Rethinking the Inception Architecture for Computer Vision

author

• Szegedy, Christian, et al

Abstract

Convolutional networks are at the core of most state-of-the-art computer vision solutions for a wide variety of tasks. Since 2014 very deep convolutional networks started to become mainstream, yielding substantial gains in various benchmarks. Although increased model size and computational cost tend to translate to immediate quality gains for most tasks (as long as enough labeled data is provided for training), computational efficiency and low parameter count are still enabling factors for various use cases such as mobile vision and big-data scenarios. Here we are exploring ways to scale up networks in ways that aim at utilizing the added computation as efficiently as possible by suitably factorized convolutions and aggressive regularization. We benchmark our methods on the ILSVRC 2012 classification challenge validation set demonstrate substantial gains over the state of the art: 21.2% top-1 and 5.6% top-5 error for single frame evaluation using a network with a computational cost of 5 billion multiply-adds per inference and with using less than 25 million parameters. With an ensemble of 4 models and multi-crop evaluation, we report 3.5% top-5 error and 17.3% top-1 error.

对许多任务而言，卷积网络是目前最新的计算机视觉解决方案的核心。从2014年开始，深度卷积网络开始变成主流，在各种基准数据集上都取得了实质性成果。对于大多数任务而言，虽然增加的模型大小和计算成本都趋向于转化为直接的质量收益（只要提供足够的标注数据去训练），但计算效率和低参数计数仍是各种应用场景的限制因素，例如移动视觉和大数据场景。目前，我们正在探索增大网络的方法，目标是通过适当的分解卷积和积极的正则化来尽可能地有效利用增加的计算。我们在ILSVRC 2012分类挑战赛的验证集上评估了我们的方法，结果证明我们的方法超过了目前最先进的方法并取得了实质性收益：对于单一框架评估错误率为：21.2% top-1和5.6% top-5，使用的网络计算代价为每次推断需要进行50亿次乘加运算并使用不到2500万的参数。通过四个模型组合和多次评估，我们报告了3.5% top-5和17.3% top-1的错误率。

1. Introduction

Since the 2012 ImageNet competition [16] winning entry by Krizhevsky et al [9], their network “AlexNet” has been successfully applied to a larger variety of computer vision tasks, for example to object-detection [5], segmentation [12], human pose estimation [22], video classification [8], object tracking [23], and superresolution [3].

从2012年Krizhevsky等人[9]赢得了ImageNet竞赛[16]起，他们的网络“AlexNet”已经成功了应用到了许多计算机视觉任务中，例如目标检测[5]，分割[12]，行人姿势评估[22]，视频分类[8]，目标跟踪[23]和超分辨率[3]。

These successes spurred a new line of research that focused on finding higher performing convolutional neural networks. Starting in 2014, the quality of network architectures significantly improved by utilizing deeper and wider networks. VGGNet [18] and GoogLeNet [20] yielded similarly high performance in the 2014 ILSVRC [16] classification challenge. One interesting observation was that gains in the classification performance tend to transfer to significant quality gains in a wide variety of application domains. This means that architectural improvements in deep convolutional architecture can be utilized for improving performance for most other computer vision tasks that are increasingly reliant on high quality, learned visual features. Also, improvements in the network quality resulted in new application domains for convolutional networks in cases where AlexNet features could not compete with hand engineered, crafted solutions, e.g. proposal generation in detection[4].

