneck architectures. If the identity short-
|
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left). This comparison verifies the effectiveness of residual cut in Fig.5(right) is replaced with projection, one can
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learning on extremely deep systems. show that the time complexity and model size are doubled,
|
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Last, we also note that the 18-layer plain/residual nets as the shortcut is connected to the two high-dimensional
|
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are comparably accurate (Table2), but the 18-layer ResNet ends. So identity shortcuts lead to more efficient models
|
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converges faster (Fig.4rightvs. left). When the net is “not for the bottleneck designs.
|
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overly deep” (18 layers here), the current SGD solver is still 50-layer ResNet:We replace each 2-layer block in the
|
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able to find good solutions to the plain net. In this case, the 4 ResNet eases the optimization by providing faster conver- Deepernon-bottleneck ResNets (e.g., Fig.5left) also gain accuracy
|
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from increased depth (as shown on CIFAR-10), but are not as economical gence at the early stage. as the bottleneck ResNets. So the usage of bottleneck designs is mainly due
|
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to practical considerations. We further note that the degradation problem Identityvs. Projection Shortcuts. We have shown that of plain nets is also witnessed for the bottleneck designs.
|
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6 34-layer net with this 3-layer bottleneck block, resulting in method error (%)
|
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|
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a 50-layer ResNet (Table1). We use option B for increasing Maxout [10] 9.38
|
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|
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dimensions. This model has 3.8 billion FLOPs. NIN [25] 8.81
|
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|
|
101-layer and 152-layer ResNets:We construct 101- DSN [24] 8.22
|
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|
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layer and 152-layer ResNets by using more 3-layer blocks # layers # params
|
|||
|
|
(Table1). Remarkably, although the depth is significantly FitNet [35] 19 2.5M 8.39
|
|||
|
|
increased, the 152-layer ResNet (11.3 billion FLOPs) still Highway [42,43] 19 2.3M 7.54 (7.72 0.16)
|
|||
|
|
haslower complexitythan VGG-16/19 nets (15.3/19.6 bil- Highway [42,43] 32 1.25M 8.80
|
|||
|
|
lion FLOPs). ResNet 20 0.27M 8.75
|
|||
|
|
The 50/101/152-layer ResNets are more accurate than ResNet 32 0.46M 7.51
|
|||
|
|
the 34-layer ones by considerable margins (Table3and4). ResNet 44 0.66M 7.17
|
|||
|
|
We do not observe the degradation problem and thus en- ResNet 56 0.85M 6.97
|
|||
|
|
joy significant accuracy gains from considerably increased ResNet 110 1.7M 6.43 (6.61 0.16)
|
|||
|
|
depth. The benefits of depth are witnessed for all evaluation ResNet 1202 19.4M 7.93
|
|||
|
|
metrics (Table3and4).
|
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|
|
Table 6. Classification error on theCIFAR-10test set. All meth- Comparisons with State-of-the-art Methods.In Table4 ods are with data augmentation. For ResNet-110, we run it 5 times we compare with the previous best single-model results. and show “best (mean std)” as in [43].
|
|||
|
|
Our baseline 34-layer ResNets have achieved very compet-
|
|||
|
|
itive accuracy. Our 152-layer ResNet has a single-model
|
|||
|
|
top-5 validation error of 4.49%. This single-model result so our residual models have exactly the same depth, width,
|
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|
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outperforms all previous ensemble results (Table5). We and number of parameters as the plain counterparts.
