Test note please ignore.
Under review as a conference paper at ICLR 2016
UNSUPERVISED REPRESENTATION LEARNING
WITH DEEP CONVOLUTIONAL
GENERATIVE ADVERSARIAL NETWORKS
Alec Radford & Luke Metz
indico Research
Boston, MA
{alec,luke}@indico.io
Soumith Chintala
Facebook AI Research
New York, NY
soumith@fb.com
ABSTRACT
In recent years, supervised learning with convolutional networks (CNNs) has
seen huge adoption in computer vision applications. Comparatively, unsupervised
learning with CNNs has received less attention. In this work we hope to help
bridge the gap between the success of CNNs for supervised learning and unsuper-
vised learning. We introduce a class of CNNs called deep convolutional generative
adversarial networks (DCGANs), that have certain architectural constraints, and
demonstrate that they are a strong candidate for unsupervised learning. Training
on various image datasets, we show convincing evidence that our deep convolu-
tional adversarial pair learns a hierarchy of representations from object parts to
scenes in both the generator and discriminator. Additionally, we use the learned
features for novel tasks - demonstrating their applicability as general image repre-
sentations.
1 INTRODUCTION
Learning reusable feature representations from large unlabeled datasets has been an area of active
research. In the context of computer vision, one can leverage the practically unlimited amount of
unlabeled images and videos to learn good intermediate representations, which can then be used on
a variety of supervised learning tasks such as image classification. We propose that one way to build
good image representations is by training Generative Adversarial Networks (GANs) (Goodfellow
et al., 2014), and later reusing parts of the generator and discriminator networks as feature extractors
for supervised tasks. GANs provide an attractive alternative to maximum likelihood techniques.
One can additionally argue that their learning process and the lack of a heuristic cost function (such
as pixel-wise independent mean-square error) are attractive to representation learning. GANs have
been known to be unstable to train, often resulting in generators that produce nonsensical outputs.
There has been very limited published research in trying to understand and visualize what GANs
learn, and the intermediate representations of multi-layer GANs.
In this paper, we make the following contributions
• We propose and evaluate a set of constraints on the architectural topology of Convolutional
GANs that make them stable to train in most settings. We name this class of architectures
Deep Convolutional GANs (DCGAN)
• We use the trained discriminators for image classification tasks, showing competitive per-
formance with other unsupervised algorithms.
• We visualize the filters learnt by GANs and empirically show that specific filters have
learned to draw specific objects.
1
arXiv:1511.06434v2 [cs.LG] 7 Jan 2016
Under review as a conference paper at ICLR 2016
• We show that the generators have interesting vector arithmetic properties allowing for easy
manipulation of many semantic qualities of generated samples.
2 RELATED WORK
2.1 REPRESENTATION LEARNING FROM UNLABELED DATA
Unsupervised representation learning is a fairly well studied problem in general computer vision
research, as well as in the context of images. A classic approach to unsupervised representation
learning is to do clustering on the data (for example using K-means), and leverage the clusters for
improved classification scores. In the context of images, one can do hierarchical clustering of image
patches (Coates & Ng, 2012) to learn powerful image representations. Another popular method
is to train auto-encoders (convolutionally, stacked (Vincent et al., 2010), separating the what and
where components of the code (Zhao et al., 2015), ladder structures (Rasmus et al., 2015)) that
encode an image into a compact code, and decode the code to reconstruct the image as accurately
as possible. These methods have also been shown to learn good feature representations from image
pixels. Deep belief networks (Lee et al., 2009) have also been shown to work well in learning
hierarchical representations.
2.2 GENERATING NATURAL IMAGES
Generative image models are well studied and fall into two categories: parametric and non-
parametric.
The non-parametric models often do matching from a database of existing images, often matching
patches of images, and have been used in texture synthesis (Efros et al., 1999), super-resolution
(Freeman et al., 2002) and in-painting (Hays & Efros, 2007).
