Self-ensembling for visual domain adaptation
视觉领域自适应中的自集成方法
Abstract
摘要
This paper explores the use of self-ensembling for visual domain adaptation problems. Our technique is derived from the mean teacher variant [29] of temporal ensembling [14], a technique that achieved state of the art results in the area of semi-supervised learning. We introduce a number of modifications to their approach for challenging domain adaptation scenarios and evaluate its effectiveness. Our approach achieves state of the art results in a variety of benchmarks, including our winning entry in the VISDA-2017 visual domain adaptation challenge. In small image benchmarks, our algorithm not only outperforms prior art, but can also achieve accuracy that is close to that of a classifier trained in a supervised fashion.
本文探讨了自集成(self-ensembling)在视觉域适应问题中的应用。我们的技术源自时序集成(temporal ensembling)的均值教师变体(mean teacher variant) [29]，该技术在半监督学习领域取得了最先进的成果。我们针对具有挑战性的域适应场景对其方法进行了若干改进，并评估了其有效性。我们的方法在各种基准测试中均取得了最先进的成果，包括我们在VISDA-2017视觉域适应挑战赛中的获胜方案。在小型图像基准测试中，我们的算法不仅优于现有技术，还可以达到接近监督式训练分类器的准确度。
1 Introduction
1 引言
The strong performance of deep learning in computer vision tasks comes at the cost of requiring large datasets with corresponding ground truth labels for training. Such datasets are often expensive to produce, owing to the cost of the human labour required to produce the ground truth labels.
深度学习在计算机视觉任务中的出色表现，是以需要带有相应真实标签的大规模训练数据集为代价的。由于制作真实标签所需的人力成本高昂，这类数据集的构建往往代价不菲。
Semi-supervised learning is an active area of research that aims to reduce the quantity of ground truth labels required for training. It is aimed at common practical scenarios in which only a small subset of a large dataset has corresponding ground truth labels. Unsupervised domain adaptation is a closely related problem in which one attempts to transfer knowledge gained from a labeled source dataset to a distinct unlabeled target dataset, within the constraint that the objective (e.g.digit classification) must remain the same. Domain adaptation offers the potential to train a model using labeled synthetic data – that is often abundantly available – and unlabeled real data. The scale of the problem can be seen in the VisDA-17 domain adaptation challenge images shown in Figure 1. We will present our winning solution in Section 4.2.
半监督学习是一个活跃的研究领域，旨在减少训练所需真实标签的数量。它针对的是实际场景中常见的情况，即大型数据集中只有一小部分具有对应的真实标签。无监督领域自适应是一个密切相关的问题，其目标是在保持任务目标（例如数字分类）不变的前提下，将已标注源数据集的知识迁移到不同的未标注目标数据集。领域自适应提供了利用标注合成数据（通常大量可用）和未标注真实数据训练模型的潜力。该问题的规模可以从图1所示的VisDA-17领域自适应挑战赛图像中看出。我们将在第4.2节介绍获胜方案。
(a) VisDa-17 training set images; the labeled source domain (b) VisDa-17 validation set images; the unlabeled target domain
(a) VisDa-17 训练集图像：已标注的源域
(b) VisDa-17 验证集图像：未标注的目标域
Figure 1: Images from the VisDA-17 domain adaptation challenge
图 1: VisDA-17领域自适应挑战赛中的图像
Recent work [29] has demonstrated the effectiveness of self-ensembling with random image augmentations to achieve state of the art performance in semisupervised learning benchmarks.
近期研究[29]证明了通过随机图像增强实现自集成(self-ensembling)的有效性，该方法在半监督学习基准测试中达到了最先进性能。
We have developed the approach proposed by Tarvainen et al. [29] to work in a domain adaptation scenario. We will show that this can achieve excellent results in specific small image domain adaptation benchmarks. More challenging scenarios, notably MNIST $\rightarrow$ SVHN and the VisDA-17 domain adaptation challenge required further modifications. To this end, we developed confidence threshold ing and class balancing that allowed us to achieve state of the art results in a variety of benchmarks, with some of our results coming close to those achieved by traditional supervised learning. Our approach is sufficiently flexble to be applicable to a variety of network architectures, both randomly initialized and pre-trained.
