Generative Adversarial Networks (GANs) are a class of unsupervised generative models . GANs involve training a generator and discriminator
model in an adversarial game, such that the generator learns to produce samples from a desired data distribution. Training GANs is challenging because it involves searching for a Nash equilibrium of a non-convex game in a high-dimensional parameter space. In practice, GANs are typically trained using alternating stochastic gradient descent which is often unstable and lacks theoretical guarantees. Consequently, training may exhibit instability, divergence, cyclic behavior, or mode collapse . As a result, many techniques to stabilize GAN training have been proposed [4, 5, 6, 7, 8, 9, 10]
. A major contributor to training instability is the fact that the generator and discriminator learn in a non-stationary environment. In particular, the discriminator is a classifier for which the distribution of one class (the fake samples) shifts as the generator changes during training. In non-stationary online environments, neural networks forget previous tasks[11, 12, 13]. If the discriminator forgets previous classification boundaries, training may become unstable or cyclic. This issue is usually addressed either by reusing old samples or by applying continual learning techniques [14, 15, 16, 17, 18, 19]. These issues become more prominent in the context of complex data sets. A key technique in these settings is conditioning [9, 20, 21, 22]
whereby both the generator and discriminator have access to labeled data. Arguably, augmenting the discriminator with supervised information encourages it to learn more stable representations which opposes catastrophic forgetting. Furthermore, learning the conditional model for each class is easier than learning the joint distribution. The main drawback in this setting is the necessity for labeled data. Even when labeled data is available, it is usually sparse and covers only a limited amount of high level abstractions.
Motivated by the aforementioned challenges, our goal is to show that one can recover the benefits of conditioning, without requiring labeled data. To ensure that the representations learned by the discriminator are more stable and useful, we add an auxiliary, self-supervised loss to the discriminator. This leads to more stable training because the dependence of the discriminator’s representations on the quality of the generator’s output is reduced. We introduce a novel model – the self-supervised GAN – in which the generator and discriminator collaborate on the task of representation learning, and compete on the generative task.
We present an unsupervised generative model that combines adversarial training with self-supervised learning. Our model recovers the benefits of conditional GANs, but requires no labelled data. In particular,under the same training conditions
, the self-supervised GAN closes the gap in natural image synthesis between unconditional and conditional models. Within this setting the quality of discriminator’s representations is greatly increased which might be of separate interest in the context of transfer learning. A large-scale implementation of the model leads to promissing results onunconditional imagenet generation, a task considered daunting by the community. We believe that this work is an important step in the direction of high quality, fully unsupervised, natural image synthesis.
2 A Key Issue: Discriminator Forgetting
The original value function for GAN training is :
where is the true data distribution, and is the distribution induced by transforming a simple distribution using the deterministic mapping given by the generator, , and
is the discriminator’s Bernoulli distribution over the labels (true or fake). In the original minimax setting the generator maximizes Equation1 with respect to it’s parameters, while the discriminator minimizes it. Training is typically performed via alternating stochastic gradient descent. Therefore, at iteration during training, the discriminator classifies samples as coming from or . As the parameters of G change, the distribution changes, which implies a non-stationary online learning problem for the discriminator.
This challenge has received a great deal of attention and explicit temporal dependencies have been proposed to improve training in this setting [2, 15, 17, 19]. Furthermore, in online learning of non-convex functions, neural networks have been shown to forget previous tasks [11, 12, 13]. In the context of GANs, learning varying levels of detail, structure, and texture, can be considered different tasks. For example, if the generator first learns the global structure, the discriminator will naturally try to build a representation which allows it to efficiently penalize the generator based only on the differences in global structure, or the lack of local structure. As such, one source of instability in training is that the discriminator is not incentivised to maintain a useful data representation as long as the current representation is useful to discriminate between the classes.
Further evidence can be gathered by considering the generator and discriminator at convergence. Indeed, Goodfellow et al. 
show that the optimal discriminator estimates the likelihood ratio between the generated and real data distributions. Therefore, given a perfect generator, where, the optimal discriminator simply outputs , which is a constant and doesn’t depend on the input. Hence, this discriminator would have no requirement to retain meaningful representations. Furthermore, if regularization is applied, the discriminator might ignore all but the minor features which distinguish real and fake data.
