Improving Model Compatibility of Generative Adversarial Networks by Boundary Calibration
Authors: Si-An Chen
Chun-Liang Li
Hsuan-Tien Lin
Venue:  (2020)
Keywords: generative adversarial network
GAN
model compatibility
machine learning efficacy

Abstract: Generative Adversarial Networks (GANs) is a powerful family of models that learn an underlying distribution to generate synthetic data. Many existing studies of GANs focus on improving the realness of the generated image data for visual applications, and few of them concern about improving the quality of the generated data for training other classifiers---a task known as the model compatibility problem. As a consequence, existing GANs often prefer generating `easier' synthetic data that are far from the boundaries of the classifiers, and refrain from generating near-boundary data, which are known to play an important roles in training the classifiers. To improve GAN in terms of model compatibility, we propose Boundary-Calibration GANs (BCGANs), which leverage the boundary information from a set of pre-trained classifiers using the original data. In particular, we introduce an auxiliary Boundary-Calibration loss (BC-loss) into the generator of GAN to match the statistics between the posterior distributions of original data and generated data with respect to the boundaries of the pre-trained classifiers. The BC-loss is provably unbiased and can be easily coupled with different GAN variants to improve their model compatibility. Experimental results demonstrate that BCGANs not only generate realistic images like original GANs but also achieves superior model compatibility than the original GANs.

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IMPROVING MODEL COMPATIBILITY OF GENERATIVE ADVERSARIAL NETWORKS BY BOUNDARY CALIBRATION
Anonymous authors Paper under double-blind review
ABSTRACT
Generative Adversarial Networks (GANs) is a powerful family of models that learn an underlying distribution to generate synthetic data. Many existing studies of GANs focus on improving the realness of the generated image data for visual applications, and few of them concern about improving the quality the gener- ated data for training other classifiers-a task known the model compatibility problem. Literature also show that some GANs often prefer generating 'easier' synthetic data that far from the boundaries of the classifiers, and refrain from generating near- near-boundary data, which are known to play an important roles training the classifiers. To improve GAN in terms of model compatibility, we propose Coundary-Calibratinn information from set of pre-trained classifiers using the original data. In par- ticular, we introduce an auxiliary Boundary-Calibrude generator of GAN match the statistics between the posterior distributions of original data and generated data with respect to the boundaries of the pre-trained classifiers. The BC-loss is provably unbiased and can be easily coupled with dif- ferent GAN variants to improve their model compatibility. Experimental results demonstrate that BCGANs not only generate realistic images like original GANs but also achieves superior model compatibility than the original GANs.
GANs (BCGANs), which leverage the boundary
loss (BC-loss) into the
INTRODUCTION
The success of machine learning relies on not only the advances of different models (e.g. deep learning) but also data with sufficient quality and quantity. Nowadays, companies spend tremendous efforts and expense collecting data to build their products. To better solve complicated real-world problems with public or third-party machine learning experts, many companies now needs release mroof-of-conceyy purposes. However, considering
some data sets for competitions (e.g. Kaggle) the costs of collecting data, companies may not willing to release the dataset possible. As a result, technique which can generate synthetic data with properties similar to the original data is in demand. To be specific, we are looking for generating a dataset with the property that machine learning models trained on the generated dataset can exhibit similar performance to ones trained on the original data. This property is called model compatibility (Park et al. 2011)) or machine learning efficacy (Xu et al. 2019). The organizations can share the generated data with high model compatibility to the public and enjoy the solution derived from it without leaking the real dataset.
When it comes to data generation, generative adversarial networks (GANs, Goodfellow et al. 2014) is the most popular family of generative algorithms because of its impressive performance on gen- erating realistic images (Karras al., 2018). In GANs, the generator is trained via minimizing a neural network (discriminator) defined probability divergence (Goodfellow et al.) 2014 Arjovsky ct al. 2017 Nowozin et al. 2016). In addition to image generation, GANs are also widely used in other applications, such style transfer (Isola et al.| 2017 Zhu et al., 2017 Kim et al.) 2017) and image processing (Pathak et al. 2016 Ledig et al. 2017: Chang et al. (017)) and generating differ-
ent types of data. including time series (Luo et al. 2018 Chang al.