我们改进了Tarvainen等人[29]提出的方法，使其适用于领域自适应场景。实验表明，该方法在特定的小规模图像领域自适应基准测试中表现优异。面对更具挑战性的场景（如MNIST $\rightarrow$ SVHN和VisDA-17领域自适应挑战赛），我们进一步开发了置信度阈值和类别平衡技术，从而在多个基准测试中取得领先水平，部分结果已接近传统监督学习的性能。该方法具有足够的灵活性，可适用于随机初始化和预训练的各种网络架构。
Our paper is organised as follows; in Section 2 we will discuss related work that provides context and forms the basis of our technique; our approach is described in Section 3 with our experiments and results in Section 4; and finally we present our conclusions in Section 5.
本文结构如下：第2节将讨论相关研究工作，为我们的技术提供背景和基础；第3节描述我们的方法，第4节展示实验与结果；最后在第5节给出结论。
2 Related work
2 相关工作
In this section we will cover self-ensembling based semi-supervised methods that form the basis of our approach and domain adaptation techniques to which our work can be compared.
在本节中，我们将介绍基于自集成(self-ensembling)的半监督方法，这些方法构成了我们方法的基础，以及可以与我们的工作进行比较的领域自适应技术。
2.1 Self-ensembling for semi-supervised learning
2.1 半监督学习的自集成方法
Recent work based on methods related to self-ensembling have achieved excellent results in semi-supervised learning scenarious. A neural network is trained to make consistent predictions for unsupervised samples under different augmentation [24], dropout and noise conditions or through the use of adversarial training [18]. We will focus in particular on the self-ensembling based approaches of Laine et al. [14] and Tarvainen et al. [29] as they form the basis of our approach.
基于自集成(self-ensembling)相关方法的最新研究在半监督学习场景中取得了优异成果。这类方法通过训练神经网络，使其在不同数据增强[24]、dropout、噪声条件下或对抗训练[18]过程中对无监督样本保持预测一致性。我们将重点分析Laine等人[14]和Tarvainen等人[29]提出的自集成方法，这些方法构成了本研究的技术基础。
Laine et al. [14] present two models; their $\mathrm{II}$ -model and their temporal model. The $\mathrm{II}$ -model passes each unlabeled sample through a classifier twice, each time with different dropout, noise and image translation parameters. Their unsupervised loss is the mean of the squared difference in class probability predictions resulting from the two presentations of each sample. Their temporal model maintains a per-sample moving average of the historical network predictions and encourages subsequent predictions to be consistent with the average. Their approach achieved state of the art results in the SVHN and CIFAR-10 semisupervised classification benchmarks.
Laine等人[14]提出了两种模型：其$\mathrm{II}$模型和时序模型。$\mathrm{II}$模型将每个未标注样本两次输入分类器，每次采用不同的dropout、噪声和图像平移参数。其无监督损失函数是样本两次输入所得类别概率预测的平方差均值。时序模型通过维护每个样本历史网络预测的移动平均值，促使后续预测与该平均值保持一致。该方法在SVHN和CIFAR-10半监督分类基准测试中达到了当时最优性能。
Tarvainen et al. [29] further improved on the temporal model [14] by using an exponential moving average of the network weights rather than of the class predictions. Their approach uses two networks; a student network and a teacher network, where the student is trained using gradient descent and the weigthts of the teacher are the exponential moving average of those of the student. The unsupervised loss used to train the student is the mean square difference between the predictions of the student and the teacher, under different dropout, noise and image translation parameters.
Tarvainen等人[29]通过使用网络权重的指数移动平均而非类别预测的指数移动平均，进一步改进了时序模型[14]。该方法采用两个网络：学生网络和教师网络，其中学生网络通过梯度下降进行训练，而教师网络的权重是学生网络权重的指数移动平均。用于训练学生网络的无监督损失是在不同dropout、噪声和图像平移参数下，学生网络与教师网络预测之间的均方差。
2.2 Domain adaptation
2.2 领域自适应
There is a rich body of literature tackling the problem of domain adaptation. We focus on deep learning based methods as these are most relevant to our work.
针对领域自适应问题已有大量研究文献。我们重点关注基于深度学习的方法，因其与我们的工作最为相关。
Auto-encoders are unsupervised neural network models that reconstruct their input samples by first encoding them into a latent space and then decoding and reconstructing them. Ghifary et al. [6] describe an auto-encoder model that is trained to reconstruct samples from both the source and target domains, while a classifier is trained to predict labels from domain invariant features present in the latent representation using source domain labels. Bousmalis et al. [2] re ck ogni sed that samples from disparate domains have distinct domain specific characteristics that must be represented in the latent representation to support effective reconstruction. They developed a split model that separates the latent representation into shared domain invariant features and private features specific to the source and target domains. Their classifier operates on the domain invariant features only.