We demonstrate the impact of discriminator forgetting in two settings. (1) A simple scenario shown in Figure 3(a), and, (2) during the training of a GAN shown in Figure 2. In the first case a classifier is trained sequentially on 1-vs.-all classification tasks on each of the ten classes in cifar10. It is trained for k iterations on each task before switching to the next. At k iterations the training cycle repeats from the first task. Figure 3(a) shows substantial forgetting, despite the tasks being similar. Each time the task switches, the classifier accuracy drops substantially. After k iterations, the cycle of tasks repeats, and the accuracy is the same as the first cycle. No useful information is carried across tasks. This demonstrates that the model does not retain generalizable representations in this non-stationary environment. In the second setting shown in Figure 2 we observe a similar effect during GAN training. Every k iterations, the discriminator representations are evaluated on imagenet classification; the full protocol is described in Section 4.4. During training, classification of the unconditional GAN increases, then decreases, indicating that information about the classes is acquired and later forgotten. This forgetting correlates with training instability. Adding self-supervision, as detailed in the following section, prevents this forgetting of the classes in the discriminator representations.
3 The Self-Supervised GAN
Motivated by the main challenge of discriminator forgetting, we aim to imbue the discriminator with a mechanism which allows learning useful representations, independently of the quality of the current generator. To this end, we exploit recent advancements in self-supervised approaches for representation learning. The main idea behind self-supervision is to train a model on a pretext task like predicting rotation angle or relative location of an image patch, and then extracting representations from the resulting networks [23, 24, 25]. We propose to add a self-supervised task to our discriminator.
In particular, we apply the state-of-the-art self-supervision method based on image rotation . In this method, the images are rotated, and the angle of rotation becomes the artificial label (cf. Figure 1). The self-supervised task is then to predict the angle of rotation of an image. The effects of this additional loss on the image classification task is evident in Figure 3(b): When coupled with the self-supervised loss, the network learns representations that transfer across tasks and the performance continually improves. On the second cycle through the tasks, from k iterations onward, performance is improved. Intuitively, this loss encourages the classifier to learn useful image representations to detect the rotation angles, which transfers to the image classification task.
We augment the discriminator with a rotation-based loss which results in the following loss functions:
where is the value function from Equation 1, is a rotation selected from a set of possible rotations. In this work we use as in Gidaris et al. . Image rotated by degrees is denoted as , and is the discriminator’s predictive distribution over the angles of rotation of the sample.
Collaborative Adversarial Training
In our model, the generator and discriminator are adversarial with respect to the true vs. fake prediction loss, , however, they are collaborative with respect to the rotation task. First, consider the value function of the generator which biases the generation towards images, that when rotated, the discriminator can detect their rotation angle. Note that the generator is not conditional but only generates “upright” images which are subsequently rotated and fed to the discriminator. On the other hand, the discriminator is trained to detect rotation angles based only on the true data. In other words, the parameters of the discriminator get updated only based on the rotation loss on the true data. This prevents the undesirable collaborative solution whereby the generator generates images whose subsequent rotation is easy to detect. As a result, the generator is encouraged to generate images that are rotation-detectable because they share features with real images that are used for rotation classification.
In practice, we use a single discriminator network with two heads to compute and . Figure 1 depicts the training pipeline. We rotate the real and generated images in four major rotations. The goal of the discriminator on non-rotated images is to predict whether the input is true or fake. On rotated real images, its goal is to detect the rotation angle. The goal of the generator is to generate images matching the observed data, whose representation in the feature space of the discriminator allows detecting rotations. With convergence to the true data distribution is not guaranteed. However, annealing towards zero during training will restore the guarantees.
We demonstrate empirically that (1) self-supervision improves the representation quality with respect to baseline GAN models, and that (2) it leads to improved unconditional generation for complex datasets, matching the performance of conditional GANs, under equal training conditions.
4.1 Experimental Settings
We focus primarily on imagenet, the largest and most diverse image dataset commonly used to evaluate GANs. Until now, most GANs trained on imagenet are conditional. imagenet contains M training images and k test images. We resize the images to as done in Miyato and Koyama  and Zhang et al. . We provide additional comparison on three smaller datasets, namely cifar10, celeba-hq, lsun-bedroom, for which unconditional GANs can be successfully trained. The lsun-bedroom dataset  contains M images. We partition these randomly into a test set containing approximately k images and a train set containing the rest. celeba-hq contains k images . We use the version obtained by running the code provided by the authors.111https://github.com/tkarras/progressive_growing_of_gans. We use k examples as the test set and the remaining examples as the training set. cifar10 contains k images (), partitioned into k training instances and k test instances.