|
|||
|
|
combine six models of different depth to form an ensemble We use a weight decay of 0.0001 and momentum of 0.9,
|
|||
|
|
(only with two 152-layer ones at the time of submitting). and adopt the weight initialization in [13] and BN [16] but
|
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|
|
This leads to3.57%top-5 error on the test set (Table5). with no dropout. These models are trained with a mini-
|
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|
|
This entry won the 1st place in ILSVRC 2015. batch size of 128 on two GPUs. We start with a learning
|
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|
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rate of 0.1, divide it by 10 at 32k and 48k iterations, and
|
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|
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4.2. CIFAR-10 and Analysis terminate training at 64k iterations, which is determined on
|
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|
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a 45k/5k train/val split. We follow the simple data augmen-We conducted more studies on the CIFAR-10 dataset tation in [24] for training: 4 pixels are padded on each side,[20], which consists of 50k training images and 10k test- and a 32 32 crop is randomly sampled from the paddeding images in 10 classes. We present experiments trained image or its horizontal flip. For testing, we only evaluateon the training set and evaluated on the test set. Our focus the single view of the original 32 32 image.is on the behaviors of extremely deep networks, but not on We comparen=f3;5;7;9g, leading to 20, 32, 44, andpushing the state-of-the-art results, so we intentionally use 56-layer networks. Fig.6(left) shows the behaviors of thesimple architectures as follows. plain nets. The deep plain nets suffer from increased depth,The plain/residual architectures follow the form in Fig.3 and exhibit higher training error when going deeper. This(middle/right). The network inputs are 32 32 images, with phenomenon is similar to that on ImageNet (Fig.4, left) andthe per-pixel mean subtracted. The first layer is 3 3 convo- on MNIST (see [42]), suggesting that such an optimizationlutions. Then we use a stack of6nlayers with 3 3 convo- difficulty is a fundamental problem.lutions on the feature maps of sizesf32;16;8grespectively, Fig.6(middle) shows the behaviors of ResNets. Alsowith 2nlayers for each feature map size. The numbers of similar to the ImageNet cases (Fig.4, right), our ResNetsfilters aref16;32;64grespectively. The subsampling is per- manage to overcome the optimization difficulty and demon-formed by convolutions with a stride of 2. The network ends strate accuracy gains when the depth increases.with a global average pooling, a 10-way fully-connected We further exploren= 18that leads to a 110-layerlayer, and softmax. There are totally 6n+2 stacked weighted ResNet. In this case, we find that the initial learning ratelayers. The following table summarizes the architecture: of 0.1 is slightly too large to start converging 5 . So we use
|
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|
|
0.01 to warm up the training until the training error is below output map size 32 32 16 16 8 8 80% (about 400 iterations), and then go back to 0.1 and con- # layers 1+2n 2n 2n tinue training. The rest of the learning schedule is as done # filters 16 32 64 previously. This 110-layer network converges well (Fig.6,
|
|||
|
|
When shortcut connections are used, they are connected middle). It hasfewerparameters than other deep and thin
|
|||
|
|
to the pairs of 3 3 layers (totally3nshortcuts). On this 5 With an initial learning rate of 0.1, it starts converging (<90% error) dataset we use identity shortcuts in all cases (i.e., option A), after several epochs, but still reaches similar accuracy.
|
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7 20 20 20
|
|||
|
|
ResNet-20 residual-110
|
|||
|
|
ResNet-32 residual-1202
|
|||
|
|
ResNet-44
|
|||
|
|
ResNet-56
|
|||
|
|
56-layer ResNet-110
|
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|
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error (%)
|
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|
|
error (%) error (%) 10 10 20-layer 20-layer 10
|
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|
|||
|
|
110-layer 5 plain-20 5 5
|
|||
|
|
plain-32
|
|||
|
|
plain-44
|
|||
|
|
plain-56 10 0 00 1 2 3 4 5 6 0 1 2 3 4 5 6 4 5 6
|
|||
|
|
Figure 6. Training onCIFAR-10 iter. (1e4) . Dashed lines denote training error, and bold lines denote testing error. iter. (1e4) Left: plain networks. The error iter. (1e4)
|
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|
|
of plain-110 is higher than 60% and not displayed.Middle: ResNets.Right: ResNets with 110 and 1202 layers.