Parametric models for generating images has been explored extensively (for example on MNIST
digits or for texture synthesis (Portilla & Simoncelli, 2000)). However, generating natural images
of the real world have had not much success until recently. A variational sampling approach to
generating images (Kingma & Welling, 2013) has had some success, but the samples often suffer
from being blurry. Another approach generates images using an iterative forward diffusion process
(Sohl-Dickstein et al., 2015). Generative Adversarial Networks (Goodfellow et al., 2014) generated
images suffering from being noisy and incomprehensible. A laplacian pyramid extension to this
approach (Denton et al., 2015) showed higher quality images, but they still suffered from the objects
looking wobbly because of noise introduced in chaining multiple models. A recurrent network
approach (Gregor et al., 2015) and a deconvolution network approach (Dosovitskiy et al., 2014) have
also recently had some success with generating natural images. However, they have not leveraged
the generators for supervised tasks.
2.3 VISUALIZING THE INTERNALS OF CNNS
One constant criticism of using neural networks has been that they are black-box methods, with little
understanding of what the networks do in the form of a simple human-consumable algorithm. In the
context of CNNs, Zeiler et. al. (Zeiler & Fergus, 2014) showed that by using deconvolutions and
filtering the maximal activations, one can find the approximate purpose of each convolution filter in
the network. Similarly, using a gradient descent on the inputs lets us inspect the ideal image that
activates certain subsets of filters (Mordvintsev et al.).
3 APPROACH AND MODEL ARCHITECTURE
Historical attempts to scale up GANs using CNNs to model images have been unsuccessful. This
motivated the authors of LAPGAN (Denton et al., 2015) to develop an alternative approach to it-
eratively upscale low resolution generated images which can be modeled more reliably. We also
encountered difficulties attempting to scale GANs using CNN architectures commonly used in the
supervised literature. However, after extensive model exploration we identified a family of archi-
2
Under review as a conference paper at ICLR 2016
tectures that resulted in stable training across a range of datasets and allowed for training higher
resolution and deeper generative models.
Core to our approach is adopting and modifying three recently demonstrated changes to CNN archi-
tectures.
The first is the all convolutional net (Springenberg et al., 2014) which replaces deterministic spatial
pooling functions (such as maxpooling) with strided convolutions, allowing the network to learn
its own spatial downsampling. We use this approach in our generator, allowing it to learn its own
spatial upsampling, and discriminator.
Second is the trend towards eliminating fully connected layers on top of convolutional features.
The strongest example of this is global average pooling which has been utilized in state of the
art image classification models (Mordvintsev et al.). We found global average pooling increased
model stability but hurt convergence speed. A middle ground of directly connecting the highest
convolutional features to the input and output respectively of the generator and discriminator worked
well. The first layer of the GAN, which takes a uniform noise distribution Z as input, could be called
fully connected as it is just a matrix multiplication, but the result is reshaped into a 4-dimensional
tensor and used as the start of the convolution stack. For the discriminator, the last convolution layer
is flattened and then fed into a single sigmoid output. See Fig. 1 for a visualization of an example
model architecture.
Third is Batch Normalization (Ioffe & Szegedy, 2015) which stabilizes learning by normalizing the
input to each unit to have zero mean and unit variance. This helps deal with training problems that
arise due to poor initialization and helps gradient flow in deeper models. This proved critical to get
deep generators to begin learning, preventing the generator from collapsing all samples to a single
point which is a common failure mode observed in GANs. Directly applying batchnorm to all layers
however, resulted in sample oscillation and model instability. This was avoided by not applying
batchnorm to the generator output layer and the discriminator input layer.
The ReLU activation (Nair & Hinton, 2010) is used in the generator with the exception of the output
layer which uses the Tanh function. We observed that using a bounded activation allowed the model
to learn more quickly to saturate and cover the color space of the training distribution. Within the
discriminator we found the leaky rectified activation (Maas et al., 2013) (Xu et al., 2015) to work
well, especially for higher resolution modeling. This is in contrast to the original GAN paper, which
used the maxout activation (Goodfellow et al., 2013).
Architecture guidelines for stable Deep Convolutional GANs
• Replace any pooling layers with strided convolutions (discriminator) and fractional-strided
convolutions (generator).
• Use batchnorm in both the generator and the discriminator.
• Remove fully connected hidden layers for deeper architectures.
• Use ReLU activation in generator for all layers except for the output, which uses Tanh.
• Use LeakyReLU activation in the discriminator for all layers.