|gradient penalty||1||0.0||0.900||1||121.05 31.44||25.8 0.71||183.36 77.21||80.67 0.43|
|2||28.11 0.66||26.98 0.54||85.13 2.88||83.08 0.38|
|0.5||0.999||1||78.54 6.23||25.89 0.33||104.73 2.71||91.63 2.78|
|10||0.0||0.900||1||188.52 64.54||28.48 0.68||227.04 31.45||85.38 2.7|
|2||29.11 0.85||27.74 0.73||227.74 16.82||80.82 0.64|
|0.5||0.999||1||117.67 17.46||25.22 0.38||242.71 13.62||144.35 91.4|
|spectral norm||0||0.0||0.900||1||87.86 3.44||19.65 0.9||129.96 6.6||86.09 7.66|
|2||20.24 0.62||17.88 0.64||80.05 1.33||70.64 0.31|
|0.5||0.999||1||86.87 8.03||18.23 0.56||201.94 27.28||99.97 2.75|
FID for unconditional GANs under different hyperparameter settings. Mean and standard deviations are computed across three random seeds. Adding the self-supervision loss reduces the sensitivity of GAN training to hyperparameters.
We compare the self-supervised GAN (SS-GAN) to two well-performing baseline models, namely (1) the unconditional GAN with spectral normalization proposed in Miyato et al. , denoted Uncond-GAN, and (2) the conditional GAN using the label-conditioning strategy and the Projection Conditional GAN (Cond-GAN) . We chose the latter as it was shown to outperform the AC-GAN , and is adopted by the best performing conditional GANs [9, 3, 22].
We use ResNet architectures for the generator and discriminator as in Miyato et al. 
. For the conditional generator in Cond-GAN, we apply label-conditional batch normalization. In contrast, SS-GAN does not use conditional batch normalization. However, to have a similar effect on the generator, we consider a variant of SS-GAN where we apply the self-modulated batch normalization which does not require labels and denote it SS-GAN (sBN). We note that labels are available only for cifar10 and imagenet, so Cond-GAN is only applied on those data sets.
We use a batch size of 64 and to implement the rotation-loss we rotate 16 images in the batch in all four considered directions. We do not add any new images into the batch to compute the rotation loss. For the true vs. fake task we use the hinge loss from Miyato et al. . We set or the the self-supervised loss. For we performed a small sweep , and select for all datasets (see the appendix for details). For all other hyperparameters, we use the values in Miyato et al.  and Miyato and Koyama . We train cifar10, lsun-bedroom and celeba-hq for k steps on a single P100 GPU. For imagenet we train for M steps. For all datasets we use the Adam optimizer with learning rate .
4.2 Comparison of Sample Quality
To evaluate generated samples from different methods quantitatively, we use the Frechet Inception Distance (FID) . In FID, the true data and generated samples are first embedded in a specific layer of a pre-trained Inception network. Then, a multivariate Gaussian is fit to the data and the distance computed as , where and denote the empirical mean and covariance and subscripts and denote the true and generated data respectively. FID is shown to be sensitive to both the addition of spurious modes and to mode dropping [29, 30]. An alternative approximate measure of sample quality is Inceptions Score (IS) Salimans et al. . Since it has some flaws Barratt and Sharma , we use FID as the main metric in this work.
Figure 4 shows FID training curves on cifar10 and imagenet. Table 1 shows the FID of the best run across three random seeds for each dataset and model combination. The unconditional GAN is unstable on imagenet and the training often diverges. The conditional counterpart outperforms it substantially. The proposed method, namely SS-GAN, is stable on imagenet, and performs substantially better than the unconditional GAN. When equipped with self-modulation it matches the performance on the conditional GAN. In terms of mean performance (Figure 4) the proposed approach matches the conditional GAN, and in terms of the best models selected across random seeds (Table 1), the performance gap is within . On cifar10 and lsun-bedroom we observe a substantial improvement over the unconditional GAN and matching the performance of the conditional GAN. Self-supervision appears not to significantly improve the results on celeba-hq. We posit that this is due to low-diversity in celeba-hq, and also for which rotation task is less informative.