2019 text Yu et al. 2017
Press et al. 2017), point clouds (Li et al. 2018), 3) voxels (Wu et al." 2016 and tabular data PPak
al. 2018
Xu al. 2019)

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Although GANs are versatile mentioned above, most of their development focus the metrics such as quality and diversity of the data Salimans et al. (2016); Heusel et al.] (2017); Lucic et al. (0118) Generating high model compatibility data via GANs is still under explored. The pioneering
work (uu et al., 2019) first shows that data generated from conditional GANs (Mirza & Osindero,
2014) enjoys better model compatibility than VAEs (Kingma & Welling, 2013). So wonder can we improve the model compatibility if we consider information from the models trained on the original data? For example, Wasserstein GAN (WGAN, Arjovsky al. 2017) performs mean- matching between the distribution of real data and generated data. However, only mean- matahhnt is sometimes not enough to learn the whole distribution especially for those boundary cases. Appar- ently, if a GAN knows the boundary between different classes, it may be able to generate instances which are close to the boundary with correct labels. These boundary points will guide a classifier to learn the correct decision boundary.
In this work, we try to improve GANs with regards to model compatibility in classification problems. We use set of pre-trained classifiers obtain multiple decision boundaries. Then use auxiliary loss function called Boundary-Calitn Calibration loss (BC-loss) to calibrate the generating distribution according to the decision boundaries of these pre-trained classifiers. The main contributions of this work are:
In Section 2 we propose a way to evaluate model compatibility in classification problems. We consider variety of machine learning algorithms and average the performance to ob- tain a comprehensive metric.
In Section we propose a loss function called helps typical GANs to learn distribution with better model compatibility. The loss siders the decision boundaries of pre-trained classifiers and minimizes the maximum mean discrepancy (MMD, Gretton al. 2012) between the original dataset and the generated dataset. In addition, we show that optimizing the BC-loss would not change the optimal solution of the original GAN, but reduces the feasible set ensure the model compati- bility.
loss (BC-loss) which
In Section we demonstrate how BC-loss affects the boundary of the generated data with a two-dimensional toy dataset. We also show that the BC-loss improves model compatibility of the generated data with different types of classifiers and a variety of datasets. Finally, we inspect the feature selection results to examine how the interpretation of machine learning models may be effected.
Last, in Section 3] we discuss some works which are similar to our work and describe how does our work differ from them.
2 MODEL COMPATIBILITY IN CLASSIFICATION
In this work, we focus on generating data for fully supervisdd classification learning. Given a dataset
D {(z;, V: [.)] Im i== where the corresponding label of æ; according f X' + y, and 94) ~ PD. a learning algorithm A (X, - H learns hypothesis h H. to approximate the mapping function, i.e. A(D) h f- Our goal is to obtain a generator which generates a synthetic dataset D' = {x' v/ } such that A(D') = M Rv h. We call this property model compatibility as proposed in Park et al. 2018).
X represents features of an instance, y/ f(x:) E y represents
To measure the model compatibility of generated dataset quantitatively, we consider the perfor- mance of classifier trained on the generated dataset comparing to the one trained on the real dataset. We evaluate the accuracy on separate test dataset to indicate the performance of a given classifier. In addition, we calculate relative accuracy by scaling the test accuracy of the classifier trained on the generated dataset by the accuracy of the classifier trained on the real dataset. The relative accuracy allows us to average the results from different machine learning algorithms more fairly. The final evaluation is:
(achh'D(9)) aco(h, D(()) AEA
(1)
A
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where A is set of learning algorithms, D {(u,,) Vi ) is the test dataset, and acc(h, D(O) the accuracy of hypothesis on test data D We can determine A as a wide variety of learning algorithms to make the metric provide a more comprehensive measurement of model compatibility.
3 RELATED WORK
Research about generating data for classification can be divided into two categories: formulation and architecture. For formulation, Conditional GAN (CGAN, Mirza & Osindero 2014) ) is an intuitive way to generate instances with corresponding labels. We can learn the distribution of labels by counting and sample the instances from CGAN conditionally. Auxiliary Classifier GAN (ACGAN, Odena et al.) 2017) considered as better way for conditional generation. It uses an auxiliary classifier to provide information about the boundary between each classes. However, ACGAN has been proved that the objective is biased so it tends to generate data with lower entropy for the auxiliary classifier (Shu et al. 2017). Thus, the lose of instances near the decision boundary may worsen the model compatibility. In this work, we use CGAN along with the proposed BC-loss to generate data with model compatibility.