4 DETAILS OF ADVERSARIAL TRAINING
We trained DCGANs on three datasets, Large-scale Scene Understanding (LSUN) (Yu et al., 2015),
Imagenet-1k and a newly assembled Faces dataset. Details on the usage of each of these datasets
are given below.
No pre-processing was applied to training images besides scaling to the range of the tanh activation
function [-1, 1]. All models were trained with mini-batch stochastic gradient descent (SGD) with
a mini-batch size of 128. All weights were initialized from a zero-centered Normal distribution
with standard deviation 0.02. In the LeakyReLU, the slope of the leak was set to 0.2 in all models.
While previous GAN work has used momentum to accelerate training, we used the Adam optimizer
(Kingma & Ba, 2014) with tuned hyperparameters. We found the suggested learning rate of 0.001,
to be too high, using 0.0002 instead. Additionally, we found leaving the momentum term β
1
at the
3
Under review as a conference paper at ICLR 2016
Figure 1: DCGAN generator used for LSUN scene modeling. A 100 dimensional uniform distribu-
tion Z is projected to a small spatial extent convolutional representation with many feature maps.
A series of four fractionally-strided convolutions (in some recent papers, these are wrongly called
deconvolutions) then convert this high level representation into a 64 × 64 pixel image. Notably, no
fully connected or pooling layers are used.
suggested value of 0.9 resulted in training oscillation and instability while reducing it to 0.5 helped
stabilize training.
4.1 LSUN
As visual quality of samples from generative image models has improved, concerns of over-fitting
and memorization of training samples have risen. To demonstrate how our model scales with more
data and higher resolution generation, we train a model on the LSUN bedrooms dataset containing
a little over 3 million training examples. Recent analysis has shown that there is a direct link be-
tween how fast models learn and their generalization performance (Hardt et al., 2015). We show
samples from one epoch of training (Fig.2), mimicking online learning, in addition to samples after
convergence (Fig.3), as an opportunity to demonstrate that our model is not producing high quality
samples via simply overfitting/memorizing training examples. No data augmentation was applied to
the images.
4.1.1 DEDUPLICATION
To further decrease the likelihood of the generator memorizing input examples (Fig.2) we perform a
simple image de-duplication process. We fit a 3072-128-3072 de-noising dropout regularized RELU
autoencoder on 32x32 downsampled center-crops of training examples. The resulting code layer
activations are then binarized via thresholding the ReLU activation which has been shown to be an
effective information preserving technique (Srivastava et al., 2014) and provides a convenient form
of semantic-hashing, allowing for linear time de-duplication . Visual inspection of hash collisions
showed high precision with an estimated false positive rate of less than 1 in 100. Additionally, the
technique detected and removed approximately 275,000 near duplicates, suggesting a high recall.
4.2 FACES
We scraped images containing human faces from random web image queries of peoples names. The
people names were acquired from dbpedia, with a criterion that they were born in the modern era.
This dataset has 3M images from 10K people. We run an OpenCV face detector on these images,
keeping the detections that are sufficiently high resolution, which gives us approximately 350,000
face boxes. We use these face boxes for training. No data augmentation was applied to the images.
4
Under review as a conference paper at ICLR 2016
Figure 2: Generated bedrooms after one training pass through the dataset. Theoretically, the model
could learn to memorize training examples, but this is experimentally unlikely as we train with a
small learning rate and minibatch SGD. We are aware of no prior empirical evidence demonstrating
memorization with SGD and a small learning rate.
Figure 3: Generated bedrooms after five epochs of training. There appears to be evidence of visual
under-fitting via repeated noise textures across multiple samples such as the base boards of some of
the beds.
4.3 IMAGENET-1K
We use Imagenet-1k (Deng et al., 2009) as a source of natural images for unsupervised training. We
train on 32 × 32 min-resized center crops. No data augmentation was applied to the images.
5
Under review as a conference paper at ICLR 2016
5 EMPIRICAL VALIDATION OF DCGANS CAPABILITIES
5.1 CLASSIFYING CIFAR-10 USING GANS AS A FEATURE EXTRACTOR
One common technique for evaluating the quality of unsupervised representation learning algo-
rithms is to apply them as a feature extractor on supervised datasets and evaluate the performance
of linear models fitted on top of these features.