Robustness across hyperparameters
GANs are fragile; changes to the hyperparameter settings have a substantial impact to their performance [30, 32]. Therefore, we evaluate different hyperparameter settings to test the stability of SS-GAN. We consider two classes of hyperparameters: First, those controlling the Lipschitz constant of the discriminator, a central quantity analyzed in the GAN literature [6, 33]. We evaluate two state-of-the-art techniques: gradient penalty , and spectral normalization . The gradient penalty introduces a regularization strength parameter, . We test two values . Second, we vary the hyperparmeters of the Adam optimizer. We test two popular settings : and . Previous studies find that multiple discriminator steps per generator step help training [1, 2], so we try both and discriminator steps per generator step.
Table 2 compares the mean FID scores of the unconditional models across penalties and optimization hyperparameters. We observe that the proposed approach yields consistent performance improvements. We observe that in settings where the unconditional GAN collapses (yielding FIDs larger than 100) the self-supervised model does not exhibit such a collapse.
4.3 Scaling up the Self-Supervised GAN
We scale up training of the SS-GAN to attain the best possible FID for unconditional imagenet generation. We train the proposed model on 128 cores of Google TPU v3 Pod for k steps using batch size of 1024 and attain an FID score of 33.5. The details of the architectures are provided in the appendix.
Figure 5 shows a random sample of images generated by the model. Training unconditionally on imagenet is much harder than conditional training, therefore, there is not much prior art. Unconditional imagenet
generation results using autoregressive models have been presented, however, FID score are not reported. Using many additional tricks and techniques, a very recent approach based on conditional generation has attained an FID of 9.6 with large scale training. Although our unconditional model is still far behind, our results in Section 4.2 indicate that under the same conditions, SS-GAN can match conditional settings. We are hopeful that this results, which dramatically improves upon previous unconditional models, paves the way to attaining comparable scores with unconditional models in the future. To our knowledge, this is the best results attained training unconditionally on imagenet.
4.4 Representation Quality
We test empirically whether self-supervision encourages the discriminator to learn meaningful representations. For this, we compare the quality of the representations extracted from the intermediate layers of the discriminator’s ResNet architecture. We apply a common evaluation method for representation learning, proposed in Zhang et al. 
. In particular, we train a logistic regression classifier on the feature maps from each ResNet block to perform the 1000-way classification task onimagenet or 10-way on cifar10 and report top-1 classification accuracy.
We report results using the Cond-GAN, Uncond-GAN, and SS-GAN models. We also ablate the adversarial loss from our SS-GAN which results in a purely rotation-based self-supervised model (Rot-only) which uses the same architecture and hyperparameters as the SS-GAN discriminator. We report the mean accuracy and standard deviation across three independent models with different random seeds. Training details for the logistic classifier are in the appendix.
, except for Uncond-GAN whose results exhibit high variance due to training instability. All standard deviations are reported in the appendix.
Table 4 shows the quality of representation at after M training steps on imagenet. Figure 9 shows the learning curves for representation quality of the final ResNet block on imagenet. The curves for the other blocks are provided in appendix. Note that “training steps” refers to the training iterations of the original GAN, and not to the linear classifier which is always trained to convergence. Overall, the SS-GAN yields the best representations across all blocks and training iterations. We observe similar results on cifar10 provided in Table 3.
In detail, the imagenet ResNet contains six blocks. For Uncond-GAN and Rot-only, Block 3 performs best, for Cond-GAN and SS-GAN, the final Block 5 performs best. The representation quality for Uncond-GAN drops at 500k steps, which is consistent with the FID drop in Figure 4. Overall, the SS-GAN and Cond-GAN representations are better than Uncond-GAN, which correlates with their improved sample quality. Surprisingly, the the SS-GAN overtakes Cond-GAN after training for k steps. One possibility is that the Cond-GAN is overfitting the training data. We inspect the representation performance of Cond-GAN on the training set and indeed see a very large generalization gap, which indicates overfitting.
When we ablate the GAN loss, leaving just the rotation loss, the representation quality substantially decreases. It seems that the adversarial and rotation losses complement each other both in terms of FID and representation quality. We emphasize that our discriminator architecture is optimized for image generation, not representation quality. Rot-only, therefore, is an ablation method, and is not a state-of-the-art self-supervised learning algorithm. We discuss these next.
Table 5 compares the representation quality of SS-GAN to state-of-the-art published self-supervised learning algorithms. Despite the architecture and hyperparameters being optimized for image quality, the SS-GAN model achieves competitive results on imagenet. Among those methods, only BiGAN  also uses a GAN to learn representations; but SS-GAN performs substantially (0.073 accuracy points) better. BiGAN learns the representation with an additional encoder network, while SS-GAN is arguably simpler because it extracts the representation directly from the discriminator. The best performing method is the recent DeepClustering algorithm 
. This method is just 0.027 accuracy points ahead of SS-GAN and requires expensive offline clustering after every training epoch.
