ImageNet Classification with Deep Convolutional Neural Networks论文翻译 上
code
AlexNet实现地址(基于PyTorch): https://github.com/Lornatang/pytorch/blob/master/official/net/alexnet.py
4 Reducing Overfitting
4减少过度配合
Our neural network architecture has 60 million parameters. Although the 1000 classes of ILSVRC make each training example impose 10 bits of constraint on the mapping from image to label, this turns out to be insufficient to learn so many parameters without considerable overfitting. Below, we describe the two primary ways in which we combat overfitting.
我们的神经网络架构拥有6000万个参数。尽管ILSVRC的1000个类别使得每个训练示例对从图像到标签的映射施加10比特的约束，但事实证明没有足够的过度配合学习如此多的参数是不够的。在下面，我们描述了我们与配合作战的两种主要方式。
4.1 Data Augmentation
4.1数据增强
The easiest and most common method to reduce overfitting on image data is to artificially enlarge the dataset using label-preserving transformations (e.g., [25, 4, 5]). We employ two distinct forms of data augmentation, both of which allow transformed images to be produced from the original images with very little computation, so the transformed images do not need to be stored on disk. In our implementation, the transformed images are generated in Python code on the CPU while the GPU is training on the previous batch of images. So these data augmentation schemes are, in effect, computationally free.
减少图像数据过度拟合的最简单和最常见的方法是使用标签保留变换（例如[25,4,5]）人工放大数据集。我们采用两种不同形式的数据增强，这两种形式都允许通过很少的计算从原始图像生成变换图像，所以变换后的图像不需要存储在磁盘上。在我们的实现中，转换后的图像是在CPU上的Python代码中生成的，而GPU正在训练上一批图像。所以这些数据增强方案实际上是计算上免费的。
The first form of data augmentation consists of generating image translations and horizontal reflections. We do this by extracting randomThe second form of data augmentation consists of altering the intensities of the RGB channels in training images. Specifically, we perform PCA on the set of RGB pixel values throughout the ImageNet training set. To each training image, we add multiples of the found principal components,
第二种形式的数据增强包括改变训练图像中RGB通道的强度。具体而言，我们在整个ImageNet训练集的RGB像素值集上执行PCA。对于每个训练图像，我们添加多个找到的主要组件，
只绘制一次，直到该图像再次用于训练，此时它将被重新绘制。该方案近似捕捉自然图像的重要属性，即对象身份对于照度的强度和颜色的变化是不变的。该方案将前1个错误率降低1％以上。
4.2 Dropout
4.2辍学
Combining the predictions of many different models is a very successful way to reduce test errors [1, 3], but it appears to be too expensive for big neural networks that already take several days to train. There is, however, a very efficient version of model combination that only costs about a factor of two during training. The recently-introduced technique, called “dropout” [10], consists of setting to zero the output of each hidden neuron with probability 0.5. The neurons which are “dropped out” in this way do not contribute to the forward pass and do not participate in backpropagation. So every time an input is presented, the neural network samples a different architecture, but all these architectures share weights. This technique reduces complex co-adaptations of neurons, since a neuron cannot rely on the presence of particular other neurons. It is, therefore, forced to learn more robust features that are useful in conjunction with many different random subsets of the other neurons. At test time, we use all the neurons but multiply their outputs by 0.5, which is a reasonable approximation to taking the geometric mean of the predictive distributions produced by the exponentially-many dropout networks.
结合许多不同模型的预测是减少测试错误的一种非常成功的方法[1,3]，但对于已经花费数天时间训练的大型神经网络来说，它似乎太昂贵了。然而，有一个非常有效的模型组合版本，在培训期间，其成本只有两倍。最近引入的称为“丢失”[10]的技术包括将每个隐藏神经元的输出设置为零，概率为0.5。以这种方式“退出”的神经元对前向传球没有贡献，并且不参与反向传播。所以每次提交输入时，神经网络都会采样不同的体系结构，但所有这些体系结构共享权重。这种技术减少了神经元的复杂适应性，因为神经元不能依赖特定其他神经元的存在。因此，它被迫学习更强大的功能，这些功能可以与其他神经元的许多不同的随机子集结合使用。在测试时间，我们使用所有的神经元，但将它们的输出乘以0.5，这对于采用指数衰减网络产生的预测分布的几何平均数是一个合理的近似。
We use dropout in the first two fully-connected layers of Figure 2. Without dropout, our network exhibits substantial overfitting. Dropout roughly doubles the number of iterations required to converge.