自动编码器是一种无监督神经网络模型，它通过先将输入样本编码到潜在空间，再进行解码和重构来重建输入样本。Ghifary等人[6]描述了一种自动编码器模型，该模型被训练用于从源域和目标域重建样本，同时训练一个分类器，利用源域标签从潜在表示中的域不变特征预测标签。Bousmalis等人[2]认识到，来自不同域的样本具有独特的域特定特征，这些特征必须在潜在表示中体现以支持有效重建。他们开发了一个分割模型，将潜在表示分离为共享的域不变特征以及特定于源域和目标域的私有特征。他们的分类器仅作用于域不变特征。
Ganin et al. [5] propose a bifurcated classifier that splits into label classification and domain classification branches after common feature extraction layers. A gradient reversal layer is placed between the common feature extraction layers and the domain classification branch; while the domain classification layers attempt to determine which domain a sample came from the gradient reversal operation encourages the feature extraction layers to confuse the domain classifier by extracting domain invariant features. An alternative and simpler implementation described in their appendix minimises the label cross-entropy loss in the feature and label classification layers, minimises the domain crossentropy in the domain classification layers but maximises it in the feature layers. The model of Tzeng et al. [30] runs along similar lines but uses separate feature extraction sub-networks for source and domain samples and train the model in two distinct stages.
Ganin 等人 [5] 提出了一种分叉分类器，在公共特征提取层后分为标签分类和域分类分支。在公共特征提取层与域分类分支之间放置了一个梯度反转层：当域分类层试图判断样本来自哪个域时，梯度反转操作会促使特征提取层通过提取域不变特征来混淆域分类器。其附录描述的另一种更简单实现方式是：在特征层和标签分类层最小化标签交叉熵损失，在域分类层最小化域交叉熵损失，但在特征层最大化该损失。Tzeng 等人 [30] 的模型采用类似思路，但为源样本和域样本使用独立的特征提取子网络，并分两个不同阶段训练模型。
Saito et al. [22] use tri-training [32]; feature extraction layers are used to drive three classifier sub-networks. The first two are trained on samples from the source domain, while a weight similarity penalty encourages them to learn different weights. Pseudo-labels generated for target domain samples by these source domain class if i ers are used to train the final classifier to operate on the target domain.
Saito等人[22]采用三重训练(tri-training)[32]方法：特征提取层驱动三个分类器子网络。前两个分类器在源域样本上训练，同时通过权重相似性惩罚促使它们学习不同的权重。这些源域分类器为目标域样本生成的伪标签(pseudo-labels)用于训练最终能在目标域上运行的分类器。
Generative Adversarial Networks [7] (GANs) are unsupervised models that consist of a generator network that is trained to generate samples that match the distribution of a dataset by fooling a disc rim in at or network that is simultaneously trained to distinguish real samples from generates samples. Some GAN based models – such as that of Sankara narayan an et al. [25] – use a GAN to help learn a domain invariant embedding for samples. Many GAN based domain adaptation approaches use a generator that transforms samples from one domain to another.
生成对抗网络 [7] (GANs) 是一种无监督模型，由生成器网络和判别器网络组成。生成器通过欺骗判别器来生成与数据集分布匹配的样本，而判别器则被训练用于区分真实样本与生成样本。部分基于GAN的模型（例如Sankaranarayanan等人 [25] 提出的方法）利用GAN帮助学习样本的域不变嵌入。许多基于GAN的域适应方法采用生成器将样本从一个域转换到另一个域。
Bousmalis et al. [1] propose a GAN that adapts synthetic images to better match the characteristics of real images. Their generator takes a synthetic image and noise vector as input and produces an adapted image. They train a classifier to predict annotations for source and adapted samples alonside the GAN, while encouraing the generator to preserve aspects of the image important for annotation. The model of [26] consists of a refiner network (in the place of a generator) and disc rim in at or that have a limited receptive field, limiting their model to making local changes while preserving ground truth annotations. The use of refined simulated images with corresponding ground truths resulted in improved performance in gaze and hand pose estimation.