这些成功推动了一个新研究领域，这个领域主要专注于寻找更高效运行的卷积神经网络。从2014年开始，通过利用更深更宽的网络，网络架构的质量得到了明显改善。VGGNet[18]和GoogLeNet[20]在2014 ILSVRC [16]分类挑战上取得了类似的高性能。一个有趣的发现是在分类性能上的收益趋向于转换成各种应用领域上的显著质量收益。这意味着深度卷积架构上的架构改进可以用来改善大多数越来越多地依赖于高质量、可学习视觉特征的其它计算机视觉任务的性能。网络质量的改善也导致了卷积网络在新领域的应用，在AlexNet特征不能与手工精心设计的解决方案竞争的情况下，例如，检测时的候选区域生成[4]。

Although VGGNet [18] has the compelling feature of architectural simplicity, this comes at a high cost: evaluating the network requires a lot of computation. On the other hand, the Inception architecture of GoogLeNet [20] was also designed to perform well even under strict constraints on memory and computational budget. For example, GoogleNet employed only 5 million parameters, which represented a 12× reduction with respect to its predecessor AlexNet, which used 60 million parameters. Furthermore, VGGNet employed about 3x more parameters than AlexNet.

尽管VGGNet[18]具有架构简洁的强有力特性，但它的成本很高：评估网络需要大量的计算。另一方面，GoogLeNet[20]的Inception架构也被设计为在内存和计算预算严格限制的情况下也能表现良好。例如，GoogleNet只使用了500万参数，与其前身AlexNet相比减少了12倍，AlexNet使用了6000万参数。此外，VGGNet使用了比AlexNet大约多3倍的参数。

The computational cost of Inception is also much lower than VGGNet or its higher performing successors [6]. This has made it feasible to utilize Inception networks in big-data scenarios[17], [13], where huge amount of data needed to be processed at reasonable cost or scenarios where memory or computational capacity is inherently limited, for example in mobile vision settings. It is certainly possible to mitigate parts of these issues by applying specialized solutions to target memory use [2], [15] or by optimizing the execution of certain operations via computational tricks [10]. However, these methods add extra complexity. Furthermore, these methods could be applied to optimize the Inception architecture as well, widening the efficiency gap again.

Inception的计算成本也远低于VGGNet或其更高性能的后继者[6]。这使得可以在大数据场景中[17]，[13]，在大量数据需要以合理成本处理的情况下或在内存或计算能力固有地受限情况下，利用Inception网络变得可行，例如在移动视觉设定中。通过应用针对内存使用的专门解决方案[2]，[15]或通过计算技巧优化某些操作的执行[10]，可以减轻部分这些问题。但是这些方法增加了额外的复杂性。此外，这些方法也可以应用于优化Inception架构，再次扩大效率差距。

Still, the complexity of the Inception architecture makes it more difficult to make changes to the network. If the architecture is scaled up naively, large parts of the computational gains can be immediately lost. Also, [20] does not provide a clear description about the contributing factors that lead to the various design decisions of the GoogLeNet architecture. This makes it much harder to adapt it to new use-cases while maintaining its efficiency. For example, if it is deemed necessary to increase the capacity of some Inception-style model, the simple transformation of just doubling the number of all filter bank sizes will lead to a 4x increase in both computational cost and number of parameters. This might prove prohibitive or unreasonable in a lot of practical scenarios, especially if the associated gains are modest. In this paper, we start with describing a few general principles and optimization ideas that that proved to be useful for scaling up convolution networks in efficient ways. Although our principles are not limited to Inception-type networks, they are easier to observe in that context as the generic structure of the Inception style building blocks is flexible enough to incorporate those constraints naturally. This is enabled by the generous use of dimensional reduction and parallel structures of the Inception modules which allows for mitigating the impact of structural changes on nearby components. Still, one needs to be cautious about doing so, as some guiding principles should be observed to maintain high quality of the models.