我们在图2的前两个完全连接层中使用了丢失。没有辍学，我们的网络展示了大量的过度配合。辍学率大约是收敛所需的迭代次数的两倍。
5 Details of learning
5学习细节
We trained our models using stochastic gradient descent with a batch size of 128 examples, momentum of 0.9, and weight decay of 0.0005. We found that this small amount of weight decay was important for the model to learn. In Figure 3: 96 convolutional kernels of size other words, weight decay here is not merely a regularizer:is
其中i是迭代指数，v是动量变量，ε是学习率，是
We initialized the weights in each layer from a zero-mean Gaussian distribution with standard deviation 0.01. We initialized the neuron biases in the second, fourth, and fifth convolutional layers, as well as in the fully-connected hidden layers, with the constant 1. This initialization accelerates the early stages of learning by providing the ReLUs with positive inputs. We initialized the neuron biases in the remaining layers with the constant 0.
我们用标准偏差为0.01的零均值高斯分布初始化各层的权重。我们初始化了第二，第四和第五卷积层以及完全连通的隐层中的神经元偏差，其常数为1。这种初始化通过向ReLU提供正输入来加速学习的早期阶段。我们用常数0初始化剩余层中的神经元偏差。
We used an equal learning rate for all layers, which we adjusted manually throughout training. The heuristic which we followed was to divide the learning rate by 10 when the validation error rate stopped improving with the current learning rate. The learning rate was initialized at 0.01 and reduced three times prior to termination. We trained the network for roughly 90 cycles through the training set of 1.2 million images, which took five to six days on two NVIDIA GTX 580 3GB GPUs.
我们对所有图层使用相同的学习率，我们在整个培训过程中手动进行了调整。我们遵循的启发式是当验证错误率以当前学习速率停止改进时，将学习速率除以10。学习率初始化为0.01，在终止前减少三次。我们通过120万张图像的训练集对网络进行了大约90个周期的训练，这些图像在两个NVIDIA GTX 580 3GB GPU上花费了五天时间。
6 Results
6结果
Our results on ILSVRC-2010 are summarized in Table 1. Our network achieves top-1 and top-5 test set error rates of 37.5% and 17.0%5. The best performance achieved during the ILSVRC2010 competition was 47.1% and 28.2% with an approach that averages the predictions produced from six sparse-coding models trained on different features [2], and since then the best published results are 45.7% and 25.7% with an approach that averages the predictions of two classifiers trained on Fisher Vectors (FVs) computed from two types of densely-sampled features [24].
表1总结了我们在ILSVRC-2010上的结果。我们的网络达到37.5％和17.0％的前1名和前5名测试集错误率5。在ILSVRC2010大赛中获得的最佳成绩是47.1％和28.2％，其中一种方法是对六种针对不同特征进行训练的稀疏编码模型所产生的预测进行平均[2]，此后最佳公布结果分别为45.7％和25.7％，一种方法是对两种经过密集采样的特征计算得到的Fisher矢量（FV）进行训练的两个分类器的预测值的平均值[24]。
We also entered our model in the ILSVRC-2012 competition and report our results in Table 2. Since the ILSVRC-2012 test set labels are not publicly available, we cannot report test error rates for all the models that we tried. In the remainder of this paragraph, we use validation and test error rates interchangeably because Table 1: Comparison of results on ILSVRCin our experience they do not differ by more than 0.1% 2010 test set. In italics are best results (see Table 2). The CNN described in this paper achieves achieved by others. a top-5 error rate of 18.2%. Averaging the predictions of five similar CNNs gives an error rate of 16.4%. Training one CNN, with an extra sixth convolutional layer over the last pooling layer, to classify the entire ImageNet Fall 2011 release (15M images, 22K categories), and then “fine-tuning” it on ILSVRC-2012 gives an error rate of 16.6%. Averaging the predictions of two CNNs that were pre-trained on the entire Fall 2011 release with the aforementioned five CNNs gives an error rate of 15.3%. The second-best contest entry achieved an error rate of 26.2% with an approach that averages the predictions of several classifiers trained on FVs computed from different types of densely-sampled features [7].