On the CIFAR-10 dataset, a very strong baseline performance has been demonstrated from a well
tuned single layer feature extraction pipeline utilizing K-means as a feature learning algorithm.
When using a very large amount of feature maps (4800) this technique achieves 80.6% accuracy.
An unsupervised multi-layered extension of the base algorithm reaches 82.0% accuracy (Coates &
Ng, 2011). To evaluate the quality of the representations learned by DCGANs for supervised tasks,
we train on Imagenet-1k and then use the discriminator’s convolutional features from all layers,
maxpooling each layers representation to produce a 4 × 4 spatial grid. These features are then
flattened and concatenated to form a 28672 dimensional vector and a regularized linear L2-SVM
classifier is trained on top of them. This achieves 82.8% accuracy, out performing all K-means
based approaches. Notably, the discriminator has many less feature maps (512 in the highest layer)
compared to K-means based techniques, but does result in a larger total feature vector size due to
the many layers of 4 × 4 spatial locations. The performance of DCGANs is still less than that of
Exemplar CNNs (Dosovitskiy et al., 2015), a technique which trains normal discriminative CNNs
in an unsupervised fashion to differentiate between specifically chosen, aggressively augmented,
exemplar samples from the source dataset. Further improvements could be made by finetuning the
discriminator’s representations, but we leave this for future work. Additionally, since our DCGAN
was never trained on CIFAR-10 this experiment also demonstrates the domain robustness of the
learned features.
Table 1: CIFAR-10 classification results using our pre-trained model. Our DCGAN is not pre-
trained on CIFAR-10, but on Imagenet-1k, and the features are used to classify CIFAR-10 images.
Model Accuracy Accuracy (400 per class) max # of features units
1 Layer K-means 80.6% 63.7% (±0.7%) 4800
3 Layer K-means Learned RF 82.0% 70.7% (±0.7%) 3200
View Invariant K-means 81.9% 72.6% (±0.7%) 6400
Exemplar CNN 84.3% 77.4% (±0.2%) 1024
DCGAN (ours) + L2-SVM 82.8% 73.8% (±0.4%) 512
5.2 CLASSIFYING SVHN DIGITS USING GANS AS A FEATURE EXTRACTOR
On the StreetView House Numbers dataset (SVHN)(Netzer et al., 2011), we use the features of
the discriminator of a DCGAN for supervised purposes when labeled data is scarce. Following
similar dataset preparation rules as in the CIFAR-10 experiments, we split off a validation set of
10,000 examples from the non-extra set and use it for all hyperparameter and model selection. 1000
uniformly class distributed training examples are randomly selected and used to train a regularized
linear L2-SVM classifier on top of the same feature extraction pipeline used for CIFAR-10. This
achieves state of the art (for classification using 1000 labels) at 22.48% test error, improving upon
another modifcation of CNNs designed to leverage unlabled data (Zhao et al., 2015). Additionally,
we validate that the CNN architecture used in DCGAN is not the key contributing factor of the
model’s performance by training a purely supervised CNN with the same architecture on the same
data and optimizing this model via random search over 64 hyperparameter trials (Bergstra & Bengio,
2012). It achieves a signficantly higher 28.87% validation error.
6 INVESTIGATING AND VISUALIZING THE INTERNALS OF THE NETWORKS
We investigate the trained generators and discriminators in a variety of ways. We do not do any
kind of nearest neighbor search on the training set. Nearest neighbors in pixel or feature space are
6
Under review as a conference paper at ICLR 2016
Table 2: SVHN classification with 1000 labels
Model error rate
KNN 77.93%
TSVM 66.55%
M1+KNN 65.63%
M1+TSVM 54.33%
M1+M2 36.02%
SWWAE without dropout 27.83%
SWWAE with dropout 23.56%
DCGAN (ours) + L2-SVM 22.48%
Supervised CNN with the same architecture 28.87% (validation)
trivially fooled (Theis et al., 2015) by small image transforms. We also do not use log-likelihood
metrics to quantitatively assess the model, as it is a poor (Theis et al., 2015) metric.