|
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|
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|
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|
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|
|
plain-20 training data 07+12 07++12 3 plain-56
|
|||
|
|
ResNet-20 test data VOC 07 test VOC 12 test
|
|||
|
|
std 2 ResNet-56
|
|||
|
|
ResNet-110 VGG-16 73.2 70.4
|
|||
|
|
1 ResNet-101 76.4 73.8
|
|||
|
|
0 20 40 60 80 100 layer index (original) Table 7. Object detection mAP (%) on the PASCAL VOC
|
|||
|
|
plain-203 2007/2012 test sets usingbaselineFaster R-CNN. See also Ta- plain-56
|
|||
|
|
ResNet-20 ble10and11for better results.
|
|||
|
|
std 2 ResNet-56
|
|||
|
|
ResNet-110 metric mAP@.5 mAP@[.5, .95] 1
|
|||
|
|
VGG-16 41.5 21.2 0 20 40 60 80 100 layer index (sorted by magnitude) Figure 7. Standard deviations (std) of layer responses on CIFAR- ResNet-101 48.4 27.2
|
|||
|
|
10. The responses are the outputs of each 3 3 layer, after BN and Table 8. Object detection mAP (%) on the COCO validation set
|
|||
|
|
before nonlinearity.Top: the layers are shown in their original usingbaselineFaster R-CNN. See also Table9for better results.
|
|||
|
|
order.Bottom: the responses are ranked in descending order.
|
|||
|
|
have similar training error. We argue that this is because of
|
|||
|
|
networks such as FitNet [35] and Highway [42] (Table6), overfitting. The 1202-layer network may be unnecessarily
|
|||
|
|
yet is among the state-of-the-art results (6.43%, Table6). large (19.4M) for this small dataset. Strong regularization
|
|||
|
|
such as maxout [10] or dropout [14] is applied to obtain theAnalysis of Layer Responses.Fig.7shows the standard best results ([10,25,24,35]) on this dataset. In this paper,deviations (std) of the layer responses. The responses are we use no maxout/dropout and just simply impose regular-the outputs of each 3 3 layer, after BN and before other ization via deep and thin architectures by design, withoutnonlinearity (ReLU/addition). For ResNets, this analy- distracting from the focus on the difficulties of optimiza-sis reveals the response strength of the residual functions. tion. But combining with stronger regularization may im-Fig.7shows that ResNets have generally smaller responses prove results, which we will study in the future.than their plain counterparts. These results support our ba-
|
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sic motivation (Sec.3.1) that the residual functions might 4.3. Object Detection on PASCAL and MS COCO
|
|||
|
|
be generally closer to zero than the non-residual functions. Our method has good generalization performance onWe also notice that the deeper ResNet has smaller magni- other recognition tasks. Table7and8show the object de-tudes of responses, as evidenced by the comparisons among tection baseline results on PASCAL VOC 2007 and 2012ResNet-20, 56, and 110 in Fig.7. When there are more [5] and COCO [26]. We adoptFaster R-CNN[32] as the de-layers, an individual layer of ResNets tends to modify the tection method. Here we are interested in the improvementssignal less. of replacing VGG-16 [41] with ResNet-101. The detection
|
|||
|
|
Exploring Over 1000 layers.We explore an aggressively implementation (see appendix) of using both models is the
|
|||
|
|
deep model of over 1000 layers. We setn= 200that same, so the gains can only be attributed to better networks.
|
|||
|
|
leads to a 1202-layer network, which is trained as described Most remarkably, on the challenging COCO dataset we ob-
|
|||
|
|
above. Our method showsno optimization difficulty, and tain a 6.0% increase in COCO’s standard metric (mAP@[.5,
|
|||
|
|
this10 3 -layer network is able to achievetraining error .95]), which is a 28% relative improvement. This gain is
|
|||
|
|
<0.1% (Fig.6, right). Its test error is still fairly good solely due to the learned representations.
|
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|
|
(7.93%, Table6). Based on deep residual nets, we won the 1st places in
|
|||
|
|
But there are still open problems on such aggressively several tracks in ILSVRC & COCO 2015 competitions: Im-
|
|||
|
|
deep models. The testing result of this 1202-layer network ageNet detection, ImageNet localization, COCO detection,
|
|||
|
|
is worse than that of our 110-layer network, although both and COCO segmentation. The details are in the appendix.