我们也参加了ILSVRC-2012比赛的模型，并在表2中报告了我们的结果。由于ILSVRC-2012测试集标签没有公开提供，因此我们无法报告我们尝试的所有模型的测试错误率。在这段的其余部分中,我们使用验证和测试错误率互换,因为表1:比较结果ILSVRCin我们的经验他们不相差超过0.1% 2010测试集。在斜体是最好的结果(见表2)。本文中描述的CNN获得通过。前五名的错误率是18.2%。对五个相似CNN的预测进行平均，得出错误率为16.4％。培训一个CNN，在最后一个池层上增加一个额外的第六个卷积层，对整个ImageNet 2011秋季发布（15M图像，22K种类）进行分类，然后在ILSVRC-2012上“微调”它，错误率为16.6 ％。对整个2011年秋季发行版预先训练的两个CNN与上述五个CNN进行平均，得出错误率为15.3％。第二好的比赛录入达到了26.2％的错误率，其方法是对从不同类型的密集采样特征计算出的FV进行训练的几个分类器的预测进行平均[7]。
Finally, we also report our error rates on the Fall 2009 version of ImageNet with 10,184 categories and 8.9 million images. On this dataset we follow the convention in the literature of using half of the images for training and half for testing. Since there is no established test set, our split necesTable 2: Comparison of error rates on ILSVRC-2012 validation and sarily differs from the splits used test sets. In italics are best results achieved by others. Models with an by previous authors, but this does asterisk* were “pre-trained” to classify the entire ImageNet 2011 Fall not affect the results appreciably.
最后，我们还在2009年秋季版ImageNet上报告了10,184个类别和890万个图像的错误率。在这个数据集中，我们遵循文献中使用一半图像进行训练和一半进行测试的惯例。由于没有建立测试集，因此我们的拆分必要性表2：ILSVRC-2012验证错误率的比较与测试集的拆分不同。斜体是其他人取得的最好结果。有以前作者的模型，但是星号*是“预先训练好的”，用于对整个ImageNet 2011进行分类，不会对结果产生显着影响。
release. See Section 6 for details.
发布。详情请参阅第6节。
Our top-1 and top-5 error rates on this dataset are 67.4% and 40.9%, attained by the net described above but with an additional, sixth convolutional layer over the last pooling layer. The best published results on this dataset are 78.1% and 60.9% [19].
在这个数据集中，我们的前1和前5的错误率分别是67.4％和40.9％，通过上面描述的网络获得，但是在最后的池化层上具有额外的第六卷积层。该数据集的最佳公布结果是78.1％和60.9％[19]。
6.1 Qualitative Evaluations
6.1定性评估
Figure 3 shows the convolutional kernels learned by the network’s two data-connected layers. The network has learned a variety of frequency- and orientation-selective kernels, as well as various colored blobs. Notice the specialization exhibited by the two GPUs, a result of the restricted connectivity described in Section 3.5. The kernels on GPU 1 are largely color-agnostic, while the kernels on on GPU 2 are largely color-specific. This kind of specialization occurs during every run and is independent of any particular random weight initialization (modulo a renumbering of the GPUs).
图3显示了网络的两个数据连接层学习的卷积核。该网络已经学习了各种频率和方向选择内核，以及各种彩色斑点。注意两个GPU所展示的专业化，这是第3.5节中描述的受限连接的结果。GPU 1上的内核在很大程度上与颜色无关，而GPU 2上的内核在很大程度上是颜色特定的。这种专业化发生在每次运行期间，并且独立于任何特定的随机权重初始化（以GPU的重新编号为模）。
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5The error rates without averaging predictions over ten patches as described in Section 4.1 are 39.0% and 18.3%.
5如第4.1节所述，没有平均预测超过10个补丁的错误率分别为39.0％和18.3％。
Figure 4: (Left) Eight ILSVRC-2010 test images and the five labels considered most probable by our model.
图4 :(左）八个ILSVRC-2010测试图像和我们模型最可能考虑的五个标签。
The correct label is written under each image, and the probability assigned to the correct label is also shown
正确的标签写在每张图像下，并且还显示了分配给正确标签的概率
with a red bar (if it happens to be in the top 5). (Right) Five ILSVRC-2010 test images in the first column. The
与一个红色酒吧（如果它碰巧在前五）。 （右）第一列有5个ILSVRC-2010测试图像。该
remaining columns show the six training images that produce feature vectors in the last hidden layer with the
剩下的列显示了六个训练图像，它们在最后一个隐藏层中产生特征向量
smallest Euclidean distance from the feature vector for the test image.
