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This paper explores the use of self-ensembling for visual domain adaptation problems.
Our technique is derived from the mean teacher variant (Tarvainen et.
al 2017) of temporal ensembling (Laine et al. 2017), 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.
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.
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 FIG3 .
We will present our winning solution in Section 4.2.Recent work BID28 ) has demonstrated the effectiveness of self-ensembling with random image augmentations to achieve state of the art performance in semi-supervised learning benchmarks.
We have developed the approach proposed by BID28 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 → SVHN and the VisDA-17 domain adaptation challenge required further modifications.
To this end, we developed confidence thresholding 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.
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.
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.
Recent work based on methods related to self-ensembling have achieved excellent results in semisupervised learning scenarious.
A neural network is trained to make consistent predictions for unsupervised samples under different augmentation BID23 , dropout and noise conditions or through the use of adversarial training .
We will focus in particular on the self-ensembling based approaches of BID13 and BID28 as they form the basis of our approach.
BID13 present two models; their Π-model and their temporal model.
The Π-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 semi-supervised classification benchmarks.
BID28 further improved on the temporal model of BID13 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.
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.
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.
BID5 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.
BID0 reckognised 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.
BID4 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 cross-entropy in the domain classification layers but maximises it in the feature layers.
The model of Tzeng et al. (2017) runs along similar lines but uses separate feature extraction sub-networks for source and domain samples and train the model in two distinct stages.
BID21 ) use tri-training (Zhou & Li (2005 ); 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 classifiers are used to train the final classifier to operate on the target domain.
Generative Adversarial Networks (GANs; BID6 ) 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 discriminator network that is simultaneously trained to distinguish real samples from generates samples.
Some GAN based models -such as that of BID24 -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.
BID1 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 BID25 consists of a refiner network (in the place of a generator) and discriminator 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.
BID20 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, by Zhu et al. (2017) .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 Sun & Saenko (2016) minimises the difference between the feature covariance matrices for a mini-batch of samples from the source and target domains.
Tzeng et al. (2014) and BID16 minimise the Maximum Mean Discrepancy metric BID7 .
described adaptive batch normalization, a variant of batch normalization BID11 ) 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.
Our model builds upon the mean teacher semi-supervised learning model of BID28 , which we will describe.
Subsequently we will present our modifications that enable domain adaptation.
The structure of the mean teacher model of BID28 -also discussed in section 2.1 -is shown in FIG1 .
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) andz i (teacher).
Different dropout, noise and image translation parameters are used for the student and teacher pathways.
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 (z i ) networks for the same input sample.
It is computed using the mean squared difference between the class probability predictions z i andz i .Laine & Aila FORMULA0 and BID28 found that it was necessary to apply a timedependent 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.
In the following subsections we will describe our contributions in detail along with the motivations for introducing them.
We minimise the same loss as in BID28 ; we apply cross-entropy loss to labeled source samples and unsupervised self-ensembling loss to target samples.
As in BID28 , self-ensembling loss is computed as the mean-squared difference between predictions produced by the student (z T i ) and teacher (z T i ) networks with different augmentation, dropout and noise parameters.
The models of BID28 and of BID13 were designed for semisupervised 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 minibatch.
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 FIG1 -has separate source (X Si ) and target (X T i ) paths.
Inspired by the work of , 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 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.
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 → SVHN, STL → CIFAR-10 and Syn-digits → SVHN benchmarks however require additional modifications to achieve good performance.
We found that replacing the Gaussian ramp-up factor that scales the unsupervised loss with confidence thresholding stabilized training in more challenging domain adaptation scenarios.
For each unlabeled sample x T i the teacher network produces the predicted class probabilty vectorz T ijwhere j is the class index drawn from the set of classes C -from which we compute the confidencẽ f T i = max j∈C (z T ij ); the predicted probability of the predicted class of the sample.
Iff 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.Our working hypothesis is that confidence thresholding 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 by BID13 , we believe that the higher signal-to-noise ratio underlies the success of this component of our approach.
The use of confidence thresholding achieves a state of the art results in the STL → CIFAR-10 and Syn-digits → SVHN benchmarks, as seen in the 'MT+CT+TF' row of Table 1 .
While confidence thresholding can result in very slight reductions in performance (see the MNIST ↔ 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 BID13 .
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 σ = 0.1) added to the pixel values.
The standard scheme (indicated by 'TF' in Table 1 ) was used by BID13 and adds translations in the interval [−2, 2] and horizontal flips for the CIFAR-10 ↔ STL experiments.