In summary, the representation quality evaluation highlights the correlation between representation quality and image quality. It also confirms that the SS-GAN does learn relatively powerful image represenatations.
5 Related Work
Catastrophic forgetting was previously considered as a major cause for GAN training instability. The main remedy suggested in the literature is to introduce temporal memory into the training algorithm in various ways. For example, Grnarova et al.  induce discriminator memory by replaying previously generated images. An alternative is to instead reuse previous models: Salimans et al.  introduce checkpoint averaging, where a running average of the parameters of each player is kept, and Grnarova et al.  maintain a queue of models that are used at each training iteration. Kim et al.  add memory to retain information about previous samples. Other papers frame GAN training as a continual learning task. Thanh-Tung et al.  study catastrophic forgetting in the discriminator and mode collapse, relating these to training instability. Anonymous  counter discriminator forgetting by leveraging techniques from continual learning directly (Elastic Weight Sharing 
and Intelligent Synapses).
Conditional GANs are currently the best approach for generative modeling of complex data sets, such as ImageNet. The AC-GAN was the first model to introduce an auxiliary classification loss for the discriminator . The main difference between AC-GAN and the proposed approach is that self-supervised GAN requires no labels. Furthermore, the AC-GAN generator generates images conditioned on the class, whereas our generator is unconditional and the images are subsequently rotated to produce the artificial label. Finally, the self-supervision loss for the discriminator is applied only over real images, whereas the AC-GAN uses both real and fake.
More recently, the P-cGAN model proposed by Miyato and Koyama  includes one real/fake head per class . This architecture improves performance over AC-GAN. The best performing GANs trained on GPUs  and TPUs 
use P-cGAN style conditioning in the discriminator. We note that conditional GANs also use labels in the generator, either by concatenating with the latent vector, or via FiLM modulation.
Self-supervised learning is a family of methods that learn the high level semantic representation by solving a surrogate task. It has been widely used in the video domain [39, 40], the robotics domain [41, 42] and the image domain [24, 36]. We focused on the image domain in this paper. Gidaris et al.  proposed to rotate the image and predict the rotation angle. This conceptually simple task yields useful representations for downstream image classification tasks. Apart form trying to predict the rotation, one can also make edits to the given image and ask the network to predict the edited part. For example, the network can be trained to solve the context prediction problem, like the relative location of disjoint patches [24, 43] or the patch permutation of a jigsaw puzzle 
. Other surrogate tasks include image inpainting, predicting the color channels from a grayscale image , and predicting the unsupervised clustering classes .
6 Conclusions and Future Work
Motivated by the desire to counter discriminator forgetting, we propose a deep generative model that combines adversarial and self-supervised learning. The resulting novel model, namely self-supervised GAN when combined with the recently introduced self-modulation, can match equivalent conditional GANs on the task of image synthesis, without having access to labeled data. We then show that this model can be scaled to attain an FID of 33 on unconditional ImageNet generation which is an extremely challenging task.
This line of work opens several avenues for future research. First, it would be interesting to use a state-of-the-art self-supervised architecture for the discriminator, and optimize for best possible representations. Second, the self-supervised GAN could be used in a semi-supervised setting where a small number of labels could be used to fine-tune the model. Finally, one may exploit several recently introduced techniques, such as self-attention, orthogonal normalization and regularization, and sampling truncation [9, 22], to yield even better performance in unconditional image synthesis.
We hope that this approach, combining collaborative self-supervision with adversarial training, can pave the way towards high quality, fully unsupervised, generative modelling of complex data.
- Goodfellow et al.  Ian Goodfellow, Jean Pouget-Abadie, Mehdi Mirza, Bing Xu, David Warde-Farley, Sherjil Ozair, Aaron Courville, and Yoshua Bengio. Generative adversarial nets. In Advances in Neural Information Processing Systems (NIPS), 2014.
- Salimans et al.  Tim Salimans, Ian Goodfellow, Wojciech Zaremba, Vicki Cheung, Alec Radford, and Xi Chen. Improved techniques for training gans. In Advances in Neural Information Processing Systems (NIPS), 2016.
Mescheder et al. 
Lars Mescheder, Andreas Geiger, and Sebastian Nowozin.
Which training methods for gans do actually converge?