然而，Inception架构的复杂性使得更难以对网络进行更改。如果单纯地放大架构，大部分的计算收益可能会立即丢失。此外，[20]并没有提供关于导致GoogLeNet架构的各种设计决策的贡献因素的明确描述。这使得它更难以在适应新用例的同时保持其效率。例如，如果认为有必要增加一些Inception模型的能力，将滤波器组大小的数量加倍的简单变换将导致计算成本和参数数量增加4倍。这在许多实际情况下可能会被证明是禁止或不合理的，尤其是在相关收益适中的情况下。在本文中，我们从描述一些一般原则和优化思想开始，对于以有效的方式扩展卷积网络来说，这被证实是有用的。虽然我们的原则不局限于Inception类型的网络，但是在这种情况下，它们更容易观察，因为Inception类型构建块的通用结构足够灵活，可以自然地合并这些约束。这通过大量使用降维和Inception模块的并行结构来实现，这允许减轻结构变化对邻近组件的影响。但是，对于这样做需要谨慎，因为应该遵守一些指导原则来保持模型的高质量。

2. General Design Principles

Here we will describe a few design principles based on large-scale experimentation with various architectural choices with convolutional networks. At this point, the utility of the principles below are speculative and additional future experimental evidence will be necessary to assess their accuracy and domain of validity. Still, grave deviations from these principles tended to result in deterioration in the quality of the networks and fixing situations where those deviations were detected resulted in improved architectures in general.

2. 通用设计原则

这里我们将介绍一些具有卷积网络的、具有各种架构选择的、基于大规模实验的设计原则。在这一点上，以下原则的效用是推测性的，另外将来的实验证据将对于评估其准确性和有效领域是必要的。然而，严重偏移这些原则往往会导致网络质量的恶化，修正检测到的这些偏差状况通常会导致改进的架构。

1. Avoid representational bottlenecks, especially early in the network. Feed-forward networks can be represented by an acyclic graph from the input layer(s) to the classifier or regressor. This defines a clear direction for the information flow. For any cut separating the inputs from the outputs, one can access the amount of information passing though the cut. One should avoid bottlenecks with extreme compression. In general the representation size should gently decrease from the inputs to the outputs before reaching the final representation used for the task at hand. Theoretically, information content can not be assessed merely by the dimensionality of the representation as it discards important factors like correlation structure; the dimensionality merely provides a rough estimate of information content.
2. Higher dimensional representations are easier to process locally within a network. Increasing the activations per tile in a convolutional network allows for more disentangled features. The resulting networks will train faster.
3. Spatial aggregation can be done over lower dimensional embeddings without much or any loss in representational power. For example, before performing a more spread out (e.g. 3 × 3) convolution, one can reduce the dimension of the input representation before the spatial aggregation without expecting serious adverse effects. We hypothesize that the reason for that is the strong correlation between adjacent unit results in much less loss of information during dimension reduction, if the outputs are used in a spatial aggregation context. Given that these signals should be easily compressible, the dimension reduction even promotes faster learning.
4. Balance the width and depth of the network. Optimal performance of the network can be reached by balancing the number of filters per stage and the depth of the network. Increasing both the width and the depth of the network can contribute to higher quality networks. However, the optimal improvement for a constant amount of computation can be reached if both are increased in parallel. The computational budget should therefore be distributed in a balanced way between the depth and width of the network.
5. 避免表征瓶颈，尤其是在网络的前面。前馈网络可以由从输入层到分类器或回归器的非循环图表示。这为信息流定义了一个明确的方向。对于分离输入输出的任何切口，可以访问通过切口的信息量。应该避免极端压缩的瓶颈。一般来说，在达到用于着手任务的最终表示之前，表示大小应该从输入到输出缓慢减小。理论上，信息内容不能仅通过表示的维度来评估，因为它丢弃了诸如相关结构的重要因素；维度仅提供信息内容的粗略估计。
6. 更高维度的表示在网络中更容易局部处理。在卷积网络中增加每个图块的激活允许更多解耦的特征。所产生的网络将训练更快。
7. 空间聚合可以在较低维度嵌入上完成，而不会在表示能力上造成许多或任何损失。例如，在执行更多展开（例如3×3）卷积之前，可以在空间聚合之前减小输入表示的维度，没有预期的严重不利影响。我们假设，如果在空间聚合上下文中使用输出，则相邻单元之间的强相关性会导致维度缩减期间的信息损失少得多。鉴于这些信号应该易于压缩，因此尺寸减小甚至会促进更快的学习。
8. 平衡网络的宽度和深度。通过平衡每个阶段的滤波器数量和网络的深度可以达到网络的最佳性能。增加网络的宽度和深度可以有助于更高质量的网络。然而，如果两者并行增加，则可以达到恒定计算量的最佳改进。因此，计算预算应该在网络的深度和宽度之间以平衡方式进行分配。