测试图像的特征向量的最小欧几里得距离。
In the left panel of Figure 4 we qualitatively assess what the network has learned by computing its top-5 predictions on eight test images. Notice that even off-center objects, such as the mite in the top-left, can be recognized by the net. Most of the top-5 labels appear reasonable. For example, only other types of cat are considered plausible labels for the leopard. In some cases (grille, cherry) there is genuine ambiguity about the intended focus of the photograph.
在图4的左侧面板中，我们通过计算八个测试图像的前5个预测来定性评估网络学到的内容。请注意，即使偏心的物体，如左上角的螨虫，也可以被网络识别。大多数前五名的标签显得合理。例如，只有其他类型的猫被认为是豹的合理标签。在某些情况下（格栅，樱桃），照片的预期焦点存在真正的模糊性。
Another way to probe the network’s visual knowledge is to consider the feature activations induced by an image at the last, 4096-dimensional hidden layer. If two images produce feature activation vectors with a small Euclidean separation, we can say that the higher levels of the neural network consider them to be similar. Figure 4 shows five images from the test set and the six images from the training set that are most similar to each of them according to this measure. Notice that at the pixel level, the retrieved training images are generally not close in L2 to the query images in the first column. For example, the retrieved dogs and elephants appear in a variety of poses. We present the results for many more test images in the supplementary material.
探测网络视觉知识的另一种方法是考虑由最后一个4096维隐藏层中的图像引发的特征激活。如果两幅图像产生具有较小欧几里德分离的特征激活向量，我们可以说更高层次的神经网络认为它们是相似的。图4显示了来自测试集的五幅图像以及来自训练集的六幅图像，这些图像根据此测量与它们中的每一幅最相似。请注意，在像素级别，检索到的训练图像一般不会在第一列的查询图像中靠近L2。例如，检索到的狗和大象出现在各种姿势中。我们在补充材料中提供更多测试图像的结果。
Computing similarity by using Euclidean distance between two 4096-dimensional, real-valued vectors is inefficient, but it could be made efficient by training an auto-encoder to compress these vectors to short binary codes. This should produce a much better image retrieval method than applying autoencoders to the raw pixels [14], which does not make use of image labels and hence has a tendency to retrieve images with similar patterns of edges, whether or not they are semantically similar.
通过使用两个4096维实值向量之间的欧几里得距离来计算相似性是不够的，但是通过训练一个自动编码器将这些向量压缩为短二进制代码可以提高效率。与应用自编码器到原始像素[14]相比，这应该产生更好的图像检索方法，它不利用图像标签，因此倾向于检索具有相似图案边缘的图像，而不管它们在语义上是否相似。
7 Discussion
7讨论
Our results show that a large, deep convolutional neural network is capable of achieving recordbreaking results on a highly challenging dataset using purely supervised learning. It is notable that our network’s performance degrades if a single convolutional layer is removed. For example, removing any of the middle layers results in a loss of about 2% for the top-1 performance of the network. So the depth really is important for achieving our results.
我们的研究结果表明，一个庞大的深层卷积神经网络能够使用纯监督学习在高度具有挑战性的数据集上实现破纪录的结果。值得注意的是，如果单个卷积层被删除，我们的网络性能会下降。例如，删除任何中间层导致网络性能前1的性能损失约2％。所以深度对于实现我们的结果真的很重要。
To simplify our experiments, we did not use any unsupervised pre-training even though we expect that it will help, especially if we obtain enough computational power to significantly increase the size of the network without obtaining a corresponding increase in the amount of labeled data. Thus far, our results have improved as we have made our network larger and trained it longer but we still have many orders of magnitude to go in order to match the infero-temporal pathway of the human visual system. Ultimately we would like to use very large and deep convolutional nets on video sequences where the temporal structure provides very helpful information that is missing or far less obvious in static images.
为了简化我们的实验，我们没有使用任何无监督的预训练，即使我们预计它会有帮助，特别是如果我们获得足够的计算能力来显着增加网络的大小而不会相应增加标记数据的数量。到目前为止，我们的结果已经改善，因为我们已经使我们的网络更大并且训练了它更长的时间，但为了匹配人类视觉系统的时间 - 地球路径，我们仍然有许多数量级要去。最终，我们希望对视频序列使用非常大而深的卷积网络，其中时间结构提供了非常有用的信息，这些信息在静态图像中丢失或不太明显。
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