Title: SEMI-SUPERVISED LEARNING WITH CONTEXT-CONDITIONAL GENERATIVE ADVERSARIAL NETWORKS

Abstract: We introduce a simple semi-supervised learning approach for images based on in-painting using an adversarial loss. Images with random patches removed are presented to a generator whose task is to fill in the hole, based on the surrounding pixels. The in-painted images are then presented to a discriminator network that judges if they are real (unaltered training images) or not. This task acts as a regularizer for standard supervised training of the discriminator. Using our approach we are able to directly train large VGG-style networks in a semi-supervised fashion. We evaluate on STL-10 and PASCAL datasets, where our approach obtains performance comparable or superior to existing methods.

1. INTRODUCTION:

Deep neural networks have yielded dramatic performance gains in recent years on tasks such as object classification (Krizhevsky et al., 2012 ), text classification (Zhang et al., 2015) and machine translation (Sutskever et al., 2014; Bahdanau et al., 2015) . These successes are heavily dependent on large training sets of manually annotated data. In many settings however, such large collections of labels may not be readily available, motivating the need for methods that can learn from data where labels are rare.

We propose a method for harnessing unlabeled image data based on image in-painting. A generative model is trained to generate pixels within a missing hole, based on the context provided by surrounding parts of the image. These in-painted images are then used in an adversarial setting (Goodfellow et al., 2014) to train a large discriminator model whose task is to determine if the image was real (from the unlabeled training set) or fake (an in-painted image). The realistic looking fake examples provided by the generative model cause the discriminator to learn features that generalize to the related task of classifying objects. Thus adversarial training for the in-painting task can be used to regularize large discriminative models during supervised training on a handful of labeled images.

1.1. RELATED WORK:

Learning From Context: The closest work to ours is the independently developed context-encoder approach of Pathak et al. (2016) . This introduces an encoder-decoder framework, shown in Fig. 1(a) , that is used to in-paint images where a patch has been randomly removed. After using this as a pre-training task, a classifier is added to the encoder and the model is fine-tuned using the labeled examples. Although both approaches use the concept of in-painting, they differ in several important ways. First, the architectures are different (see Fig. 1 ): in Pathak et al. (2016) , the features for the classifier are taken from the encoder, whereas ours come from the discriminator network. In practice this makes an important difference as we are able to directly train large models such as VGG (Simonyan & Zisserman, 2015) using adversarial loss alone. By contrast, Pathak et al. (2016) report difficulties in training an AlexNet encoder with this loss. This leads to the second difference, namely that on account of these issues, they instead employ an 2 loss when training models for classification and detection (however they do use a joint 2 and adversarial loss to achieve impressive in-painting results). Finally, the unsupervised learning task differs between the two models. The context-encoder learns a feature representation suitable for in-painting whereas our model learns a feature representation suitable for differentiating real/fake in-paintings. Notably, while we also use a neural network to generate the in-paintings, this model is only used as an adversary for the discriminator, rather than as a feature extractor. In section 4, we compare the performance of our model to the context-encoder on the PASCAL dataset.

Other forms of spatial context within images have recently been utilized for representation learning. Doersch et al. (2015) propose training a CNN to predict the spatial location of one image patch relative to another. Noroozi & Favaro (2016) propose a model that learns by unscrambling image patches, essentially solving a jigsaw puzzle to learn visual representations. In the text domain, context has been successfully leveraged as an unsupervised criterion for training useful word and sentence level representations (Collobert et al., 2011; Mikolov et al., 2015; Kiros et al., 2015) .

Deep unsupervised and semi-supervised learning: A popular method of utilizing unlabeled data is to layer-wise train a deep autoencoder or restricted Botlzmann machine (Hinton et al., 2006) and then fine tune with labels on a discriminative task. More recently, several autoencoding variants have been proposed for unsupervised and semi-supervised learning, such as the ladder network (Rasmus et al., 2015) , stacked what-where autoencoders (Zhao et al., 2016) and variational autoencoders (Kingma & Welling, 2014; Kingma et al., 2014) . Dosovitskiy et al. (2014) achieved state-of-the-art results by training a CNN with a different class for each training example and introducing a set of transformations to provide multiple examples per class. The pseudo-label approach (Lee, 2013 ) is a simple semi-supervised method that trains using the maximumly predicted class as a label when labels are unavailable. Springenberg (2015) propose a categorical generative adversarial network (CatGAN) which can be used for unsupervised and semi-supervised learning. The discriminator in a CatGAN outputs a distribution over classes and is trained to minimize the predicted entropy for real data and maximize the predicted entropy for fake data. Similar to our model, CatGANs use the feature space learned by the discriminator for the final supervised learning task. Salimans et al. (2016) recently proposed a semi-supervised GAN model in which the discriminator outputs a softmax over classes rather than a probability of real vs. fake. An additional 'generated' class is used as the target for generated samples. This method differs from our work in that it does not utilize context information and has only been applied to datasets of small resolution. However, the discriminator loss is similar to the one we propose and could be combined with our context-conditional approach.