|
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|
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8 References [28]G. Montufar, R. Pascanu, K. Cho, and Y. Bengio. On the number of´
|
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linear regions of deep neural networks. InNIPS, 2014.[1]Y. Bengio, P. Simard, and P. Frasconi. Learning long-term dependen- [29]V. Nair and G. E. Hinton. Rectified linear units improve restrictedcies with gradient descent is difficult.IEEE Transactions on Neural boltzmann machines. InICML, 2010.Networks, 5(2):157–166, 1994. [30]F. Perronnin and C. Dance. Fisher kernels on visual vocabularies for[2]C. M. Bishop. Neural networks for pattern recognition. Oxford image categorization. InCVPR, 2007.university press, 1995. [31]T. Raiko, H. Valpola, and Y. LeCun. Deep learning made easier by[3]W. L. Briggs, S. F. McCormick, et al.A Multigrid Tutorial. Siam, linear transformations in perceptrons. InAISTATS, 2012.2000. [32]S. Ren, K. He, R. Girshick, and J. Sun. Faster R-CNN: Towards[4]K. Chatfield, V. Lempitsky, A. Vedaldi, and A. Zisserman. The devil real-time object detection with region proposal networks. InNIPS,is in the details: an evaluation of recent feature encoding methods. 2015.InBMVC, 2011. [33]S. Ren, K. He, R. Girshick, X. Zhang, and J. Sun. Object detection[5]M. Everingham, L. Van Gool, C. K. Williams, J. Winn, and A. Zis- networks on convolutional feature maps.arXiv:1504.06066, 2015.serman. The Pascal Visual Object Classes (VOC) Challenge.IJCV, [34]B. D. Ripley.Pattern recognition and neural networks. Cambridgepages 303–338, 2010. university press, 1996.[6]S. Gidaris and N. Komodakis. Object detection via a multi-region & [35]A. Romero, N. Ballas, S. E. Kahou, A. Chassang, C. Gatta, andsemantic segmentation-aware cnn model. InICCV, 2015. Y. Bengio. Fitnets: Hints for thin deep nets. InICLR, 2015.[7]R. Girshick. Fast R-CNN. InICCV, 2015. [36]O. Russakovsky, J. Deng, H. Su, J. Krause, S. Satheesh, S. Ma,[8]R. Girshick, J. Donahue, T. Darrell, and J. Malik. Rich feature hier- Z. Huang, A. Karpathy, A. Khosla, M. Bernstein, et al. Imagenetarchies for accurate object detection and semantic segmentation. In large scale visual recognition challenge.arXiv:1409.0575, 2014.CVPR, 2014. [37]A. M. Saxe, J. L. McClelland, and S. Ganguli. Exact solutions to[9]X. Glorot and Y. Bengio. Understanding the difficulty of training the nonlinear dynamics of learning in deep linear neural networks.deep feedforward neural networks. InAISTATS, 2010. arXiv:1312.6120, 2013.[10]I. J. Goodfellow, D. Warde-Farley, M. Mirza, A. Courville, and [38]N. N. Schraudolph. Accelerated gradient descent by factor-centeringY. Bengio. Maxout networks.arXiv:1302.4389, 2013. decomposition. Technical report, 1998.[11]K. He and J. Sun. Convolutional neural networks at constrained time [39]N. N. Schraudolph. Centering neural network gradient factors. Incost. InCVPR, 2015. Neural Networks: Tricks of the Trade, pages 207–226. Springer,[12]K. He, X. Zhang, S. Ren, and J. Sun. Spatial pyramid pooling in deep 1998.convolutional networks for visual recognition. InECCV, 2014. [40]P. Sermanet, D. Eigen, X. Zhang, M. Mathieu, R. Fergus, and Y. Le-[13]K. He, X. Zhang, S. Ren, and J. Sun. Delving deep into rectifiers: Cun. Overfeat: Integrated recognition, localization and detectionSurpassing human-level performance on imagenet classification. In using convolutional networks. InICLR, 2014.ICCV, 2015. [41]K. Simonyan and A. Zisserman. Very deep convolutional networks[14]G. E. Hinton, N. Srivastava, A. Krizhevsky, I. Sutskever, and for large-scale image recognition. InICLR, 2015.R. R. Salakhutdinov. Improving neural networks by preventing co- [42]R. K. Srivastava, K. Greff, and J. Schmidhuber. Highway networks.adaptation o
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[24]C.-Y. Lee, S. Xie, P. Gallagher, Z. Zhang, and Z. Tu. Deeply-
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supervised nets.arXiv:1409.5185, 2014.