On the other hand, the other line of research focuses on generating data with different network archi- tecture or data processing procedure. Recent works that also consider model compatibility are Table GAN (Park et al.) 2018) and Tabular GAN (Xu et al., 2019). Table GAN focuses on the privacy of generated data and thus their is trade off between privacy and model compatibility. To achieve privacy preserving. they do not improve the model compatibility compared to the original GAN. On the other hand, Tabular GAN puts emphasis on increasing model compatibility of generated data. They propose a framework with a more complicated data processing procedure and use LSTM to better parameterize the target distribution. In contrast these works, our work focus on the formu- lation of GANs and can be applied to most variants of GANs, including Table-GAN and Tabular GAN. Moreover, while these former works only focus on tabular data, our BC-loss is applicable to generate image datasets as well.
Some GAN variants are named similarly to our work but they pay attention different problems. For example, the boundary described in boundary-seeking GAN (Hjelm et al. 2017) means the de- cision boundary of the discriminator rather than the decision boundary for the supervised labels. To the best of our knowledge, we are the first work trying to improve model compatibility by modifying the formulation of GANs.
BOUNDARY-CALIBRATUN GAN
To achieve better model compatibility of GAN, we propose an auxiliary GAN loss which we call loss (or BC-loss). We assume that we have set of pre-trained classifiers which are well-trained on the original dataset. The BC-loss helps GANs to calibrate the distribution with respect to the distribution of decision values predicted by pre-trained classifiers. The calibra- tion leads to more accurate data generation near the decision boundary and thus enabling a machine learning algorithm to learn a similar hypothesis to one that learns from the original dataset. To case the complexity of learning to generate (æ, y) jointly, we infer P(y) by counting the proportion of each class in the original dataset and train a conditional generator G such that G(z, y) ~ Px|=- where Pxt is the conditional data distribution and ~ Pz is the initial randomness such Gaus- sian distribution. Therefore
generate (I., y) by sampling y P(y) and G( v).
4.1 BOUNDARY CALIBRATION
Given a pre-trained classifier C, we hope the generated dataset will adopt the same statistics as the original dataset while considering the decision boundary of C. To include the information about the boundary, we calculate posterior Po(y æ;;) from the decision values predicted by the classifier. In practice, we can apply a softmax function to the outputs of a classifier to obtain the posterior. The posterior provides information of an instance from the classifier's rs aspect. Therefore, given the real dataset X = {x1, Ø2, ..., Dn), we can obtain a set of posterior vector C(X) = (Po(y x Pc 222)... Po(y x.))). To generate data X' with the same distribution of posteriors to the boundary,
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match the statisties of C(X) and C(X)) by optimizing distance M:
CB (X, C) = M(C(X),((X))
(2)
Here M can be any distance metric which measures the distance between two sets of samples. In statistics, distinguishing whether two sets of samples are from the same distribution is called Two- Sample Test. A classical solution two-sample Gretton et al. (012). The idea is to compare the statistics between the two sets of samples. the statistics are similar then these two sets might be sampled from the same distribution. Given two sets of samples X {æi and Y = {y, an unbiased estimator of MMD with kernel is defined as:
is kernel maximum mean discrepancy (MMD,
Mx Σ mp) mp)
2
Σ k( Us)
Σ Uy) j#9
In practice, we use Gaussian kernel k(æ, x²) = exp x 22 in MMD since Gaussian kernel is characteristic kernel which ensures that the distance zero if and only if the two distributions the same (Gretton et al.) 2012).
The BC-loss can be applied in generator of any GAN variants to improve the model compatibility. In addition, to better fit the real unknown boundary, we can use multiple classifiers to calibrate the distributions from different aspects. As result, for a loss function of generator Ca, we can modify the loss to be:
LG = La
M((C(())
CEC
where Z is a set of noises, C a set pre-trained classifiers and a hyper-parameter to control the weight of Bo-loss.