More traditional semi-supervised methods include graph-based approaches (Zhou et al., 2004; Zhu, 2006) that show impressive performance when good image representations are available. However, the focus of our work is on learning such representations.

Generative models of images: Restricted Boltzmann machines (Salakhutdinov, 2015) , de-noising autoencoders (Vincent et al., 2008) and variational autoencoders (Kingma & Welling, 2014) optimize a maximum likelihood criterion and thus learn decoders that map from latent space to image space. More recently, generative adversarial networks (Goodfellow et al., 2014) and generative mo-ment matching networks (Li et al., 2015; Dziugaite et al., 2015) have been proposed. These methods ignore data likelihoods and instead directly train a generative model to produce realistic samples. Several extensions to the generative adversarial network framework have been proposed to scale the approach to larger images (Denton et al., 2015; Radford et al., 2016; Salimans et al., 2016) . Our work draws on the insights of Radford et al. (2016) regarding adversarial training practices and architecture for the generator network, as well as the notion that the discriminator can produce useful features for classification tasks.

Other models used recurrent approaches to generate images (Gregor et al., 2015; Theis & Bethge, 2015; Mansimov et al., 2016; van den Oord et al., 2016) . Dosovitskiy et al. (2015) trained a CNN to generate objects with different shapes, viewpoints and color. Sohl-Dickstein et al. (2015) propose a generative model based on a reverse diffusion process. While our model does involve image generation, it differs from these approaches in that the main focus is on learning a good representation for classification tasks.

Predictive generative models of videos aim to extrapolate from current frames to future ones and in doing so learn a feature representation that is useful for other tasks. In this vein, Ranzato et al. ( 2014) used an 2 -loss in pixel-space. Mathieu et al. (2015) combined an adversarial loss with 2 , giving models that generate crisper images. While our model is also predictive, it only considers interpolation within an image, rather than extrapolation in time.

2. APPROACH:

We present a semi-supervised learning framework built on generative adversarial networks (GANs) of Goodfellow et al. (2014) . We first review the generative adversarial network framework and then introduce context conditional generative adversarial networks (CC-GANs). Finally, we show how combining a classification objective and a CC-GAN objective provides a unified framework for semi-supervised learning.

2.1. GENERATIVE ADVERSARIAL NETWORKS:

The generative adversarial network approach (Goodfellow et al., 2014 ) is a framework for training generative models, which we briefly review. It consists of two networks pitted against one another in a two player game: A generative model, G, is trained to synthesize images resembling the data distribution and a discriminative model, D, is trained to distinguish between samples drawn from G and images drawn from the training data.

More formally, let X = {x 1 , ..., x n } be a dataset of images of dimensionality d. Let D denote a discriminative function that takes as input an image x ∈ R d and outputs a scalar representing the probability of input x being a real sample. Let G denote the generative function that takes as input a random vector z ∈ R z sampled from a prior noise distribution p Noise and outputs a synthesized image x = G(z) ∈ R d . Ideally, D(x) = 1 when x ∈ X and D(x) = 0 when x was generated from G. The GAN objective is given by:

EQUATION

The conditional generative adversarial network (Mirza & Osindero, 2014 ) is an extension of the GAN in which both D and G receive an additional vector of information y as input. The conditional GAN objective is given by:

EQUATION

2.2. CONTEXT-CONDITIONAL GENERATIVE ADVERSARIAL NETWORKS:

We propose context-conditional generative adversarial networks (CC-GANs) which are conditional GANs where the generator is trained to fill in a missing image patch and the generator and discriminator are conditioned on the surrounding pixels.

In particular, the generator G receives as input an image with a randomly masked out patch. The generator outputs an entire image. We fill in the missing patch from the generated output and then pass the completed image into D. We pass the completed image into D rather than the context and the patch as two separate inputs so as to prevent D from simply learning to identify discontinuities along the edge of the missing patch.

More formally, let m ∈ R d denote to a binary mask that will be used to drop out a specified portion of an image. The generator receives as input m x where denotes element-wise multiplication.