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[25]M. Lin, Q. Chen, and S. Yan. Network in network.arXiv:1312.4400,
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2013.
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[26]T.-Y. Lin, M. Maire, S. Belongie, J. Hays, P. Perona, D. Ramanan,
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P. Dollar, and C. L. Zitnick. Microsoft COCO: Common objects in´
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context. InECCV. 2014.
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[27]J. Long, E. Shelhamer, and T. Darrell. Fully convolutional networks
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for semantic segmentation. InCVPR, 2015.
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9 A. Object Detection Baselines 8 images (i.e., 1 per GPU) and the Fast R-CNN step has a
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mini-batch size of 16 images. The RPN step and Fast R-In this section we introduce our detection method based CNN step are both trained for 240k iterations with a learn-on the baseline Faster R-CNN [32] system. The models are ing rate of 0.001 and then for 80k iterations with 0.0001.initialized by the ImageNet classification models, and then Table8shows the results on the MS COCO validationfine-tuned on the object detection data. We have experi- set. ResNet-101 has a 6% increase of mAP@[.5, .95] overmented with ResNet-50/101 at the time of the ILSVRC & VGG-16, which is a 28% relative improvement, solely con-COCO 2015 detection competitions. tributed by the features learned by the better network. Re-Unlike VGG-16 used in [32], our ResNet has no hidden markably, the mAP@[.5, .95]’s absolute increase (6.0%) isfc layers. We adopt the idea of “Networks on Conv fea- nearly as big as mAP@.5’s (6.9%). This suggests that ature maps” (NoC) [33] to address this issue. We compute deeper network can improve both recognition and localiza-the full-image shared conv feature maps using those lay- tion.ers whose strides on the image are no greater than 16 pixels
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(i.e., conv1, conv2x, conv3x, and conv4x, totally 91 conv
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layers in ResNet-101; Table1). We consider these layers as B. Object Detection Improvements
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analogous to the 13 conv layers in VGG-16, and by doing For completeness, we report the improvements made forso, both ResNet and VGG-16 have conv feature maps of the the competitions. These improvements are based on deep same total stride (16 pixels). These layers are shared by a features and thus should benefit from residual learning. region proposal network (RPN, generating 300 proposals)
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[32] and a Fast R-CNN detection network [7]. RoI pool- MS COCO
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ing [7] is performed before conv51. On this RoI-pooled Box refinement.Our box refinement partially follows the it-
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feature, all layers of conv5x and up are adopted for each erative localization in [6]. In Faster R-CNN, the final output
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region, playing the roles of VGG-16’s fc layers. The final is a regressed box that is different from its proposal box. So
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classification layer is replaced by two sibling layers (classi- for inference, we pool a new feature from the regressed box
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fication and box regression [7]). and obtain a new classification score and a new regressed
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For the usage of BN layers, after pre-training, we com- box. We combine these 300 new predictions with the orig-
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pute the BN statistics (means and variances) for each layer inal 300 predictions. Non-maximum suppression (NMS) is
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on the ImageNet training set. Then the BN layers are fixed applied on the union set of predicted boxes using an IoU
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during fine-tuning for object detection. As such, the BN threshold of 0.3 [8], followed by box voting [6]. Box re-
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layers become linear activations with constant offsets and finement improves mAP by about 2 points (Table9).