6.1 WALKING IN THE LATENT SPACE
The first experiment we did was to understand the landscape of the latent space. Walking on the
manifold that is learnt can usually tell us about signs of memorization (if there are sharp transitions)
and about the way in which the space is hierarchically collapsed. If walking in this latent space
results in semantic changes to the image generations (such as objects being added and removed), we
can reason that the model has learned relevant and interesting representations. The results are shown
in Fig.4.
6.2 VISUALIZING THE DISCRIMINATOR FEATURES
Previous work has demonstrated that supervised training of CNNs on large image datasets results in
very powerful learned features (Zeiler & Fergus, 2014). Additionally, supervised CNNs trained on
scene classification learn object detectors (Oquab et al., 2014). We demonstrate that an unsupervised
DCGAN trained on a large image dataset can also learn a hierarchy of features that are interesting.
Using guided backpropagation as proposed by (Springenberg et al., 2014), we show in Fig.5 that the
features learnt by the discriminator activate on typical parts of a bedroom, like beds and windows.
For comparison, in the same figure, we give a baseline for randomly initialized features that are not
activated on anything that is semantically relevant or interesting.
6.3 MANIPULATING THE GENERATOR REPRESENTATION
6.3.1 FORGETTING TO DRAW CERTAIN OBJECTS
In addition to the representations learnt by a discriminator, there is the question of what representa-
tions the generator learns. The quality of samples suggest that the generator learns specific object
representations for major scene components such as beds, windows, lamps, doors, and miscellaneous
furniture. In order to explore the form that these representations take, we conducted an experiment
to attempt to remove windows from the generator completely.
On 150 samples, 52 window bounding boxes were drawn manually. On the second highest con-
volution layer features, logistic regression was fit to predict whether a feature activation was on a
window (or not), by using the criterion that activations inside the drawn bounding boxes are posi-
tives and random samples from the same images are negatives. Using this simple model, all feature
maps with weights greater than zero ( 200 in total) were dropped from all spatial locations. Then,
random new samples were generated with and without the feature map removal.
The generated images with and without the window dropout are shown in Fig.6, and interestingly,
the network mostly forgets to draw windows in the bedrooms, replacing them with other objects.
7
Under review as a conference paper at ICLR 2016
Figure 4: Top rows: Interpolation between a series of 9 random points in Z show that the space
learned has smooth transitions, with every image in the space plausibly looking like a bedroom. In
the 6th row, you see a room without a window slowly transforming into a room with a giant window.
In the 10th row, you see what appears to be a TV slowly being transformed into a window.
6.3.2 VECTOR ARITHMETIC ON FACE SAMPLES
In the context of evaluating learned representations of words (Mikolov et al., 2013) demonstrated
that simple arithmetic operations revealed rich linear structure in representation space. One canoni-
cal example demonstrated that the vector(”King”) - vector(”Man”) + vector(”Woman”) resulted in a
vector whose nearest neighbor was the vector for Queen. We investigated whether similar structure
emerges in the Z representation of our generators. We performed similar arithmetic on the Z vectors
of sets of exemplar samples for visual concepts. Experiments working on only single samples per
concept were unstable, but averaging the Z vector for three examplars showed consistent and stable
generations that semantically obeyed the arithmetic. In addition to the object manipulation shown
in (Fig. 7), we demonstrate that face pose is also modeled linearly in Z space (Fig. 8).
These demonstrations suggest interesting applications can be developed using Z representations
learned by our models. It has been previously demonstrated that conditional generative models can
learn to convincingly model object attributes like scale, rotation, and position (Dosovitskiy et al.,
2014). This is to our knowledge the first demonstration of this occurring in purely unsupervised
8
Under review as a conference paper at ICLR 2016
Figure 5: On the right, guided backpropagation visualizations of maximal axis-aligned responses
for the first 6 learned convolutional features from the last convolution layer in the discriminator.
Notice a significant minority of features respond to beds - the central object in the LSUN bedrooms
dataset. On the left is a random filter baseline. Comparing to the previous responses there is little to
no discrimination and random structure.