The generator outputs x G = G(m x, z) ∈ R d and the in-painted image x I is given by:

EQUATION

The CC-GAN objective is given by:

EQUATION

2.3. COMBINED GAN AND CC-GAN:

While the generator of the CC-GAN outputs a full image, only a portion of it (corresponding to the missing hole) is seen by the discriminator. In the combined model, which we denote by CC-GAN 2 , the fake examples for the discriminator include both the in-painted image x I and the full image x G produced by the generator (i.e. not just the missing patch). By combining the GAN and CC-GAN approaches, we introduce a wider array of negative examples to the discriminator. The CC-GAN 2 objective given by:

EQUATION

EQUATION

2.4. SEMI-SUPERVISED LEARNING WITH CC-GANS:

A common approach to semi-supervised learning is to combine a supervised and unsupervised objective during training. As a result unlabeled data can be leveraged to aid the supervised task.

Intuitively, a GAN discriminator must learn something about the structure of natural images in order to effectively distinguish real from generated images. Recently, Radford et al. (2016) showed that a GAN discriminator learns a hierarchical image representation that is useful for object classification. Such results suggest that combining an unsupervised GAN objective with a supervised classification objective would produce a simple and effective semi-supervised learning method. This approach, denoted by SSL-GAN, is illustrated in Fig. 1(b ). The discriminator network receives a gradient from the real/fake loss for every real and generated image. The discriminator also receives a gradient from the classification loss on the subset of (real) images for which labels are available.

Generative adversarial networks have shown impressive performance on many diverse datasets. However, samples are most coherent when the set of images the network is trained on comes from a limited domain (eg. churches or faces). Additionally, it is difficult to train GANs on very large images. Both these issues suggest semi-supervised learning with vanilla GANs may not scale well to datasets of large diverse images. Rather than determining if a full image is real or fake, context conditional GANs address a different task: determining if a part of an image is real or fake given the surrounding context.

Formally, let X L = {(x 1 , y 1 ), ..., (x n , y n )} denote a dataset of labeled images. Let D c (x) denote the output of the classifier head on the discriminator (see Fig. 1(c ) for details). Then the semisupervised CC-GAN objective is:

min G max D E x∼X [log D(x)] + E x∼X ,m∼M [log(1 -D(x I ))] + λ c E x,y∼X L [log(D c (y|x))] (8)

The hyperparameter λ c balances the classification and adversarial losses. We only consider the CC-GAN in the semi-supervised setting and thus drop the SSL notation when referring to this model.

2.5. MODEL ARCHITECTURE AND TRAINING DETAILS:

The architecture of our generative model, G, is inspired by the generator architecture of the DCGAN (Radford et al., 2016) . The model consists of a sequence of convolutional layers with subsampling (but no pooling) followed by a sequence of fractionally-strided convolutional layers. For the discriminator, D, we used the VGG-A network (Simonyan & Zisserman, 2015) without the fully connected layers (which we call the VGG-A' architecture). Details of the generator and discriminator are given in Fig. 2 . The input to the generator is an image with a patch zeroed out. In preliminary experiments we also tried passing in a separate mask to the generator to make the missing area more explicit but found this did not effect performance.

Even with the context conditioning it is difficult to generate large image patches that look realistic, making it problematic to scale our approach to high resolution images. To address this, we propose conditioning the generator on both the high resolution image with a missing patch and a low resolution version of the whole image (with no missing region). In this setting, the generators task becomes one of super-resolution on a portion of an image. However, the discriminator does not receive the low resolution image and thus is still faced with the same problem of determining if a given in-painting is viable or not. Where indicated, we used this approach in our PASCAL VOC 2007 experiments, with the original image being downsampled by a factor of 4. This provided enough information for the generator to fill in larger holes but not so much that it made the task trivial. This optional low resolution image is illustrated in Fig. 2 (left) with the dotted line.

We followed the training procedures of Radford et al. (2016) . We used the Adam optimizer (Kingma & Ba, 2015) in all our experiments with learning rate of 0.0002, momentum term β 1 of 0.5, and the remaining Adam hyperparameters set to their default values. We set λ c = 1 for all experiments.

Method Accuracy Multi-task Bayesian Optimization (Swersky et al., 2013) 70.10 ± 0.6 Exemplar CNN (Dosovitskiy et al., 2014) 75.40 ± 0.3 Stacked What-Where Autoencoder (Zhao et al., 2016) 74 

3. EXPERIMENTS:

3.1 STL-10 CLASSIFICATION STL-10 is a dataset of 96×96 color images with a 1:100 ratio of labeled to unlabeled examples, making it an ideal fit for our semi-supervised learning framework. The training set consists of 5000 labeled images, mapped to 10 pre-defined folds of 1000 images each, and 100,000 unlabeled images. The labeled images belong to 10 classes and were extracted from the ImageNet dataset and the unlabeled images come from a broader distribution of classes. We follow the standard testing protocol and train 10 different models on each of the 10 predefined folds of data. We then evaluate classification accuracy of each model on the test set and report the mean and standard deviation.