4.2 ANALYSIS OF OPTIMAL SOLUTION
Next we prove that adding our proposed BC-loss would not change the optimal solution of the original objective. Here we assume the loss of the generator LG achieves its optimal value in the its GAN objectives Le if and only if the distribution of G(z, y) recovers Px for all y E V, which holds for the vanilla GAN (Goodfellow et 2014) and most of other GAN variants.
Theorem (Gretton et al. 2012). Given kernel k if is characteristic kernel, then M&
P P=Q.
Theorem (Equivalence of optimal solution). G is an optimal solution of LG = G is an optimal solution of La
Proof. (=) According to the assumption, G' is an optimal solution of Le implies G(Z, y) recovers
Pxly for all E y. Therefore, Pa(x) = Po(a(z,y)) and Ma(Pe(x), PeIc(z,))) = 0 by Theo- rem Now La La + LG and G is an optimal solution of La, so G is also an optimal solution of Lc.
(+) Since LBC 2 0, we have LG = La + LBC 2 Lg. From above, we know LG(G) = 0 if G = Px. Thus, for an optimal solution G*, 0 2 Lo(G") > Lo(G*) 2 0, which implies La(G)) LG O. Therefore, G is also optimal solution of Lg-
The proof shows that the proposed BC-loss does not change the optimal solution of the original optimization problem. However, we can consider BC-loss Lagrangian constraint which restricts the solution to subspace where the generator owns higher model compatibility.
4.3 COMPARISON TO MMD GAN
MMD GAN Li et al. 2017) is a variant GAN where the generator tries to minimize the MMD between generated data and original data and the discriminator learns kernel which maximizes the MMD. Though the formulation of MMD GAN and BC-loss are similar, they still do not con- flict because MMD GAN do not known the information about the classifier and the objective of
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(a) Real accuracy 0.995
ACGAN accuracy 0.932
WGAN accuracy 0.979
BWGAN (proposed) accuracy 0.984
Figure 1: A toy dataset generated by different GAN methods. Figure (a) is the original training data and the others are data generated by ACGAN, WGAN and our BWGAN respectively. The background color indicates the decision boundary of a random forest trained on corresponding data. The captions show the test accuracy of the random forest.
MMD GAN would not lead the discriminator to classifier. Therefore, BC-loss may still improve MMD GAN by guiding the generator to not generate points across the boundary. To understand the improvement in MMD GAN from BC-loss, use MMD GAN one of the baselines in our experiments.
EXPERIMENTS
In this section, we use a toy dataset to illustrate how the proposed method improves the model compatibility. To be more realistic, provide more comprehensive results for four different real- world dataset from UCT dataset repository (Dua & Graff, 2017): Adult, Connect-4, Covertype and Sensorless. We then show method is also applicable in image dataset: MNIST and Cifar10 without losing the image quality. addition, we investigate the results of feature selections on the generated dataset to whether the generated data preserve the interpretation of machine learning models.
5.1 EXPERIMENTAL SETTINGS
EVALUATION
In this work, we focus on model compatibility of generated datasets. We use a wide variety of machine learning algorithms including linear SVM, decision tree (DT), random forest (RF), and
multi-layer perception (MLP) to evaluate the model compatibility. As described in Section 2 we evaluate the relative accuracy for each type of machine learning model, where the relative accuracy is calculated by dividing the accuracy of classifier trained on generated data to the accuracy of classifier trained on original data.
COMPARED METHODS
We take Wasserstein GAN (WGAN) and MMD GAN baselines to evaluate the effective- ness of the proposed boundary-calibratie technique. We denotes their counterparts with BC-loss BWGAN and BMMDGAN respectively. All of the methods
gradient penalty to enforce the Lipschitz constraint on the discriminator (Gulrajani et al.) 2017; Li et al.) 2017). To achieve condi- tional data generation described in Section 4 add an embedding layer to learn the embedding vector for each class. The embedding vector Is concatenated as additional input features for both generators and discriminators on UCI datasets. For image datasets, the embedding vectors are used as described in Mirza & Osindero 2014).
5.2
2D TOY DATASET
We use a 2D toy dataset with two classes to illustrate the results generated by different GAN methods in Figure I Figure 2a shows the distribution of the original training data. We use these generated data to tram a random forest and depict the decision boundary by different background color. From Figure 2h
see that although ACGAN make use of the auxiliary classifier during training.