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scales, and BN statistics are not updated by fine-tuning. We Global context. We combine global context in the Fastfix the BN layers mainly for reducing memory consumption R-CNN step. Given the full-image conv feature map, wein Faster R-CNN training. pool a feature by global Spatial Pyramid Pooling [12] (with
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PASCAL VOC a “single-level” pyramid) which can be implemented as
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Following [7,32], for the PASCAL VOC 2007testset, “RoI” pooling using the entire image’s bounding box as the
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we use the 5ktrainvalimages in VOC 2007 and 16ktrain- RoI. This pooled feature is fed into the post-RoI layers to
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valimages in VOC 2012 for training (“07+12”). For the obtain a global context feature. This global feature is con-
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PASCAL VOC 2012testset, we use the 10ktrainval+test catenated with the original per-region feature, followed by
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images in VOC 2007 and 16ktrainvalimages in VOC 2012 the sibling classification and box regression layers. This
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for training (“07++12”). The hyper-parameters for train- new structure is trained end-to-end. Global context im-
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ing Faster R-CNN are the same as in [32]. Table7shows proves mAP@.5 by about 1 point (Table9).
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the results. ResNet-101 improves the mAP by>3% over Multi-scale testing.In the above, all results are obtained byVGG-16. This gain is solely because of the improved fea- single-scale training/testing as in [32], where the image’stures learned by ResNet. shorter side iss= 600pixels. Multi-scale training/testing
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MS COCO has been developed in [12,7] by selecting a scale from a
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The MS COCO dataset [26] involves 80 object cate- feature pyramid, and in [33] by using maxout layers. In
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gories. We evaluate the PASCAL VOC metric (mAP @ our current implementation, we have performed multi-scale
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IoU = 0.5) and the standard COCO metric (mAP @ IoU = testingfollowing [33]; we have not performed multi-scale
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.5:.05:.95). We use the 80k images on the train set for train- training because of limited time. In addition, we have per-
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ing and the 40k images on the val set for evaluation. Our formed multi-scale testing only for the Fast R-CNN step
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detection system for COCO is similar to that for PASCAL (but not yet for the RPN step). With a trained model, we
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VOC. We train the COCO models with an 8-GPU imple- compute conv feature maps on an image pyramid, where the
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mentation, and thus the RPN step has a mini-batch size of image’s shorter sides ares2 f200;400;600;800;1000g.
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10 training data COCO train COCO trainval
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test data COCO val COCO test-dev
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mAP @.5 @[.5, .95] @.5 @[.5, .95]
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baseline Faster R-CNN (VGG-16) 41.5 21.2
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baseline Faster R-CNN (ResNet-101) 48.4 27.2
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+box refinement 49.9 29.9
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+context 51.1 30.0 53.3 32.2
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+multi-scale testing 53.8 32.5 55.7 34.9
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ensemble 59.0 37.4
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Table 9. Object detection improvements on MS COCO using Faster R-CNN and ResNet-101.
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system net data mAP areo bike bird boat bottle bus car cat chair cow table dog horse mbike person plant sheep sofa train tv
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baseline VGG-16 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
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baseline ResNet-101 07+12 76.4 79.8 80.7 76.2 68.3 55.9 85.1 85.389.856.7 87.8 69.4 88.3 88.9 80.9 78.4 41.7 78.6 79.8 85.3 72.0
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baseline+++ResNet-101 COCO+07+12 85.6 90.0 89.6 87.8 80.8 76.1 89.9 89.989.675.5 90.0 80.7 89.6 90.3 89.1 88.7 65.4 88.1 85.6 89.0 86.8
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Table 10. Detection results on the PASCAL VOC 2007 test set. The baseline is the Faster R-CNN system. The system “baseline+++”
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include box refinement, context, and multi-scale testing in Table9.
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system net data mAP areo bike bird boat bottle bus car cat chair cow table dog horse mbike person plant sheep sofa train tv
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baseline VGG-16 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
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baseline ResNet-101 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
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baseline+++ResNet-101COCO+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
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Table 11. Detection results on the PASCAL VOC 2012 test set (http://host.robots.ox.ac.uk:8080/leaderboard/
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displaylb.php?challengeid=11&compid=4). The baseline is the Faster R-CNN system. The system “baseline+++” include
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box refinement, context, and multi-scale testing in Table9.