We trained our CC-GAN and CC-GAN 2 models on 64×64 crops of the 96×96 image. The hole was 32×32 pixels and the location of the hole varied randomly (see Fig. 3(top) ). We trained for 100 epochs and then fine-tuned the discriminator on the 96x96 labeled images, stopping when training accuracy reached 100%. As shown in Table 1 , the CC-GAN model performs comparably to current state of the art (Dosovitskiy et al., 2014) and the CC-GAN 2 model improves upon it.

We also trained two baseline models in an attempt to tease apart the contributions of adversarial training and context conditional adversarial training. The first is a purely supervised training of the VGG-A' model (the same architecture as the discriminator in the CC-GAN framework). This was trained using a dropout of 0.5 on the final layer and weight decay of 0.001. The performance of this model is significantly worse than the CC-GAN model.

We also trained a semi-supervised GAN (SSL-GAN, see Fig. 1 (b)) on STL-10. This consisted of the same discriminator as the CC-GAN (VGG-A' architecture) and generator from the DCGAN model (Radford et al., 2016) . The training setup in this case is identical to the CC-GAN model. The SSL-GAN performs almost as well as the CC-GAN, confirming our hypothesis that the GAN objective is a useful unsupervised criterion.

3.2. PASCAL VOC CLASSIFICATION:

In order to compare against other methods that utilize spatial context we ran the CC-GAN model on PASCAL VOC 2007 dataset. This dataset consists of natural images coming from 20 classes. The dataset contains a large amount of variability with objects varying in size, pose, and position. The training and validation sets combined contain 5,011 images, and the test set contains 4,952 images. The standard measure of performance is mean average precision (mAP).

We trained each model on the combined training and validation set for ∼5000 epochs and evaluated on the test set once1 . Following Pathak et al. (2016) , we train using random cropping, and then evaluate using the average prediction from 10 random crops.

Our best performing model was trained on images of resolution 128×128 with a hole size of 64×64 and a low resolution input of size 32×32. in-paintings and the discriminator performs comparable to or better than existing semi-supervised methods on two classification benchmarks.

discrimination of real/fake in-paintings is more closely related to the target task of object classification than extracting a feature representation suitable for in-filling, it is not surprising that we are able to exceed the performance of Pathak et al. (2016) on PASCAL classification. Furthermore, since our model operates on images half the resolution as those used by other approaches (128×128 vs. 224×244), there is potential for further gains if improvements in the generator resolution can be made. Our models and code are available at https://github.com/edenton/cc-gan.

:

Hyperparameters were determined by initially training on the training set alone and measuring performance on the validation set.

Figures and Tables:

Figure 1: (a) Context-encoder of Pathak et al. (2016), configured for object classification task. (b) Semi-supervised learning with GANs (SSL-GAN). (c) Semi-supervised learning with CC-GANs. In (a-c) the blue network indicates the feature representation being learned (encoder network in the context-encoder model and discriminator network in the GAN and CC-GAN models).

Figure 2: Architecture of our context-conditional generative adversarial network (CC-GAN). conv(64, 4x4, 2x2) denotes a conv layer with 64 channels, 4x4 kernels and stride 2x2. Each convolution layer is followed by a spatial batch normalization and rectified linear layer. Dashed lines indicate optional pathways.

Figure 3: STL-10 in-painting with CC-GAN training and varying methods of dropping out the image.

Figure 4: STL-10 in-painting with combined CC-GAN 2 training.

Figure 5: PASCAL in-painting with CC-GAN.

Figure 6: PASCAL in-painting with CC-GAN conditioned on low resolution image. Top two rows show input to generator. Third row shows inpainting my bilinear upsampling. Bottom row shows inpainted image by generator.

Comparison of CC-GAN and other published results on STL-10.

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Table 2 compares our CC-GAN method to other feature learning approaches on the PASCAL test set. It outperforms them, beating the current state of the art(Wang & Gupta, 2015) by 3.8%. It is important to note that our feature extractor is the VGG-A' model which is larger than the AlexNet architecture(Krizhevsky et al., 2012) used by other approaches in Table2. However, purely supervised training of the two models reveals that VGG-A'

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Peer review (iclr2017):
This paper presents a semi-supervised algorithm for regularizing deep convolutional neural networks. They propose an adversarial approach for image inpainting where the discriminator learns to identify whether an inpainted image comes from the data distribution or the generator, while at the same time it learns to recognize objects in an image from the data distribution. In experiments, they show the usefulness of their algorithm in which the features learned by the discriminator result in comparable or better object recognition performance to the reported state-of-the-art in two datasets. Overall, the proposed idea seems a simple yet an effective way for regularize CNNs to improve the classification performance.