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Table Summary result of model compatibility evaluate on UCI datasets. The numbers are relative accuracy.
adult
connect4
covertype
sensorless
average
ACGAN
97.78
83.71
51.98
77.47
77.74
WGAN
96.60
87.59
79.56
84.63
87.10
BWGAN
98.79
88.95
83.16
93.34
91.06
MMDGAN
95.67
86.29
77.14
86.28
86.35
BMMDGAN
97.23
87.38
79.82
88.14
88.14
(a) Real mislabeled 0.8%
(b) ACGAN mislabeled = 12.57%
(c) WGAN mislabeled = 9.35%
(d) BWGAN (proposed) mislabeled=7.39%%
Figure 2D visualization of real and generated Sensorless dataset. The mislabeled points are emphasized with border lines. The background color indicates the spaces of each class according to the projection classifier.
learns a biased distribution that push the generated data away from the boundary. The large margin between the two clusters brings more uncertainty to the decision boundary and thus leads to worse test accuracy. In Figure 2c WGAN approximates the original distribution well in the center part of the two cluster, but do not get clear boundary between the two classes. It generates some ambiguous points near the boundary that would confuse the classifier. Finally, our BWGAN generates points near the boundary
precisely, shown in Figure
5.3
UCI DATASET
We evaluate our proposed BC-GAN on four datasets from UCI repository. The attributes of the datasets can be found in Appendix A Discrete features are processed to one-hot encoding and con- tinuous features are scaled to [0, 1I. For each dataset, we train six multi-layer perceptrons with random split of half of training data as pre-trained classifiers. In these experiments, generators and discriminators are consist of 3 cally-connected hidden layer with 128 units. A logistic function is applied to the output layer of generators to generate features within 0 and 1. The weight of BC-loss is set to be X = 100 for all datasets.
Table T summarize the comparison between different methods. We calculate the relative accuracy of different machine learning models mentioned in Section [5.1 and average the relative accuracy indicate the model compatibility generated data for each dataset. The table shows that the proposed BC-loss improves the accuracy of classifiers generally compared to original WGAN and MMD GAN. Moreover, ACGAN performs worst on three out of four datasets and exhibit signifi- cant deficiency though it is proved to have the state-of-the-ee generation quality. This again prove that the biased objective ACGAN worsen the model compatibility seriously. The breakdown re- sults and real accuracy are provided in Appendix B
Noundary-callbratinn we visualize the generated results of Sensorless in Figure We train fully-connected neural network with 2-units hidden layer before the output layer to project the generated samples to a 2-dimensional embedding space. The projec- tion classifier is well-trained and achieves over 99% testing accuracy so we can use it to determine whether sample is generated with incorrect label. The figure shows that there are less mislabeled data generated by BWGAN, especially at the center and the bottom-let region. The fact indicates that boundary-callla callbraaiooiiiiiinnnnnoooaoooooc helps GANs generate labeled data more accurately, which may lead to the improvement of classification accuracy.