Although these principles might make sense, it is not straightforward to use them to improve the quality of networks out of box. The idea is to use them judiciously in ambiguous situations only.

虽然这些原则可能是有意义的，但并不是开箱即用的直接使用它们来提高网络质量。我们的想法是仅在不明确的情况下才明智地使用它们。

3. Factorizing Convolutions with Large Filter Size

Much of the original gains of the GoogLeNet network [20] arise from a very generous use of dimension reduction. This can be viewed as a special case of factorizing convolutions in a computationally efficient manner. Consider for example the case of a 1 × 1 convolutional layer followed by a 3 × 3 convolutional layer. In a vision network, it is expected that the outputs of near-by activations are highly correlated. Therefore, we can expect that their activations can be reduced before aggregation and that this should result in similarly expressive local representations.

3. 基于大滤波器尺寸分解卷积

GoogLeNet网络[20]的大部分初始收益来源于大量地使用降维。这可以被视为以计算有效的方式分解卷积的特例。考虑例如1×1卷积层之后接一个3×3卷积层的情况。在视觉网络中，预期相近激活的输出是高度相关的。因此，我们可以预期，它们的激活可以在聚合之前被减少，并且这应该会导致类似的富有表现力的局部表示。

Here we explore other ways of factorizing convolutions in various settings, especially in order to increase the computational efficiency of the solution. Since Inception networks are fully convolutional, each weight corresponds to one multiplication per activation. Therefore, any reduction in computational cost results in reduced number of parameters. This means that with suitable factorization, we can end up with more disentangled parameters and therefore with faster training. Also, we can use the computational and memory savings to increase the filter-bank sizes of our network while maintaining our ability to train each model replica on a single computer.

在这里，我们将在各种设定中探索卷积分解的其它方法，特别是为了提高解决方案的计算效率。由于Inception网络是全卷积的，每个权重对应每个激活的一次乘法。因此，任何计算成本的降低会导致参数数量减少。这意味着，通过适当的分解，我们可以得到更多的解耦参数，从而加快训练。此外，我们可以使用计算和内存节省来增加我们网络的滤波器组的大小，同时保持我们在单个计算机上训练每个模型副本的能力。

3.1. Factorization into smaller convolutions

Convolutions with larger spatial filters (e.g. 5 × 5 or 7 × 7) tend to be disproportionally expensive in terms of computation. For example, a 5 × 5 convolution with n filters over a grid with m filters is 25/9 = 2.78 times more computationally expensive than a 3 × 3 convolution with the same number of filters. Of course, a 5 × 5 filter can capture dependencies between signals between activations of units further away in the earlier layers, so a reduction of the geometric size of the filters comes at a large cost of expressiveness. However, we can ask whether a 5 × 5 convolution could be replaced by a multi-layer network with less parameters with the same input size and output depth. If we zoom into the computation graph of the 5 × 5 convolution, we see that each output looks like a small fully-connected network sliding over 5 × 5 tiles over its input (see Figure 1). Since we are constructing a vision network, it seems natural to exploit translation invariance again and replace the fully connected component by a two layer convolutional architecture: the first layer is a 3 × 3 convolution, the second is a fully connected layer on top of the 3 × 3 output grid of the first layer (see Figure 1). Sliding this small network over the input activation grid boils down to replacing the 5 × 5 convolution with two layers of 3 × 3 convolution (compare Figure 4 with 5).