The affine scheme (indicated by 'TFA') adds random affine transformations defined by the matrix in (1), where N (0, 0.1) denotes a real value drawn from a normal distribution with mean 0 and standard deviation 0.1.
DISPLAYFORM0 The use of translations and horizontal flips has a significant impact in a number of our benchmarks.
It is necessary in order to outpace prior art in the MNIST ↔ USPS and SVHN → MNIST benchmarks and improves performance in the CIFAR-10 ↔ STL benchmarks.
The use of affine augmentation can improve performance in experiments involving digit and traffic sign recognition datasets, as seen in the 'MT+CT+TFA' row of Table 1 .
In contrast it can impair performance when used with photographic datasets, as seen in the the STL → CIFAR-10 experiment.
It also impaired performance in the VisDA-17 experiment (section 4.2).
With the adaptations made so far the challenging MNIST → SVHN benchmark remains undefeated due to training instabilities.
During training we noticed that the error rate on the SVHN test set decreases at first, then rises and reaches high values before training completes.
We diagnosed the problem by recording the predictions for the SVHN target domain samples after each epoch.
The rise in error rate correlated with the predictions evolving toward a condition in which most samples are predicted as belonging to the '1' class; the most populous class in the SVHN dataset.
We hypothesize that the class imbalance in the SVHN dataset caused the unsupervised loss to reinforce the '1' class more often than the others, resulting in the network settling in a degenerate local minimum.
Rather than distinguish between digit classes as intended it seperated MNIST from SVHN samples and assigned the latter to the '1' class.
We addressed this problem by introducing a class balance loss term that penalises the network for making predictions that exhibit large class imbalance.
For each target domain mini-batch we compute the mean of the predicted sample class probabilities over the sample dimension, resulting in the mini-batch mean per-class probability.
The loss is computed as the binary cross entropy between the mean class probability vector and a uniform probability vector.
We balance the strength of the class balance loss with that of the self-ensembling loss by multiplying the class balance loss by the average of the confidence threshold mask (e.g. if 75% of samples in a mini-batch pass the confidence threshold, then the class balance loss is multiplied by 0.75).
We would like to note the similarity between our class balance loss and the entropy maximisation loss in the IMSAT clustering model of BID10 ; IMSAT employs entropy maximisation to encourage uniform cluster sizes and entropy minimisation to encourage unambiguous cluster assignments.
Our implementation was developed using PyTorch (Chintala et al.) and is publically available at http://github.com/Britefury/self-ensemble-visual-domain-adapt.
Our results can be seen in Table 1 .
The 'train on source' and 'train on target' results report the target domain performance of supervised training on the source and target domains.
They represent the exepected baseline and best achievable result.
The 'Specific aug.' experiments used data augmentation specific to the MNIST → SVHN adaptation path that is discussed further down.
The small datasets and data preparation procedures are described in Appendix A. Our training procedure is described in Appendix B and our network architectures are described in Appendix D. The same network architectures and augmentation parameters were used for domain adaptation experiments and the supervised baselines discussed above.
It is worth noting that only the training sets of the small image datasets were used during training; the test sets used for reporting scores only.
MNIST ↔ USPS (see FIG2 .
MNIST and USPS are both greyscale hand-written digit datasets.
In both adaptation directions our approach not only demonstrates a significant improvement over prior art but nearly achieves the performance of supervised learning using the target domain ground truths.
The strong performance of the base mean teacher model can be attributed to the similarity of the datasets to one another.
It is worth noting that data augmentation allows our 'train on source' baseline to outpace prior domain adaptation methods.
CIFAR-10 ↔ STL (see FIG2 ).
CIFAR-10 and STL are both 10-class image datasets, although we removed one class from each (see Appendix A.2).
We obtained strong performance in the STL → CIFAR-10 path, but only by using confidence thresholding.
The CIFAR-10 → STL results are more interesting; the 'train on source' baseline performance outperforms that of a network trained on the STL target domain, most likely due to the small size of the STL training set.
Our self-ensembling results outpace both the baseline performance and the 'theoretical maximum' of a network trained Table 1 : Small image benchmark classification accuracy; each result is presented as mean ± standard deviation, computed from 5 independent runs.
The abbreviations for components of our models are as follows: MT = mean teacher, CT = confidence thresholding, TF = translation and horizontal flip augmentation, TFA = translation, horizontal flip and affine augmentation, * indicates minimal augmentation.on the target domain, lending further evidence to the view of BID23 and BID13 that self-ensembling acts as an effective regulariser.
Syn-Digits → SVHN (see FIG2 .