Figure 6: Top row: un-modified samples from model. Bottom row: the same samples generated
with dropping out ”window” filters. Some windows are removed, others are transformed into objects
with similar visual appearance such as doors and mirrors. Although visual quality decreased, overall
scene composition stayed similar, suggesting the generator has done a good job disentangling scene
representation from object representation. Extended experiments could be done to remove other
objects from the image and modify the objects the generator draws.
models. Further exploring and developing the above mentioned vector arithmetic could dramat-
ically reduce the amount of data needed for conditional generative modeling of complex image
distributions.
7 CONCLUSION AND FUTURE WORK
We propose a more stable set of architectures for training generative adversarial networks and we
give evidence that adversarial networks learn good representations of images for supervised learning
and generative modeling. There are still some forms of model instability remaining - we noticed as
models are trained longer they sometimes collapse a subset of filters to a single oscillating mode.
9
Under review as a conference paper at ICLR 2016
Figure 7: Vector arithmetic for visual concepts. For each column, the Z vectors of samples are
averaged. Arithmetic was then performed on the mean vectors creating a new vector Y . The center
sample on the right hand side is produce by feeding Y as input to the generator. To demonstrate
the interpolation capabilities of the generator, uniform noise sampled with scale +-0.25 was added
to Y to produce the 8 other samples. Applying arithmetic in the input space (bottom two examples)
results in noisy overlap due to misalignment.
Further work is needed to tackle this from of instability. We think that extending this framework
10
Under review as a conference paper at ICLR 2016
Figure 8: A ”turn” vector was created from four averaged samples of faces looking left vs looking
right. By adding interpolations along this axis to random samples we were able to reliably transform
their pose.
to other domains such as video (for frame prediction) and audio (pre-trained features for speech
synthesis) should be very interesting. Further investigations into the properties of the learnt latent
space would be interesting as well.
ACKNOWLEDGMENTS
We are fortunate and thankful for all the advice and guidance we have received during this work,
especially that of Ian Goodfellow, Tobias Springenberg, Arthur Szlam and Durk Kingma. Addition-
ally we’d like to thank all of the folks at indico for providing support, resources, and conversations,
especially the two other members of the indico research team, Dan Kuster and Nathan Lintz. Finally,
we’d like to thank Nvidia for donating a Titan-X GPU used in this work.
REFERENCES
Bergstra, James and Bengio, Yoshua. Random search for hyper-parameter optimization. JMLR,
2012.
Coates, Adam and Ng, Andrew. Selecting receptive fields in deep networks. NIPS, 2011.
Coates, Adam and Ng, Andrew Y. Learning feature representations with k-means. In Neural Net-
works: Tricks of the Trade, pp. 561–580. Springer, 2012.
Deng, Jia, Dong, Wei, Socher, Richard, Li, Li-Jia, Li, Kai, and Fei-Fei, Li. Imagenet: A large-scale
hierarchical image database. In Computer Vision and Pattern Recognition, 2009. CVPR 2009.
IEEE Conference on, pp. 248–255. IEEE, 2009.
Denton, Emily, Chintala, Soumith, Szlam, Arthur, and Fergus, Rob. Deep generative image models
using a laplacian pyramid of adversarial networks. arXiv preprint arXiv:1506.05751, 2015.
Dosovitskiy, Alexey, Springenberg, Jost Tobias, and Brox, Thomas. Learning to generate chairs
with convolutional neural networks. arXiv preprint arXiv:1411.5928, 2014.
11
Under review as a conference paper at ICLR 2016
Dosovitskiy, Alexey, Fischer, Philipp, Springenberg, Jost Tobias, Riedmiller, Martin, and Brox,
Thomas. Discriminative unsupervised feature learning with exemplar convolutional neural net-
works. In Pattern Analysis and Machine Intelligence, IEEE Transactions on, volume 99. IEEE,
2015.
Efros, Alexei, Leung, Thomas K, et al. Texture synthesis by non-parametric sampling. In Computer
Vision, 1999. The Proceedings of the Seventh IEEE International Conference on, volume 2, pp.
1033–1038. IEEE, 1999.
Freeman, William T, Jones, Thouis R, and Pasztor, Egon C. Example-based super-resolution. Com-
puter Graphics and Applications, IEEE, 22(2):56–65, 2002.
Goodfellow, Ian J, Warde-Farley, David, Mirza, Mehdi, Courville, Aaron, and Bengio, Yoshua.