International Conference on Machine Learning (ICML), 2018.
Mao et al. 
Xudong Mao, Qing Li, Haoran Xie, Raymond YK Lau, Zhen Wang, and Stephen Paul
Least squares generative adversarial networks.
International Conference on Computer Vision (ICCV), 2016.
- Gulrajani et al.  Ishaan Gulrajani, Faruk Ahmed, Martin Arjovsky, Vincent Dumoulin, and Aaron Courville. Improved training of Wasserstein GANs. Advances in Neural Information Processing Systems (NIPS), 2017.
- Miyato et al.  Takeru Miyato, Toshiki Kataoka, Masanori Koyama, and Yuichi Yoshida. Spectral normalization for generative adversarial networks. International Conference on Learning Representations (ICLR), 2018.
- Chen et al.  Ting Chen, Mario Lucic, Neil Houlsby, and Sylvain Gelly. On self modulation for generative adversarial networks. arXiv preprint arXiv:1810.01365, 2018.
- Radford et al.  Alec Radford, Luke Metz, and Soumith Chintala. Unsupervised representation learning with deep convolutional generative adversarial networks. In International Conference on Learning Representations (ICLR), 2016.
- Zhang et al.  Han Zhang, Ian Goodfellow, Dimitris Metaxas, and Augustus Odena. Self-attention generative adversarial networks. arXiv preprint arXiv:1805.08318, 2018.
- Karras et al.  Tero Karras, Timo Aila, Samuli Laine, and Jaakko Lehtinen. Progressive growing of gans for improved quality, stability, and variation. In International Conference on Learning Representations (ICLR), 2018.
- Kirkpatrick et al.  James Kirkpatrick, Razvan Pascanu, Neil Rabinowitz, Joel Veness, Guillaume Desjardins, Andrei A Rusu, Kieran Milan, John Quan, Tiago Ramalho, Agnieszka Grabska-Barwinska, et al. Overcoming catastrophic forgetting in neural networks. Proceedings of the national academy of sciences, 2017.
- McCloskey and Cohen  Michael McCloskey and Neal J Cohen. Catastrophic interference in connectionist networks: The sequential learning problem. In Psychology of learning and motivation, volume 24. Elsevier, 1989.
- French  Robert M French. Catastrophic forgetting in connectionist networks. Trends in cognitive sciences, 1999.
- Thanh-Tung et al.  Hoang Thanh-Tung, Truyen Tran, and Svetha Venkatesh. On catastrophic forgetting and mode collapse in generative adversarial networks. ICML Workshop on Theoretical Foundations and Applications of Deep Generative Models, 2018.
- Anonymous [2019a] Anonymous. Generative adversarial network training is a continual learning problem. In Submitted to International Conference on Learning Representations (ICLR), 2019a. URL https://openreview.net/forum?id=SJzuHiA9tQ. under review.
- Seff et al.  Ari Seff, Alex Beatson, Daniel Suo, and Han Liu. Continual learning in generative adversarial nets. arXiv preprint arXiv:1705.08395, 2017.
Shrivastava et al. 
Ashish Shrivastava, Tomas Pfister, Oncel Tuzel, Joshua Susskind, Wenda Wang,
and Russell Webb.
Learning from simulated and unsupervised images through adversarial
Computer Vision and Pattern Recognition (CVPR), 2017.
- Kim et al.  Youngjin Kim, Minjung Kim, and Gunhee Kim. Memorization precedes generation: Learning unsupervised gans with memory networks. International Conference on Learning Representations (ICLR), 2018.
- Grnarova et al.  Paulina Grnarova, Kfir Y Levy, Aurelien Lucchi, Thomas Hofmann, and Andreas Krause. An online learning approach to generative adversarial networks. In International Conference on Learning Representations (ICLR), 2018.
- Odena et al.  Augustus Odena, Christopher Olah, and Jonathon Shlens. Conditional image synthesis with auxiliary classifier GANs. In International Conference on Machine Learning (ICML), 2017.
- Miyato and Koyama  Takeru Miyato and Masanori Koyama. cgans with projection discriminator. International Conference on Learning Representations (ICLR), 2018.
- Brock et al.  Andrew Brock, Jeff Donahue, and Karen Simonyan. Large scale gan training for high fidelity natural image synthesis. arXiv preprint arXiv:1809.11096, 2018.
Dosovitskiy et al. 