Figure 1. Mini-network replacing the 5×5 convolutions.

Figure 4. Original Inception module as described in [20].

Figure 5. Inception modules where each 5 × 5 convolution is replaced by two 3 × 3 convolution, as suggested by principle 3 of Section 2.

3.1. 分解到更小的卷积

具有较大空间滤波器（例如5×5或7×7）的卷积在计算方面往往不成比例地昂贵。例如，具有n个滤波器的5×5卷积在具有m个滤波器的网格上比具有相同数量的滤波器的3×3卷积的计算量高25/9=2.78倍。当然，5×5滤波器在更前面的层可以捕获更远的单元激活之间、信号之间的依赖关系，因此滤波器几何尺寸的减小带来了很大的表现力。然而，我们可以询问5×5卷积是否可以被具有相同输入尺寸和输出深度的参数较小的多层网络所取代。如果我们放大5×5卷积的计算图，我们看到每个输出看起来像一个小的完全连接的网络，在其输入上滑过5×5的块（见图1）。由于我们正在构建视觉网络，所以通过两层的卷积结构再次利用平移不变性来代替全连接的组件似乎是很自然的：第一层是3×3卷积，第二层是在第一层的3×3输出网格之上的一个全连接层（见图1）。通过在输入激活网格上滑动这个小网络，用两层3×3卷积来替换5×5卷积（比较图4和5）。

图1。Mini网络替换5×5卷积

图4。[20]中描述的最初的Inception模块.

图5。Inception模块中每个5×5卷积由两个3×3卷积替换，正如第2小节中原则3建议的那样。

This setup clearly reduces the parameter count by sharing the weights between adjacent tiles. To analyze the expected computational cost savings, we will make a few simplifying assumptions that apply for the typical situations: We can assume that n=αmn=αm, that is that we want to change the number of activations/unit by a constant alpha factor. Since the 5 × 5 convolution is aggregating, αα is typically slightly larger than one (around 1.5 in the case of GoogLeNet). Having a two layer replacement for the 5 × 5 layer, it seems reasonable to reach this expansion in two steps: increasing the number of filters by α−−√α in both steps. In order to simplify our estimate by choosing α=1α=1(no expansion), if we would naivly slide a network without reusing the computation between neighboring grid tiles, we would increase the computational cost. Sliding this network can be represented by two 3 × 3 convolutional layers which reuses the activations between adjacent tiles. This way, we end up with a net 9+925×9+925× reduction of computation, resulting in a relative gain of 28% by this factorization. The exact same saving holds for the parameter count as each parameter is used exactly once in the computation of the activation of each unit. Still, this setup raises two general questions: Does this replacement result in any loss of expressiveness? If our main goal is to factorize the linear part of the computation, would it not suggest to keep linear activations in the first layer? We have ran several control experiments (for example see figure 2) and using linear activation was always inferior to using rectified linear units in all stages of the factorization. We attribute this gain to the enhanced space of variations that the network can learn especially if we batch-normalize [7] the output activations. One can see similar effects when using linear activations for the dimension reduction components.

Figure 2. One of several control experiments between two Inception models, one of them uses factorization into linear + ReLU layers, the other uses two ReLU layers. After 3.86 million operations, the former settles at 76.2%, while the latter reaches 77.2% top-1 Accuracy on the validation set.