Maxout networks. arXiv preprint arXiv:1302.4389, 2013.
Goodfellow, Ian J., Pouget-Abadie, Jean, Mirza, Mehdi, Xu, Bing, Warde-Farley, David, Ozair,
Sherjil, Courville, Aaron C., and Bengio, Yoshua. Generative adversarial nets. NIPS, 2014.
Gregor, Karol, Danihelka, Ivo, Graves, Alex, and Wierstra, Daan. Draw: A recurrent neural network
for image generation. arXiv preprint arXiv:1502.04623, 2015.
Hardt, Moritz, Recht, Benjamin, and Singer, Yoram. Train faster, generalize better: Stability of
stochastic gradient descent. arXiv preprint arXiv:1509.01240, 2015.
Hauberg, Sren, Freifeld, Oren, Larsen, Anders Boesen Lindbo, Fisher III, John W., and Hansen,
Lars Kair. Dreaming more data: Class-dependent distributions over diffeomorphisms for learned
data augmentation. arXiv preprint arXiv:1510.02795, 2015.
Hays, James and Efros, Alexei A. Scene completion using millions of photographs. ACM Transac-
tions on Graphics (TOG), 26(3):4, 2007.
Ioffe, Sergey and Szegedy, Christian. Batch normalization: Accelerating deep network training by
reducing internal covariate shift. arXiv preprint arXiv:1502.03167, 2015.
Kingma, Diederik P and Ba, Jimmy Lei. Adam: A method for stochastic optimization. arXiv
preprint arXiv:1412.6980, 2014.
Kingma, Diederik P and Welling, Max. Auto-encoding variational bayes. arXiv preprint
arXiv:1312.6114, 2013.
Lee, Honglak, Grosse, Roger, Ranganath, Rajesh, and Ng, Andrew Y. Convolutional deep belief
networks for scalable unsupervised learning of hierarchical representations. In Proceedings of the
26th Annual International Conference on Machine Learning, pp. 609–616. ACM, 2009.
Loosli, Ga
¨
elle, Canu, St
´
ephane, and Bottou, L
´
eon. Training invariant support vector machines using
selective sampling. In Bottou, L
´
eon, Chapelle, Olivier, DeCoste, Dennis, and Weston, Jason
(eds.), Large Scale Kernel Machines, pp. 301–320. MIT Press, Cambridge, MA., 2007. URL
http://leon.bottou.org/papers/loosli-canu-bottou-2006.
Maas, Andrew L, Hannun, Awni Y, and Ng, Andrew Y. Rectifier nonlinearities improve neural
network acoustic models. In Proc. ICML, volume 30, 2013.
Mikolov, Tomas, Sutskever, Ilya, Chen, Kai, Corrado, Greg S, and Dean, Jeff. Distributed repre-
sentations of words and phrases and their compositionality. In Advances in neural information
processing systems, pp. 3111–3119, 2013.
Mordvintsev, Alexander, Olah, Christopher, and Tyka, Mike. Inceptionism : Going
deeper into neural networks. http://googleresearch.blogspot.com/2015/06/
inceptionism-going-deeper-into-neural.html. Accessed: 2015-06-17.
Nair, Vinod and Hinton, Geoffrey E. Rectified linear units improve restricted boltzmann machines.
In Proceedings of the 27th International Conference on Machine Learning (ICML-10), pp. 807–
814, 2010.
12
Under review as a conference paper at ICLR 2016
Netzer, Yuval, Wang, Tao, Coates, Adam, Bissacco, Alessandro, Wu, Bo, and Ng, Andrew Y. Read-
ing digits in natural images with unsupervised feature learning. In NIPS workshop on deep learn-
ing and unsupervised feature learning, volume 2011, pp. 5. Granada, Spain, 2011.
Oquab, M., Bottou, L., Laptev, I., and Sivic, J. Learning and transferring mid-level image represen-
tations using convolutional neural networks. In CVPR, 2014.
Portilla, Javier and Simoncelli, Eero P. A parametric texture model based on joint statistics of
complex wavelet coefficients. International Journal of Computer Vision, 40(1):49–70, 2000.