Bousmalis等人[1]提出了一种GAN(生成对抗网络)，用于调整合成图像以更好地匹配真实图像的特征。他们的生成器以合成图像和噪声向量作为输入，并生成调整后的图像。在训练GAN的同时，他们还训练了一个分类器来预测源样本和调整样本的标注，同时鼓励生成器保留对标注重要的图像特征。[26]的模型由一个精炼网络(代替生成器)和感受野有限的判别器组成，使其模型只能进行局部修改，同时保留真实标注。使用带有对应真实标注的精炼模拟图像，在视线和手部姿态估计任务中取得了更好的性能。
Russo et al. [21] present a bi-directional GAN composed of two generators that transform samples from the source to the target domain and vice versa. They transform labelled source samples to the target domain using one generator and back to the source domain with the other and encourage the network to learn label class consistency. This work bears similarities to CycleGAN [33].
Russo等人[21]提出了一种双向GAN，由两个生成器组成，能够将样本从源域转换到目标域，反之亦然。他们使用一个生成器将带标签的源样本转换到目标域，再用另一个生成器将其转换回源域，以此促使网络学习标签类别一致性。这项工作与CycleGAN[33]有相似之处。
A number of domain adaptation models maximise domain confusion by minimising the difference between the distributions of features extracted from source and target domains. Deep CORAL [28] minimises the difference between the feature covariance matrices for a mini-batch of samples from the source and target domains. Tzeng et al. [31] and Long et al. [17] minimise the Maximum Mean Discrepancy metric [8]. Li et al. [15] described adaptive batch normalization, a variant of batch normalization [12] that learns separate batch normalization statistics for the source and target domains in a two-pass process, establishing new state-of-the-art results. In the first pass standard supervised learning is used to train a classifier for samples from the source domain. In the second pass, normalization statistics for target domain samples are computed for each batch normalization layer in the network, leaving the network weights as they are.
许多领域自适应模型通过最小化从源域和目标域提取的特征分布差异来最大化领域混淆。Deep CORAL [28] 最小化了源域和目标域小批量样本特征协方差矩阵之间的差异。Tzeng等人 [31] 和Long等人 [17] 最小化了最大均值差异度量 [8]。Li等人 [15] 提出了自适应批归一化 (adaptive batch normalization)，这是批归一化 [12] 的一种变体，通过两阶段过程学习源域和目标域各自的批归一化统计量，从而取得了新的最先进成果。第一阶段采用标准监督学习训练源域样本的分类器。第二阶段为网络中每个批归一化层计算目标域样本的归一化统计量，同时保持网络权重不变。
Figure 2: The network structures of the original mean teacher model and our model. Dashed lines in the mean teacher model indicate that ground truth labels – and therefore cross-entropy classification loss – are only available for labeled samples.
图 2: 原始均值教师模型与本模型的网络结构对比。均值教师模型中虚线表示仅标注样本可获得真实标签(ground truth labels)及交叉熵分类损失。
3 Method
3 方法
Our model builds upon the mean teacher semi-supervised learning model [29], which we will describe. Subsequently we will present our modifications that enable domain adaptation.
我们的模型基于均值教师半监督学习模型 [29]，接下来我们将对其进行描述。随后我们将介绍实现领域自适应的改进方法。
The structure of the mean teacher model [29] – also discussed in section 2.1 – is shown in Figure 2a. The student network is trained using gradient descent, while the weights of the teacher network are an exponential moving average of those of the student. During training each input sample $x_{i}$ is passed through both the student and teacher networks, generating predicted class probability vectors $z_{i}$ (student) and $\tilde{z}_{i}$ (teacher). Different dropout, noise and image translation parameters are used for the student and teacher pathways.
均值教师模型 [29] 的结构（第 2.1 节亦有讨论）如图 2a 所示。学生网络通过梯度下降进行训练，而教师网络的权重则是学生网络权重的指数移动平均值。训练过程中，每个输入样本 $x_{i}$ 会分别通过学生网络和教师网络，生成预测类别概率向量 $z_{i}$（学生）和 $\tilde{z}_{i}$（教师）。学生路径与教师路径采用不同的 dropout、噪声和图像平移参数。
During each training iteration a mini-batch of samples is drawn from the dataset, consisting of both labeled and unlabeled samples. The training loss is the sum of a supervised and an unsupervised component. The supervised loss is cross-entropy loss computed using $z_{i}$ (student prediction). It is masked to $0$ for unlabeled samples for which no ground truth is available. The unsupervised component is the self-ensembling loss. It penalises the difference in class predictions between student ( $z_{i}$ ) and teacher networks for the same input sample. It is computed using the mean squared difference between the class probability predictions $z_{i}$ and $\tilde{z}_{i}$ .