The Syn-Digits dataset is a synthetic dataset designed by BID4 to be used as a source dataset in domain adaptation experiments with SVHN as the target dataset.
Other approaches have achieved good scores on this benchmark, beating the baseline by a significant margin.
Our result improves on them, reducing the error rate from 6.9% to 2.9%; even slightly outpacing the 'train on target' 3.4% error rate achieved using supervised learning.
Syn-Signs → GTSRB (see FIG2 ).
Syn-Signs is another synthetic dataset designed by BID4 to target the 43-class GTSRB (German Traffic Signs Recognition Benchmark; BID26 ) dataset.
Our approach halved the best error rate of competing approaches.
Once again, our approaches slightly outpaces the 'train on target' supervised learning upper bound.
SVHN → MNIST (see FIG2 ).
Google's SVHN (Street View House Numbers) is a colour digits dataset of house number plates.
Our approach significantly outpaces other techniques and achieves an accuracy close to that of supervised learning.
MNIST → SVHN (see FIG2 ).
This adaptation path is somewhat more challenging as MNIST digits are greyscale and uniform in terms of size, aspect ratio and intensity range, in contrast to the variably sized colour digits present in SVHN.
As a consequence, adapting from MNIST to SVHN required additional work.
Class balancing loss was necessary to ensure training stability and additional experiment specific data augmentation was required to achieve good accuracy.
The use of translations and affine augmentation (see section 3.3) results in an accuracy score of 37%.
Significant improvements resulted from additional augmentation in the form of random intensity flips (negative image), and random intensity scales and offsets drawn from the intervals [0.25, 1.5] and [−0.5, 0.5] respectively.
These hyper-parameters were selected in order to augment MNIST samples to match the intensity variations present in SVHN, as illustrated in FIG2 .
With these additional modifications, we achieve a result that significantly outperforms prior art and nearly achieves the accuracy of a supervised classifier trained on the target dataset.
We found that applying these additional augmentations to the source MNIST dataset only yielded good results; applying them to the target SVHN dataset as well yielded a small improvement but was not essential.
It should also be noted that this augmentation scheme raises the performance of the 'train on source' baseline to just above that of much of the prior art.
The VisDA-2017 image classification challenge is a 12-class domain adaptation problem consisting of three datasets: a training set consisting of 3D renderings of sketchup models, and validation and test sets consisting of real images (see FIG3 ) drawn from the COCO Lin et al. (2014) and YouTube BoundingBoxes BID19 datasets respectively.
The objective is to learn from labeled computer generated images and correctly predict the class of real images.
Ground truth labels were made available for the training and validation sets only; test set scores were computed by a server operated by the competition organisers.
While the algorithm is that presented above, we base our network on the pretrained ResNet-152 BID9 ) network provided by PyTorch (Chintala et al.) , rather than using a randomly initialised network as before.
The final 1000-class classification layer is removed and replaced with two fullyconnected layers; the first has 512 units with a ReLU non-linearity while the final layer has 12 units with a softmax non-linearity.
Results from our original competition submissions and newer results using two data augmentation schemes are presented in Table 2 .
Our reduced augmentation scheme consists of random crops, random horizontal flips and random uniform scaling.
It is very similar to scheme used for ImageNet image classification in BID9 .
Our competition configuration includes additional augmentation that was specifically designed for the VisDA dataset, although we subsequently found that it makes little difference.
Our hyper-parameters and competition data augmentation scheme are described in Appendix C.1.
It is worth noting that we applied test time augmentation (we averaged predictions form 16 differently augmented images) to achieve our competition results.
We present resuts with and without test time augmentation in Table 2 .
Our VisDA competition test set score is also the result of ensembling the predictions of 5 different networks.
We have presented an effective domain adaptation algorithm that has achieved state of the art results in a number of benchmarks and has achieved accuracies that are almost on par with traditional supervised learning on digit recognition benchmarks targeting the MNIST and SVHN datasets.
The Table 2 : VisDA-17 performance, presented as mean ± std-dev of 5 independent runs.
Full results are presented in TAB6 in Appendix C. resulting networks will exhibit strong performance on samples from both the source and target domains.
Our approach is sufficiently flexible to be usable for a variety of network architectures, including those based on randomly initialised and pre-trained networks. stated that the self-ensembling methods presented by Laine & Aila (2017) -on which our algorithm is based -operate by label propagation.
This view is supported by our results, in particular our MNIST → SVHN experiment.
The latter requires additional intensity augmentation in order to sufficiently align the dataset distributions, after which good quality label predictions are propagated throughout the target dataset.