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We select two adjacent scales from the pyramid following val2 test
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[33]. RoI pooling and subsequent layers are performed on GoogLeNet [44] (ILSVRC’14) - 43.9
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the feature maps of these two scales [33], which are merged our single model (ILSVRC’15) 60.5 58.8 by maxout as in [33]. Multi-scale testing improves the mAP our ensemble (ILSVRC’15) 63.6 62.1 by over 2 points (Table9). Table 12. Our results (mAP, %) on the ImageNet detection dataset. Using validation data.Next we use the 80k+40k trainval set Our detection system is Faster R-CNN [32] with the improvements
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for training and the 20k test-dev set for evaluation. The test- in Table9, using ResNet-101.
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dev set has no publicly available ground truth and the result
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is reported by the evaluation server. Under this setting, the we achieve 85.6% mAP on PASCAL VOC 2007 (Table10)results are an mAP@.5 of 55.7% and an mAP@[.5, .95] of and 83.8% on PASCAL VOC 2012 (Table11)6 . The result34.9% (Table9). This is our single-model result. on PASCAL VOC 2012 is 10 points higher than the previ-
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Ensemble.In Faster R-CNN, the system is designed to learn ous state-of-the-art result [6].
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region proposals and also object classifiers, so an ensemble
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can be used to boost both tasks. We use an ensemble for ImageNet Detection
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proposing regions, and the union set of proposals are pro- The ImageNet Detection (DET) task involves 200 object
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cessed by an ensemble of per-region classifiers. Table9 categories. The accuracy is evaluated by mAP@.5. Our
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shows our result based on an ensemble of 3 networks. The object detection algorithm for ImageNet DET is the same
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mAP is 59.0% and 37.4% on the test-dev set.This result as that for MS COCO in Table9. The networks are pre-
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won the 1st place in the detection task in COCO 2015. trained on the 1000-class ImageNet classification set, and
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are fine-tuned on the DET data. We split the validation set
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PASCAL VOC into two parts (val1/val2) following [8]. We fine-tune the
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We revisit the PASCAL VOC dataset based on the above detection models using the DET training set and the val1
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model. With the single model on the COCO dataset (55.7% set. The val2 set is used for validation. We do not use other
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mAP@.5 in Table9), we fine-tune this model on the PAS- ILSVRC 2015 data. Our single model with ResNet-101 has
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CAL VOC sets. The improvements of box refinement, con- 6
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text, and multi-scale testing are also adopted. By doing so http://host.robots.ox.ac.uk:8080/anonymous/3OJ4OJ.html,
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submitted on 2015-11-26.
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11 LOC LOC LOC errorclassificationtop-5 LOC error top-5 localization err testing method method network on GT CLS network on predicted CLS val test VGG’s [41] VGG-16 1-crop 33.1 [41] OverFeat [40] (ILSVRC’13) 30.0 29.9 RPN ResNet-1011-crop 13.3
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RPN ResNet-101dense 11.7 GoogLeNet [44] (ILSVRC’14) - 26.7
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RPN ResNet-101dense ResNet-101 14.4 VGG [41] (ILSVRC’14) 26.9 25.3
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RPN+RCNNResNet-101dense ResNet-101 10.6 ours (ILSVRC’15) 8.9 9.0 RPN+RCNN ensemble dense ensemble 8.9
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Table 14. Comparisons of localization error (%) on the ImageNetTable 13. Localization error (%) on the ImageNet validation. In dataset with state-of-the-art methods.the column of “LOC error on GT class” ([41]), the ground truth
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class is used. In the “testing” column, “1-crop” denotes testing
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on a center crop of 224 224 pixels, “dense” denotes dense (fully ports a center-crop error of 33.1% (Table13) using ground
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convolutional) and multi-scale testing. truth classes. Under the same setting, our RPN method us-
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ing ResNet-101 net significantly reduces the center-crop er-
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ror to 13.3%. This comparison demonstrates the excellent58.8% mAP and our ensemble of 3 models has 62.1% mAP performance of our framework. With dense (fully convolu-on the DET test set (Table12).This result won the 1st place tional) and multi-scale testing, our ResNet-101 has an errorin the ImageNet detection task in ILSVRC 2015, surpassing of 11.7% using ground truth classes. Using ResNet-101 forthe second place by8.5 points(absolute). predicting classes (4.6% top-5 classification error, Table4),
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C. ImageNet Localization the top-5 localization error is 14.4%.