To further investigate the advantage

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Table 2: Precision at of feature importance ranking compared to the feature importance ranking obtained from the original dataset
REAL
ACGAN
WGAN
BWGAN
MMDGAN
BMMDGAN
dataset
metric
adult
P@ 10
0.80
0.40
0.80
0.80
0.80
0.70
P@20
0.95
0.45
0.75
0.80
0.85
0.75
P@ 30
1.00
0.63
0.90
0.90
0.87
0.87
connect4
P@ 10
0.90
0.30
1.00
1.00
0.90
0.80
P@
0.90
0.35
0.90
0.85
0.95
0.85
P@ 30
0.93
0.33
0.83
0.90
0.77
0.83
covertype
P@ 10
0.80
0.30
0.60
0.80
0,30
0.60
P@
1.00
0,50
0.75
0.85
0,90
0.85
P@30
1.00
0.70
0.93
0.87
0.87
0.87
sensorless
P@
0.80
0.60
0.80
0.90
0.70
0.70
P@-20
0.95
0.50
0.75
0.85
0.80
0.85
P@ 30
0.90
0.90
0.83
Table 3: F1 score of feature selection by & f--regularized linear SVM
REAL
ACGAN
WGAN
BWGAN
MMDGAN
BMMDGAN
dataset
metric
adult
fl (C=0.01)
0.975
0.571
0.697
0.787
0.795
0.725
(C=0.001)
0.968
0.500
0.737
0.789
0.700
0.789
connect4
(C=0.01)
0.905
0.860
0.889
0.866
0.874
0,831
(C=0.001)
0.933
0.718
0.796
0.739
0.750
0,752
covertype
fl (C=0.01)
0.989
0.923
0.911
0.935
0.730
0,773
(C=0.001)
1.000
0.825
0.912
0.825
0,800
0,815
sensorless
(C=0.01)
0,982
0.848
0,900
0,918
0.813
0.844
(C=0.001)
0.815
0.778
0.769
0.733
0.812
0,710
5.4 INTERPRETABILITY
In addition accuracy, also important that the model trained on generated data should give us the same interpretation of model trained on the original data. We investigate the interpretability by two common feature selection techniques. First, we train two random forests on the generated and original dataset respectively. Each random forest can provide the importances of the features. We evaluate the consistency of interpretation by calculating precision at Kth, which means how many features ranked top-k in random forest trained original data in the top-k importance feature of the random forest trained on generated data. The results are shown Table 2 We provide the results of training classifier the same original data with different random seed as REAL for comparison. The effect of BC-loss is not significant in this aspect. However, the scores of ACGAN drop seriously, which means training classifier on data generated by ACGAN is somehow dangerous because the meaning of model may be totally different.
Another way select feature is training a linear model with & regularization. In Table we use linear SVM with ε regularization to select features. Then we calculate the F1 score of features selected by classifiers trained on generated data to known how similar between the two sets of features selected by classifiers trained on original and generated dataset. The results again shows that using boundary-calibration does not has significant effect feature selection and ACGAN not proper to generated data for training.
5.5 IMAGE DATASET
We further use MNIST and CIFAR-10 dataset to investigate the effectiveness of boundary- calibration on image datasets. For MNIST, we train six 4-layer convolution neural networks (CNN) with random sampling half of training data as pre-trained classifiers, and use the same classifier set in Section 5. to evaluate model compatibility. For 11FAR-10, we use ResNet56v2 (He et al., 2016) to obtain three pre-trained classifier and evaluate on CNN and ResNet56v2. In both task,
DCGAN (Rafford et al. 2016) as network structure in all GANs. The weight of BC-loss is set to be for these datasets.

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(a) WGAN MNIST
(b) BWGAN MNIST
(c) WGAN CIFAR-10
(Inception:
6.00,
(d) BWGAN
CIFAR-10 (Inception: 6. 12,
FID: 49.47)
FID: 44.93)
Figure 3: Gnerated samples from WGAN and our BWGAN. The images in the same column are in the same category.
Table and Table show the relative accuracy of classifiers trained on generated data. The pro- posed B BWGN still outperforms WGAN with better accuracy in general. The results generated by WGAN and BWGAN are pictured in Figure The Inception score and Frechet Inception Distance (FID) for CIFAR-I0 are also provided in the caption of Figure 3 Though the difference of quality between the images generated from WGAN and BWGAN is not significant in visual, the quantita- tive scores for quality of generated samples of CIFAR-10 10 are slightly improved. The results indicate that even though our method seems not improve the image quality, it is still able to improve the model compatibility without losing image quality.
Table 4: Breakdown results on MNIST dataset.
Table 5: Breakdown results on CIFAR- 10 dataset.
REAL
WGAN
BWGAN
DT (d=10)
86.6
54.5 (63.0)
48.3 (55.8))
DT (d=20)
88.0
34.5 (39.2)
48.2 (54.8)
REAL
WGAN
BWGAN
Linear SVM
88.0
34.5 (39.2)
48.2 (54.8)
MLP (100)
97.6
96.2 (98.5) 96.8 (99.2)
CNN
70.8
63.5 (89.8)
63.0 (89.1)
MLP (200x2)
97.9
96.7 (98.8) 96.1 (98.2)
Resnet56v2
77.5
48.8 (62.9)
51.3 (66.2)
(n=10, d=10)
92.5
75.5 (81.7)
83.7 (90.6)
Avg.