Alexey Dosovitskiy, Jost Tobias Springenberg, Martin Riedmiller, and Thomas
Discriminative unsupervised feature learning with convolutional neural networks.In Advances in Neural Information Processing Systems (NIPS), 2014.
- Doersch et al.  Carl Doersch, Abhinav Gupta, and Alexei A Efros. Unsupervised visual representation learning by context prediction. In International Conference on Computer Vision (ICCV), 2015.
- Zhang et al.  Richard Zhang, Phillip Isola, and Alexei A Efros. Colorful image colorization. In European Conference on Computer Vision (ECCV), 2016.
- Gidaris et al.  Spyros Gidaris, Praveer Singh, and Nikos Komodakis. Unsupervised representation learning by predicting image rotations. In International Conference on Learning Representations (ICLR), 2018.
- Yu et al.  Fisher Yu, Yinda Zhang, Shuran Song, Ari Seff, and Jianxiong Xiao. Lsun: Construction of a large-scale image dataset using deep learning with humans in the loop. arXiv preprint arXiv:1506.03365, 2015.
- Heusel et al.  Martin Heusel, Hubert Ramsauer, Thomas Unterthiner, Bernhard Nessler, Günter Klambauer, and Sepp Hochreiter. GANs trained by a two time-scale update rule converge to a Nash equilibrium. In Advances in Neural Information Processing Systems (NIPS), 2017.
Sajjadi et al. 
Mehdi SM Sajjadi, Olivier Bachem, Mario Lucic, Olivier Bousquet, and Sylvain
Assessing generative models via precision and recall.In To Appear in Advances in Neural Information Processing Systems (NIPS), 2018.
- Lucic et al.  Mario Lucic, Karol Kurach, Marcin Michalski, Sylvain Gelly, and Olivier Bousquet. Are GANs Created Equal? A Large-scale Study. In To appear in Advances in Neural Information Processing Systems (NIPS), 2018.
- Barratt and Sharma  Shane Barratt and Rishi Sharma. A note on the inception score. arXiv preprint arXiv:1801.01973, 2018.
- Kurach et al.  Karol Kurach, Mario Lucic, Xiaohua Zhai, Marcin Michalski, and Sylvain Gelly. The GAN Landscape: Losses, architectures, regularization, and normalization. arXiv preprint arXiv:1807.04720, 2018.
- Zhou et al.  Zhiming Zhou, Yuxuan Song, Lantao Yu, and Yong Yu. Understanding the effectiveness of lipschitz constraint in training of gans via gradient analysis. arXiv preprint arXiv:1807.00751, 2018.
- Anonymous [2019b] Anonymous. Generating high fidelity images with subscale pixel networks and multidimensional upscaling. In Submitted to International Conference on Learning Representations (ICLR), 2019b. under review.
- Donahue et al.  Jeff Donahue, Philipp Krähenbühl, and Trevor Darrell. Adversarial feature learning. In International Conference on Learning Representations (ICLR), 2017.
- Caron et al.  Mathilde Caron, Piotr Bojanowski, Armand Joulin, and Matthijs Douze. Deep clustering for unsupervised learning of visual features. European Conference on Computer Vision (ECCV), 2018.
- Zenke et al.  Friedemann Zenke, Ben Poole, and Surya Ganguli. Continual learning through synaptic intelligence. In International Conference on Machine Learning (ICML), 2017.
- De Vries et al.  Harm De Vries, Florian Strub, Jérémie Mary, Hugo Larochelle, Olivier Pietquin, and Aaron C Courville. Modulating early visual processing by language. In Advances in Neural Information Processing Systems (NIPS), 2017.
- Agrawal et al.  Pulkit Agrawal, Joao Carreira, and Jitendra Malik. Learning to see by moving. In International Conference on Computer Vision (ICCV), 2015.
- Lee et al.  Hsin-Ying Lee, Jia-Bin Huang, Maneesh Singh, and Ming-Hsuan Yang. Unsupervised representation learning by sorting sequences. In International Conference on Computer Vision (ICCV), 2017.
- Jang et al.  Eric Jang, Coline Devin, Vincent Vanhoucke, and Sergey Levine. Grasp2vec: Learning object representations from self-supervised grasping. In Conference on Robot Learning (CoRL, 2018.
- Pinto and Gupta  Lerrel Pinto and Abhinav Gupta. Supersizing self-supervision: Learning to grasp from 50k tries and 700 robot hours. In Robotics and Automation (ICRA), 2016 IEEE International Conference on, 2016.