在每次训练迭代中，会从数据集中抽取一个小批量样本，包含已标注和未标注样本。训练损失由监督损失和无监督损失两部分组成。监督损失是使用学生预测结果$z_{i}$计算的交叉熵损失，对于没有真实标签的未标注样本会掩码为$0$。无监督部分为自集成损失，用于惩罚同一输入样本在学生网络($z_{i}$)和教师网络之间的类别预测差异，通过计算类别概率预测$z_{i}$与$\tilde{z}_{i}$之间的均方差来实现。
Laine et al. [14] and Tarvainen et al. [29] found that it was necessary to apply a time-dependent weighting to the unsupervised loss during training in order to prevent the network from getting stuck in a degenerate solution that gives poor classification performance. They used a function that follows a Gaussian curve from 0 to 1 during the first 80 epochs.
Laine等人[14]和Tarvainen等人[29]发现，在训练过程中需要对无监督损失施加时间依赖性权重，以防止网络陷入导致分类性能下降的退化解。他们采用了一个在前80个周期内从0到1遵循高斯曲线的函数。
In the following subsections we will describe our contributions in detail along with the motivations for introducing them.
在接下来的小节中，我们将详细描述我们的贡献以及引入这些贡献的动机。
3.1 Adapting to domain adaptation
3.1 适应领域自适应
We minimise the same loss as in [29]; we apply cross-entropy loss to labeled source samples and unsupervised self-ensembling loss to target samples. As in [29], self-ensembling loss is computed as the mean-squared difference between predictions produced by the student $\left(z_{T i}\right)$ and teacher $\left(\tilde{z}_{T i}\right)$ networks with different augmentation, dropout and noise parameters.
我们采用与[29]相同的损失函数：对带标签的源样本应用交叉熵损失，对目标样本应用无监督自集成损失。如[29]所述，自集成损失通过计算学生网络$\left(z_{T i}\right)$与教师网络$\left(\tilde{z}_{T i}\right)$在不同增强、dropout和噪声参数下产生的预测结果之间的均方差来实现。
The models of [29] and of [14] were designed for semi-supervised learning problems in which a subset of the samples in a single dataset have ground truth labels. During training both models mix labeled and unlabeled samples together in a mini-batch. In contrast, unsupervised domain adaptation problems use two distinct datasets with different underlying distributions; labeled source and unlabeled target. Our variant of the mean teacher model – shown in Figure 2b – has separate source $(X_{S i})$ and target $(X_{T i,}$ ) paths. Inspired by [15], we process mini-batches from the source and target datasets separately (per iteration) so that batch normalization uses different normalization statistics for each domain during training.1. We do not use the approach of [15] as-is, as they handle the source and target datasets separtely in two distinct training phases, where our approach must train using both simultaneously. We also do not maintain separate exponential moving averages of the means and variances for each dataset for use at test time.
[29]和[14]的模型专为半监督学习问题设计，这类问题中单个数据集的部分样本带有真实标签。训练时，两种模型都将标注和未标注样本混合在小批量(mini-batch)中处理。相比之下，无监督领域自适应问题使用两个具有不同底层分布的数据集：带标注的源域和不带标注的目标域。我们对均值教师模型的改进版本（如图2b所示）设有独立的源域$(X_{S i})$和目标域$(X_{T i,}$)路径。受[15]启发，我们分批次单独处理源域和目标域数据集（每次迭代），使得批量归一化(batch normalization)在训练期间能为每个领域使用不同的归一化统计量。我们未直接采用[15]的方法，因为他们在两个独立训练阶段分别处理源域和目标域数据，而我们的方法需要同时使用两者进行训练。我们也不在测试时维护各数据集均值和方差的独立指数移动平均值。
As seen in the ‘MT $^+$ TF’ row of Table 1, the model described thus far achieves state of the art results in 5 out of 8 small image benchmarks. The MNIST $\rightarrow$ SVHN, STL $\rightarrow$ CIFAR-10 and Syn-digits $\rightarrow$ SVHN benchmarks however require additional modifications to achieve good performance.