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The above results are only based on theproposal network
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The ImageNet Localization (LOC) task [36] requires to (RPN) in Faster R-CNN [32]. One may use thedetection
|
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classify and localize the objects. Following [40,41], we network(Fast R-CNN [7]) in Faster R-CNN to improve the
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assume that the image-level classifiers are first adopted for results. But we notice that on this dataset, one image usually
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predicting the class labels of an image, and the localiza- contains a single dominate object, and the proposal regions
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tion algorithm only accounts for predicting bounding boxes highly overlap with each other and thus have very similar
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based on the predicted classes. We adopt the “per-class re- RoI-pooled features. As a result, the image-centric training
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gression” (PCR) strategy [40,41], learning a bounding box of Fast R-CNN [7] generates samples of small variations,
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regressor for each class. We pre-train the networks for Im- which may not be desired for stochastic training. Motivated
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ageNet classification and then fine-tune them for localiza- by this, in our current experiment we use the original R-
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tion. We train networks on the provided 1000-class Ima- CNN [8] that is RoI-centric, in place of Fast R-CNN.
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geNet training set. Our R-CNN implementation is as follows. We apply the
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Our localization algorithm is based on the RPN frame- per-class RPN trained as above on the training images to
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work of [32] with a few modifications. Unlike the way in predict bounding boxes for the ground truth class. These
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[32] that is category-agnostic, our RPN for localization is predicted boxes play a role of class-dependent proposals.
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designed in aper-classform. This RPN ends with two sib- For each training image, the highest scored 200 proposals
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ling 1 1 convolutional layers for binary classification (cls) are extracted as training samples to train an R-CNN classi-
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and box regression (reg), as in [32]. Theclsandreglayers fier. The image region is cropped from a proposal, warped
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are both in aper-classfrom, in contrast to [32]. Specifi- to 224 224 pixels, and fed into the classification network
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cally, theclslayer has a 1000-d output, and each dimension as in R-CNN [8]. The outputs of this network consist of two
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isbinary logistic regressionfor predicting being or not be- sibling fc layers forclsandreg, also in a per-class form.
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ing an object class; thereglayer has a 1000 4-d output This R-CNN network is fine-tuned on the training set us-
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consisting of box regressors for 1000 classes. As in [32], ing a mini-batch size of 256 in the RoI-centric fashion. For
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our bounding box regression is with reference to multiple testing, the RPN generates the highest scored 200 proposals
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translation-invariant “anchor” boxes at each position. for each predicted class, and the R-CNN network is used to
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update these proposals’ scores and box positions.As in our ImageNet classification training (Sec.3.4), we This method reduces the top-5 localization error torandomly sample 224 224 crops for data augmentation. 10.6% (Table13). This is our single-model result on theWe use a mini-batch size of 256 images for fine-tuning. To validation set. Using an ensemble of networks for both clas-avoid negative samples being dominate, 8 anchors are ran- sification and localization, we achieve a top-5 localizationdomly sampled for each image, where the sampled positive error of 9.0% on the test set. This number significantly out-and negative anchors have a ratio of 1:1 [32]. For testing, performs the ILSVRC 14 results (Table14), showing a 64% the network is applied on the image fully-convolutionally. relative reduction of error.This result won the 1st place inTable13compares the localization results. Following the ImageNet localization task in ILSVRC 2015.[41], we first perform “oracle” testing using the ground truth
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class as the classification prediction. VGG’s paper [41] re-
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12
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