In cases where data augmentation is insufficient to align the dataset distributions, a pre-trained network may be used to bridge the gap, as in our solution to the VisDA-17 challenge.
This leads us to conclude that effective domain adaptation can be achieved by first aligning the distributions of the source and target datasets -the focus of much prior art in the field -and then refining their correspondance; a task to which self-ensembling is well suited.
The datasets used in this paper are described in Some of the experiments that involved datasets described in TAB3 required additional data preparation in order to match the resolution and format of the input samples and match the classification target.
These additional steps will now be described.
MNIST ↔ USPS The USPS images were up-scaled using bilinear interpolation from 16 × 16 to 28 × 28 resolution to match that of MNIST.CIFAR-10 ↔ STL CIFAR-10 and STL are both 10-class image datasets.
The STL images were down-scaled to 32 × 32 resolution to match that of CIFAR-10.
The 'frog' class in CIFAR-10 and the 'monkey' class in STL were removed as they have no equivalent in the other dataset, resulting in a 9-class problem with 10% less samples in each dataset.
Syn-Signs → GTSRB GTSRB is composed of images that vary in size and come with annotations that provide region of interest (bounding box around the sign) and ground truth classification.
We extracted the region of interest from each image and scaled them to a resolution of 40 × 40 to match those of Syn-Signs.
MNIST ↔ SVHN The MNIST images were padded to 32 × 32 resolution and converted to RGB by replicating the greyscale channel into the three RGB channels to match the format of SVHN.B SMALL IMAGE EXPERIMENT TRAINING B.1 TRAINING PROCEDURE Our networks were trained for 300 epochs.
We used the Adam BID12 gradient descent algorithm with a learning rate of 0.001.
We trained using mini-batches composed of 256 samples, except in the Syn-digits → SVHN and Syn-signs → GTSRB experiments where we used 128 in order to reduce memory usage.
The self-ensembling loss was weighted by a factor of 3 and the class balancing loss was weighted by 0.005.
Our teacher network weights t i were updated so as to be an exponential moving average of those of the student s i using the formula t i = αt i−1 + (1 − α)s i , with a value of 0.99 for α.
A complete pass over the target dataset was considered to be one epoch in all experiments except the MNIST → USPS and CIFAR-10 → STL experiments due to the small size of the target datasets, in which case one epoch was considered to be a pass over the larger soure dataset.
We found that using the proportion of samples that passed the confidence threshold can be used to drive early stopping BID18 ).
The final score was the target test set performance at the epoch at which the highest confidence threshold pass rate was obtained.
C VISDA-17 C.1 HYPER-PARAMETERS Our training procedure was the same as that used in the small image experiments, except that we used 160 × 160 images, a batch size of 56 (reduced from 64 to fit within the memory of an nVidia 1080-Ti), a self-ensembling weight of 10 (instead of 3), a confidence threshold of 0.9 (instead of 0.968) and a class balancing weight of 0.01.
We used the Adam BID12 gradient descent algorithm with a learning rate of 10 −5 for the final two randomly initialized layers and 10 DISPLAYFORM0 for the pre-trained layers.
The first convolutional layer and the first group of convolutional layers (with 64 feature channels) of the pre-trained ResNet were left unmodified during training.
Reduced data augmentation:• scale image so that its smallest dimension is 176 pixels, then randomly crop a 160 × 160 section from the scaled image • No random affine transformations as they increase confusion between the car and truck classes in the validation set • random uniform scaling in the range [0.75, 1.333]• horizontal flipping Competition data augmentation adds the following in addition to the above:• random intensity/brightness scaling in the range [0.75, 1.333]• random rotations, normally distributed with a standard deviation of 0.2π• random desaturation in which the colours in an image are randomly desaturated to greyscale by a factor between 0% and 100% • rotations in colour space, around a randomly chosen axes with a standard deviation of 0.05π• random offset in colour space, after standardisation using parameters specified by 10 × 10 × 192 Dropout, 50%10 × 10 × 192 Conv 3 × 3 × 384, pad 1, batch norm 10 × 10 × 384 Conv 3 × 3 × 384, pad 1, batch norm 10 × 10 × 384 Conv 3 × 3 × 384, pad 1, batch norm 10 × 10 × 384 Max-pool, 2x25 × 5 × 384 Dropout, 50%5 × 5 × 384 Global pooling layer 1 × 1 × 384 Fully connected, 43 units, softmax 43 Table 8 : Syn-signs → GTSRB architecture

assistant: text: Self-ensembling based algorithm for visual domain adaptation, state of the art results, won VisDA-2017 image classification domain adaptation challenge.