100.0
76.4
77.6
RF (n=10, d=20)
94.7
67.5 (71.3)
71.5 (75.4)
Avg.
100.0
70.2
75.5
DISCUSSION
We introduce an auxiliary loss in GANs which improves the model compatibility of generated dataset. We prove the new loss is unbiased and is applicable to all variants of GAN to improve model compatibility. We further demonstrate that our method has clear advantages with a variety of machine learning models trained on generated dataset. In addition, we investigate the results of feature selection and found that the BC-loss doesn't it effect the interpretation of machine learn- ing models. While this work only focus classification problem, generating data for regression problem is also worth studying. We hope our work will open the path for GANs with better model compatibility so that synthetic data can be more useful in practice.
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REFERENCES
Martín Arjovsky, Soumith Chintala, and Léon Bottou. Wasserstein GAN. CoRR, abs/ wbss/7/1..0ll00 07777,, 2017.
Rick JH Chang, Chun-L.iagg Li, Barnabas Poczos, BVK Vijaya Kumar, and Aswin C Sankara- narayanan. One network solve them all-solving linear inverse problems using deep projection models. In Proceedings of the IEEE International Conference on Computer Vision, pp. 5888- 5897, 2017.
Wei-Cheng Chang, Chun-Liang Li, Yiming Yang, and Barnabás Póczos. Kernel change-point de- tection with auxiliary deep generative models. arXiv preprint arXiv: 2019.
Dheeru Dua and Casey Graff. UCI machine learning repository, 2017.
Ian J. Goodfellow, Jean Pouget-Abadie, Mehdi Mirza, Bing Xu, David Warde-Farley, Sherjil Ozair, Aaron C. Courville, and Yoshua Bengio. Generative adversarial nets. In Advances in Neural Information Processing Systems, 2014.
Arthur Gretton, Karsten M. Borgwardt, Malte Rasch, Bernhard Schölkopf, and Alexander J. Smola. A kernel two-sample test. J. Mach. Learn. Res., 2012.
Ishaan Guirajani, Faruk Ahmed, Martín Arjovsky, Vincent Dumoulin, and Aaron C. Courville. Im- proved training of wasserstein gans. Advances in Neural Information Processing Systems, 2017.
Kaiming He, Xiangyu Zhang, Shaoqing Ren, and Jian Sun. Identity mappings deep residual net- works. In Computer Vision ECCV 2016 14th European Conference, Amsterdam, The Nether- lands, October 11-14, 2016, Proceedings, Part IV, 2016.
Martin Heusel, Hubert Ramsauer, Thomas Unterthiner, Bernhard Nessler, and Sepp Hochreiter. Gans trained by a two time-scale update rule converge local nash equilibrium. In Advances in Neural Information Processing Systems, pp. 6626-6637, 2017.
Devon Hjelm, Athul Paul Jacob, Tong Che, Adam Trischler, Kyunghyun Cho, and Yoshua Bengio. Boundary-secking generative adversarial networks. arXiv preprint arXiv:1702.08433/ 2017.
Phillip Isola, Jun-Yan Zhu, Tinghui Zhou, and Alexei A. Efros. Image-to-image translation with conditional adversarial networks. In 2017 IEEE Conference on Computer Vision and Pattern Recognition, CVPR 2017, pp. 5967-5976. 2017.
Tero Karras, Timo Aila, Samuli Laine, and Jaakko Lehtinen. Progressive growing of gans for im- proved quality, stability, and variation. In 6th International Conference on Learning Representa- fions, ICLR 2018, 2018.
Taeksoo Kim, Moonsu Cha, Hyunsoo Kim, Jung Kwon Lee, and Jiwon Kim. Learning to discover cross-domain relations with generative adversarial networks. In Proceedings of the 34th Interna- tional Conference on Machine Learning, ICML 2017, 2017.
Diederik Kingma and Max Welling. 13Xiv:1312.61 2013.
Auto-encoding variational bayes.
arXiv preprint
Christian Ledig, Lucas Theis, Ferenc Huszár, Jose Caballero, Andrew Cunningham, Alejandro Acosta, Andrew Aitken, Alykhan Tejani, Johannes Totz, Zehan Wang, et al. Photo-realistic sin- gle image super-resolution using a generative adversarial network. Proceedings of the IEEE conference on computer vision and pattern recognition, pp. 4681 4681-4690. 2017.