Rasmus, Antti, Valpola, Harri, Honkala, Mikko, Berglund, Mathias, and Raiko, Tapani. Semi-
supervised learning with ladder network. arXiv preprint arXiv:1507.02672, 2015.
Sohl-Dickstein, Jascha, Weiss, Eric A, Maheswaranathan, Niru, and Ganguli, Surya. Deep unsuper-
vised learning using nonequilibrium thermodynamics. arXiv preprint arXiv:1503.03585, 2015.
Springenberg, Jost Tobias, Dosovitskiy, Alexey, Brox, Thomas, and Riedmiller, Martin. Striving for
simplicity: The all convolutional net. arXiv preprint arXiv:1412.6806, 2014.
Srivastava, Rupesh Kumar, Masci, Jonathan, Gomez, Faustino, and Schmidhuber, J
¨
urgen. Under-
standing locally competitive networks. arXiv preprint arXiv:1410.1165, 2014.
Theis, L., van den Oord, A., and Bethge, M. A note on the evaluation of generative models.
arXiv:1511.01844, Nov 2015. URL http://arxiv.org/abs/1511.01844.
Vincent, Pascal, Larochelle, Hugo, Lajoie, Isabelle, Bengio, Yoshua, and Manzagol, Pierre-Antoine.
Stacked denoising autoencoders: Learning useful representations in a deep network with a local
denoising criterion. The Journal of Machine Learning Research, 11:3371–3408, 2010.
Xu, Bing, Wang, Naiyan, Chen, Tianqi, and Li, Mu. Empirical evaluation of rectified activations in
convolutional network. arXiv preprint arXiv:1505.00853, 2015.
Yu, Fisher, Zhang, Yinda, Song, Shuran, Seff, Ari, and Xiao, Jianxiong. Construction of a large-scale
image dataset using deep learning with humans in the loop. arXiv preprint arXiv:1506.03365,
2015.
Zeiler, Matthew D and Fergus, Rob. Visualizing and understanding convolutional networks. In
Computer Vision–ECCV 2014, pp. 818–833. Springer, 2014.
Zhao, Junbo, Mathieu, Michael, Goroshin, Ross, and Lecun, Yann. Stacked what-where auto-
encoders. arXiv preprint arXiv:1506.02351, 2015.
13
Under review as a conference paper at ICLR 2016
8 SUPPLEMENTARY MATERIAL
8.1 EVALUATING DCGANS CAPABILITY TO CAPTURE DATA DISTRIBUTIONS
We propose to apply standard classification metrics to a conditional version of our model, evaluating
the conditional distributions learned. We trained a DCGAN on MNIST (splitting off a 10K validation
set) as well as a permutation invariant GAN baseline and evaluated the models using a nearest
neighbor classifier comparing real data to a set of generated conditional samples. We found that
removing the scale and bias parameters from batchnorm produced better results for both models. We
speculate that the noise introduced by batchnorm helps the generative models to better explore and
generate from the underlying data distribution. The results are shown in Table 3 which compares
our models with other techniques. The DCGAN model achieves the same test error as a nearest
neighbor classifier fitted on the training dataset - suggesting the DCGAN model has done a superb
job at modeling the conditional distributions of this dataset. At one million samples per class, the
DCGAN model outperforms InfiMNIST (Loosli et al., 2007), a hand developed data augmentation
pipeline which uses translations and elastic deformations of training examples. The DCGAN is
competitive with a probabilistic generative data augmentation technique utilizing learned per class
transformations (Hauberg et al., 2015) while being more general as it directly models the data instead
of transformations of the data.
Table 3: Nearest neighbor classification results.
Model Test Error @50K samples Test Error @10M samples
AlignMNIST - 1.4%
InfiMNIST - 2.6%
Real Data 3.1% -
GAN 6.28% 5.65%
DCGAN (ours) 2.98% 1.48%
Figure 9: Side-by-side illustration of (from left-to-right) the MNIST dataset, generations from a
baseline GAN, and generations from our DCGAN .
14
Under review as a conference paper at ICLR 2016
Figure 10: More face generations from our Face DCGAN.
15
Under review as a conference paper at ICLR 2016
Figure 11: Generations of a DCGAN that was trained on the Imagenet-1k dataset.
16
Test note please ignore.