- Mundhenk et al.  T Nathan Mundhenk, Daniel Ho, and Barry Y Chen. Improvements to context based self-supervised learning. In Computer Vision and Pattern Recognition (CVPR), 2018.
- Noroozi and Favaro  Mehdi Noroozi and Paolo Favaro. Unsupervised learning of visual representations by solving jigsaw puzzles. In European Conference on Computer Vision (ECCV), 2016.
- Pathak et al.  Deepak Pathak, Philipp Krahenbuhl, Jeff Donahue, Trevor Darrell, and Alexei A Efros. Context encoders: Feature learning by inpainting. In Computer Vision and Pattern Recognition (CVPR), 2016.
- tfg  TFGAN: A lightweight library for generative adversarial networks, 2017. URL https://ai.googleblog.com/2017/12/tfgan-lightweight-library-for.html.
- Goyal et al.  Priya Goyal, Piotr Dollár, Ross Girshick, Pieter Noordhuis, Lukasz Wesolowski, Aapo Kyrola, Andrew Tulloch, Yangqing Jia, and Kaiming He. Accurate, large minibatch sgd: training imagenet in 1 hour. arXiv preprint arXiv:1706.02677, 2017.
Appendix A FID Metric Details
We compute the FID score using the protocol as decribed in . The image embeddings are extracted from an Inception V1 network provided by the TF library , We use the layer “pool_3”. We fit the multivariate Gaussians used to compute the metric to real samples from the test sets and fake samples. We use samples for celeba-hq and for the other datasets.
Appendix B SS-GAN Hyper-parameters
We compare different choices of , while fixing for simplicity. A reasonable value of helps aqa the generator to train using the self-supervision task, however, an inappropriate value of could bias the convergence point of the generator. Table 7 shows the effectiveness of . In the values compared, the optimal is 1 for cifar10, and 0.2 for imagenet. In our main experiments, we used for all datasets.
Appendix C Details for Scaling Up SS-GAN
We scale up SS-GAN to train on 128 cores of a Google TPU v3 Pod with a batch size of 1024. For the rotation-loss we use 512 rotated images from each batch. We use Orthogonal Initialization [saxe2013exact] instead of for initializing the weights in both generator and discriminator. We also find for of the Adam optimizer to work slightly better. We did not change the learning rate.
We use the variant of SS-GAN that incorporates self-modulated batch normalization. For the batch normalization we use a decay rate of 0.9 and epsilon set to . The batch statistics are computed across all cores.
Appendix D Representation Quality
d.1 Implementation Details
We train the linear evaluation models with batch size 128 and learning rate of following the linear scaling rule , for 50 epochs. The learning rate is decayed by a factor of 10 after epoch 30 and epoch 40. For data augmentation we resize the smaller dimension of the image to 146 and preserve the aspect ratio. After that we crop the image to . We apply a random crop for training and a central crop for testing. The model is trained on a single NVIDIA Tesla P100 GPU.
d.2 Additional Results
Table 8 shows the top-1 accuracy with on cifar10 with standard deviations. The results are stable on cifar10 as all the standard deviation is within 0.01. Table 9 shows the top-1 accuracy with on imagenet with standard deviations. Uncond-GAN representation quality shows large variance as we observe that the unconditional GAN collapses in some cases.
Figure 8 shows the representation quality on all 4 blocks on the cifar10 dataset. SS-GAN consistently outperforms other models on all 4 blocks. Figure 9 shows the representation quality on all 6 blocks on the imagenet dataset. We observe that all methods perform similarly before 500k steps on block0, which contains low level features. While going from block0 to block6, the conditional GAN and SS-GAN achieve much better representation results. The conditional GAN benefits from the supervised lables in layers closer to the classification head. However, the unconditional GAN attains worse result at the last layer and the rotation only model gets decreasing quality with more training steps. When combining the self-supervised loss and the adversarial loss, SS-GAN representation quality becomes stable and outperforms the other models.
Figure 10 and Figure 11 show the correlation between top-1 accuracy and FID score. We report the FID and top-1 accuracy from training steps 10k to 100k on cifar10, and 100k to 1M on imagenet. We evaluate models in total, where 10 is the number of training steps at which we evaluate and 3 is the number of random seeds for each run. The collapsed models with FID score larger than 100 are removed from the plot. Overall, the representation quality and the FID score is correlated for all methods on the cifar10 dataset. On imagenet, only SS-GAN gets better representation quality with better sample quality on block4 and block5.