该设定通过相邻块之间共享权重明显减少了参数数量。为了分析预期的计算成本节省，我们将对典型的情况进行一些简单的假设：我们可以假设n=αmn=αm，也就是我们想通过常数αα因子来改变激活/单元的数量。由于5×5卷积是聚合的，αα通常比1略大（在GoogLeNet中大约是1.5）。用两个层替换5×5层，似乎可以通过两个步骤来实现扩展：在两个步骤中通过α−−√α增加滤波器数量。为了简化我们的估计，通过选择α=1α=1（无扩展），如果我们单纯地滑动网络而不重新使用相邻网格图块之间的计算，我们将增加计算成本。滑动该网络可以由两个3×3的卷积层表示，其重用相邻图块之间的激活。这样，我们最终得到一个计算量减少到9+925×9+925×的网络，通过这种分解导致了28％的相对增益。每个参数在每个单元的激活计算中只使用一次，所以参数计数具有完全相同的节约。不过，这个设置提出了两个一般性的问题：这种替换是否会导致任何表征力的丧失？如果我们的主要目标是对计算的线性部分进行分解，是不是建议在第一层保持线性激活？我们已经进行了几个控制实验（例如参见图2），并且在分解的所有阶段中使用线性激活总是逊于使用修正线性单元。我们将这个收益归因于网络可以学习的增强的空间变化，特别是如果我们对输出激活进行批标准化[7]。当对维度减小组件使用线性激活时，可以看到类似的效果。

图2。两个Inception模型间几个控制实验中的一个，其中一个分解为线性层+ ReLU层，另一个使用两个ReLU层。在三亿八千六百万次运算后，在验证集上前者达到了76.2% top-1准确率，后者达到了77.2% top-1的准确率。

3.2. Spatial Factorization into Asymmetric Convolutions

The above results suggest that convolutions with filters larger 3 × 3 might not be generally useful as they can always be reduced into a sequence of 3 × 3 convolutional layers. Still we can ask the question whether one should factorize them into smaller, for example 2 × 2 convolutions. However, it turns out that one can do even better than 2 × 2 by using asymmetric convolutions, e.g. n × 1. For example using a 3 × 1 convolution followed by a 1 × 3 convolution is equivalent to sliding a two layer network with the same receptive field as in a 3 × 3 convolution (see figure 3). Still the two-layer solution is 33% cheaper for the same number of output filters, if the number of input and output filters is equal. By comparison, factorizing a 3 × 3 convolution into a two 2 × 2 convolution represents only a 11% saving of computation.

Figure 3. Mini-network replacing the 3 × 3 convolutions. The lower layer of this network consists of a 3 × 1 convolution with 3 output units.

3.2. 空间分解为不对称卷积

上述结果表明，大于3×3的卷积滤波器可能不是通常有用的，因为它们总是可以简化为3×3卷积层序列。我们仍然可以问这个问题，是否应该把它们分解成更小的，例如2×2的卷积。然而，通过使用非对称卷积，可以做出甚至比2×2更好的效果，即n×1。例如使用3×1卷积后接一个1×3卷积，相当于以与3×3卷积相同的感受野滑动两层网络（参见图3）。如果输入和输出滤波器的数量相等，那么对于相同数量的输出滤波器，两层解决方案便宜33％。相比之下，将3×3卷积分解为两个2×2卷积表示仅节省了11％的计算量。

图3。替换3×3卷积的Mini网络。网络的更低层由带有3个输出单元的3×1构成。

In theory, we could go even further and argue that one can replace any n × n convolution by a 1 × n convolution followed by a n × 1 convolution and the computational cost saving increases dramatically as n grows (see figure 6). In practice, we have found that employing this factorization does not work well on early layers, but it gives very good results on medium grid-sizes (On m × m feature maps, where m ranges between 12 and 20). On that level, very good results can be achieved by using 1 × 7 convolutions followed by 7 × 1 convolutions.