如表 1 中 "MT $^+$ TF" 行所示，目前描述的模型在 8 个小图像基准测试中有 5 项达到了最先进水平。然而，MNIST $\rightarrow$ SVHN、STL $\rightarrow$ CIFAR-10 和 Syn-digits $\rightarrow$ SVHN 基准测试需要进行额外修改才能获得良好性能。
3.2 Confidence threshold ing
3.2 置信度阈值处理
We found that replacing the Gaussian ramp-up factor that scales the unsupervised loss with confidence threshold ing stabilized training in more challenging domain adaptation scenarios. For each unlabeled sample $x T i$ the teacher network produces the predicted class probabilty vector $\tilde{z}{T i j}$ – where $j$ is the class index drawn from the set of classes $C$ – from which we compute the confidence $\tilde{f}{T i}=\mathrm{max}{j\in C}(\tilde{z}{T i j})$ ; the predicted probability of the predicted class of the sample. If $\tilde{f}{T i}$ is below the confidence threshold (a parameter search found 0.968 to be an effective value for small image benchmarks), the self-ensembling loss for the sample $x_{i}$ is masked to $0$ .
我们发现，在更具挑战性的领域自适应场景中，用置信度阈值替代用于缩放无监督损失的高斯斜坡因子能够稳定训练过程。对于每个无标签样本$x T i$，教师网络会生成预测类别概率向量$\tilde{z}{T i j}$（其中$j$是从类别集合$C$中提取的类别索引），据此我们计算置信度$\tilde{f}{T i}=\mathrm{max}{j\in C}(\tilde{z}{T i j})$，即样本预测类别的概率值。若$\tilde{f}{T i}$低于置信度阈值（参数搜索发现0.968对小图像基准测试效果最佳），则样本$x_{i}$的自集成损失将被屏蔽为$0$。
Our working hypothesis is that confidence threshold ing acts as a filter, shifting the balance in favour of the student learning correct labels from the teacher. While high network prediction confidence does not guarantee correctness there is a positive correlation. Given the tolerance to incorrect labels reported in [14], we believe that the higher signal-to-noise ratio underlies the success of this component of our approach.
我们的工作假设是，置信度阈值起到了过滤器的作用，使天平向学生从教师处学习正确标签倾斜。虽然网络预测的高置信度并不能保证正确性，但二者存在正相关性。鉴于[14]中报告的对错误标签的容忍度，我们相信更高的信噪比是我们方法这一部分成功的基础。
The use of confidence threshold ing achieves a state of the art results in the STL $\rightarrow$ CIFAR-10 and Syn-digits $\rightarrow$ SVHN benchmarks, as seen in the ‘MT $^+$ CT $^+$ TF’ row of Table 1. While confidence threshold ing can result in very slight reductions in performance (see the MNIST $\leftrightarrow$ USPS and SVHN MNIST results), its ability to stabilise training in challenging scenarios leads us to recommend it as a replacement for the time-dependent Gaussian ramp-up used in [14].
在STL $\rightarrow$ CIFAR-10和Syn-digits $\rightarrow$ SVHN基准测试中，置信度阈值(confidence thresholding)的使用达到了最先进水平，如表1中"MT$^+$CT$^+$TF"行所示。虽然置信度阈值可能导致性能轻微下降(参见MNIST $\leftrightarrow$ USPS和SVHN MNIST结果)，但其在具有挑战性的场景中稳定训练的能力，使我们推荐用它替代[14]中使用的时间相关高斯斜坡上升方法。
3.3 Data augmentation
3.3 数据增强
We explored the effect of three data augmentation schemes in our small image benchmarks (section 4.1). Our minimal scheme (that should be applicable in non-visual domains) consists of Gaussian noise (with $\sigma=0.1$ ) added to the pixel values. The standard scheme (indicated by ‘TF’ in Table 1) was used in [14] and adds translations in the interval $[-2,2]$ and horizontal flips for the CIFAR $10\leftrightarrow$ STL experiments. The affine scheme (indicated by ‘TFA’) adds random affine transformations defined by the matrix in (1), where $\mathcal{N}(0,0.1)$ denotes a real value drawn from a normal distribution with mean $0$ and standard deviation 0.1.
我们在小型图像基准测试(4.1节)中探索了三种数据增强方案的效果。基础方案(适用于非视觉领域)包含向像素值添加高斯噪声(σ=0.1)。标准方案(表1中标注为'TF')参考[14]实现，在CIFAR10↔STL实验中添加了[-2,2