Figure 6. Inception modules after the factorization of the n × n convolutions. In our proposed architecture, we chose n = 7 for the 17 × 17 grid. (The filter sizes are picked using principle 3)

在理论上，我们可以进一步论证，可以通过1×n卷积和后面接一个n×1卷积替换任何n×n卷积，并且随着n增长，计算成本节省显著增加（见图6）。实际上，我们发现，采用这种分解在前面的层次上不能很好地工作，但是对于中等网格尺寸（在m×m特征图上，其中m范围在12到20之间），其给出了非常好的结果。在这个水平上，通过使用1×7卷积，然后是7×1卷积可以获得非常好的结果。

图6。n×n卷积分解后的Inception模块。在我们提出的架构中，对17×17的网格我们选择n=7。（滤波器尺寸可以通过原则3选择）

4. Utility of Auxiliary Classifiers

[20] has introduced the notion of auxiliary classifiers to improve the convergence of very deep networks. The original motivation was to push useful gradients to the lower layers to make them immediately useful and improve the convergence during training by combating the vanishing gradient problem in very deep networks. Also Lee et al[11] argues that auxiliary classifiers promote more stable learning and better convergence. Interestingly, we found that auxiliary classifiers did not result in improved convergence early in the training: the training progression of network with and without side head looks virtually identical before both models reach high accuracy. Near the end of training, the network with the auxiliary branches starts to overtake the accuracy of the network without any auxiliary branch and reaches a slightly higher plateau.

4. 利用辅助分类器

[20]引入了辅助分类器的概念，以改善非常深的网络的收敛。最初的动机是将有用的梯度推向较低层，使其立即有用，并通过抵抗非常深的网络中的消失梯度问题来提高训练过程中的收敛。Lee等人[11]也认为辅助分类器促进了更稳定的学习和更好的收敛。有趣的是，我们发现辅助分类器在训练早期并没有导致改善收敛：在两个模型达到高精度之前，有无侧边网络的训练进度看起来几乎相同。接近训练结束，辅助分支网络开始超越没有任何分支的网络的准确性，达到了更高的稳定水平。

Also [20] used two side-heads at different stages in the network. The removal of the lower auxiliary branch did not have any adverse effect on the final quality of the network. Together with the earlier observation in the previous paragraph, this means that original the hypothesis of [20] that these branches help evolving the low-level features is most likely misplaced. Instead, we argue that the auxiliary classifiers act as regularizer. This is supported by the fact that the main classifier of the network performs better if the side branch is batch-normalized [7] or has a dropout layer. This also gives a weak supporting evidence for the conjecture that batch normalization acts as a regularizer.

另外，[20]在网络的不同阶段使用了两个侧分支。移除更下面的辅助分支对网络的最终质量没有任何不利影响。再加上前一段的观察结果，这意味着[20]最初的假设，这些分支有助于演变低级特征很可能是不适当的。相反，我们认为辅助分类器起着正则化项的作用。这是由于如果侧分支是批标准化的[7]或具有丢弃层，则网络的主分类器性能更好。这也为推测批标准化作为正则化项给出了一个弱支持证据。

5. Efficient Grid Size Reduction

Traditionally, convolutional networks used some pooling operation to decrease the grid size of the feature maps. In order to avoid a representational bottleneck, before applying maximum or average pooling the activation dimension of the network filters is expanded. For example, starting a d×d grid with k filters, if we would like to arrive at a $\frac{d}{2}\times\frac{d}{2}$ grid with 2k filters, we first need to compute a stride-1 convolution with 2k filters and then apply an additional pooling step. This means that the overall computational cost is dominated by the expensive convolution on the larger grid using $2d^2k^2 operations. One possibility would be to switch to pooling with convolution and therefore resulting in $2\frac{d}{2}^2k^2 reducing the computational cost by a quarter. However, this creates a representational bottlenecks as the overall dimensionality of the representation drops to $2\times(\frac{d}{2})^2{k^2}$ resulting in less expressive networks (see Figure 9). Instead of doing so, we suggest another variant the reduces the computational cost even further while removing the representational bottleneck. (see Figure 10). We can use two parallel stride 2 blocks: P and C. P is a pooling layer (either average or maximum pooling) the activation, both of them are stride 2 the filter banks of which are concatenated as in figure 10.

Figure 9. Two alternative ways of reducing the grid size. The solution on the left violates the principle 1 of not introducing an representational bottleneck from Section 2. The version on the right is 3 times more expensive computationally.

Figure 10. Inception module that reduces the grid-size while expands the filter banks. It is both cheap and avoids the representational bottleneck as is suggested by principle 1. The diagram on the right represents the same solution but from the perspective of grid sizes rather than the operations.

5. 有效的网格尺寸减少

传统上，卷积网络使用一些池化操作来缩减特征图的网格大小。为了避免表示瓶颈，在应用最大池化或平均池化之前，需要扩展网络滤波器的激活维度。例如，开始有一个带有k个滤波器的d×d网格，如果我们想要达到一个带有2k个滤波器的 $\frac{d}{2}\times\frac{d}{2}$网格，我们首先需要用2k个滤波器计算步长为1的卷积，然后应用一个额外的池化步骤。这意味着总体计算成本由在较大的网格上使用$2d^2k^2 次运算的昂贵卷积支配。一种可能性是转换为带有卷积的池化，因此导致$2$\frac{d}{2}^2k^2 次运算，将计算成本降低为原来的四分之一。然而，由于表示的整体维度下降到 $2\times(\frac{d}{2})^2{k^2}$，会导致表示能力较弱的网络（参见图9），这会产生一个表示瓶颈。我们建议另一种变体，其甚至进一步降低了计算成本，同时消除了表示瓶颈（见图10），而不是这样做。我们可以使用两个平行的步长为2的块：PP和CC。PP是一个池化层（平均池化或最大池化）的激活，两者都是步长为22，其滤波器组连接如图10所示。

图9。减少网格尺寸的两种替代方式。左边的解决方案违反了第2节中不引入表示瓶颈的原则1。右边的版本计算量昂贵3倍。

图10。缩减网格尺寸的同时扩展滤波器组的Inception模块。它不仅廉价并且避免了原则1中提出的表示瓶颈。右侧的图表示相同的解决方案，但是从网格大小而不是运算的角度来看。

6. Inception-v2

Here we are connecting the dots from above and propose a new architecture with improved performance on the ILSVRC 2012 classification benchmark. The layout of our network is given in table 1. Note that we have factorized the traditional 7×7 convolution into three 3×3 convolutions based on the same ideas as described in section 3.1. For the Inception part of the network, we have 33 traditional inception modules at the 35×35 with 288filters each. This is reduced to a 17×17 grid with 768 filters using the grid reduction technique described in section 5. This is is followed by 55 instances of the factorized inception modules as depicted in figure 5. This is reduced to a 8×8×1280 grid with the grid reduction technique depicted in figure 10. At the coarsest 8×8level, we have two Inception modules as depicted in figure 6, with a concatenated output filter bank size of 2048 for each tile. The detailed structure of the network, including the sizes of filter banks inside the Inception modules, is given in the supplementary material, given in the model.txt that is in the tar-file of this submission. However, we have observed that the quality of the network is relatively stable to variations as long as the principles from Section 2 are observed. Although our network is 42 layers deep, our computation cost is only about 2.5 higher than that of GoogLeNet and it is still much more efficient than VGGNet.

Table 1. The outline of the proposed network architecture. The output size of each module is the input size of the next one. We are using variations of reduction technique depicted Figure 10 to reduce the grid sizes between the Inception blocks whenever applicable. We have marked the convolution with 0-padding, which is used to maintain the grid size. 0-padding is also used inside those Inception modules that do not reduce the grid size. All other layers do not use padding. The various filter bank sizes are chosen to observe principle 4 from Section 2.

Figure 7. Inception modules with expanded the filter bank outputs. This architecture is used on the coarsest (8×88×8) grids to promote high dimensional representations, as suggested by principle 2 of Section 2. We are using this solution only on the coarsest grid, since that is the place where producing high dimensional sparse representation is the most critical as the ratio of local processing (by 1×11×1 convolutions) is increased compared to the spatial aggregation.

Figure 8. Auxiliary clas