Chun-Liang Li, Wei-Cheng Chang, Yu Cheng, Yiming Yang, and Barnabás Póezos. MMD GAN: towards deeper understanding of moment matching network. In Advances in Neural Information Processing Systems, 2017.
Chun-Liang Li, Manzil Zaheer, Yang Zhang, Barnabas Poczos, and Ruslan Salakhutdinov. Point cloud gan. arXiv preprint arXiv: 1810.0585 2018.

---

Under review as a conference paper at ICLR 2020
Mario Lucic, Karol Kurach, Marcin Michalski, Sylvain Gelly, and Olivier Bousquet. Are gans created equal? a large-scale study. In Advances in neural information processing systems, pp- 700-709, 2018.
Yonghong Luo, Xiangrui Cai, Ying Zhang, Jun Xu, al. Multivariate time series imputation with generative adversarial networks. In Advances in Neural Information Processing Systems, pp. 1596-1607, 2018.
Mehdi Mirza and Simon Osindero. Conditional generative adversarial nets. arXiv:1411.1784 2014.
arXiv preprint
Sebastian Nowozin, Botond Cseke, and Ryota Tomioka. f-gan: using variational divergence minimization. In Advances in neural information processing systems, pp. 271-279, 2016.
Training generative neural samplers
Augustus Odena, Christopher Olah, and Jonathon Shlens. Conditional image synthesis with auxil- iary classifier gans. In Proceedings of the 34th International Conference on Machine Learning, ICML 2017, pp. 2642-2662622 2221-2651220 2017.
Noseong Park, Mahmoud Mohammadi, Kshitij Gorde, Sushil Jajodia, Hongkyu Park, and Youngmin Kim. Data synthesis based generative adversarial networks. PVLDB, 2018.
Deepak Pathak, Philipp Krahenbuhl, Jeff Donahue, Trevor Darrell, and Alexei A Efros. Context encoders: Feature learning by inpainting. In Proceedings of the IEEE conference on computer vision and pattern recognition, pp. 2536-2544, 2016.
Ofir Press, Amir Bar, Ben Bogin, Jonathan Berant, and Lior Wolf. Language generation with re- current generative adversarial networks without pre-training. arXiv preprint 2017.
0199,
Alec Radford, Luke Metz, and Soumith Chintala. Unsupervised representation learning with deep convolutional generative adversarial networks. In 4th International Conference Learning Rep- resentations, ICLR 2016, 2016.
Tim Salimans, Ian J. Goodfellow, Wojciech Zaremba, Vicki Cheung, Alec Radford, and Xi Chen. Improved techniques for training gans. In Advances in Neural Information Processing Systems, 2016.
Rui Shu, Hung Bui, and Stefano Ermon. Ac-gan learns a biased distribution. In NIPS Workshop on Bayesian Deep Learning, 2017.
Jiajun Wu, Chengkai Zhang, Tianfan Xue, Bill Freeman, and Josh Tenenbaum. Learning a prob- abilistic latent space of object shapes via 3d generative-adversarial modeling. In Advances in neural information processing systems, pp. 82-90, 2016.
Lei Xu, Maria Skoularidou, Alfredo data using conditional gan. arXiv preprint arXiv: 1907.0000700 2019.
and Kalyan Veeramachaneni. Modeling tabular
Lantao Yu, Weinan Zhang, Jun Wang, and Yong Yu. Seqgan: Sequence generative adversarial nets with policy gradient. In Proceedings of the Thirty-First AAAI Conference on Artificial Intelli- gence, 2017.
Jun Yan Zhu, Taesung Park, Phillip Isola, and Alexei A. Efros. Unpaired image-to-image translation using cycle-consistent adversarial networks. In IEEE International Conference Computer Vision, ICCV 2017.
10

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Under review as a conference paper at ICLR 2020
A
DATASET INFORMATION
Table 6: Attributes of UCI datasets
Dataset
# of train
# of test
# of discrete feature
# of continuous feature
# of class
Adult
32561 54046
16281
123
0
2
Connect-4
13511
126
0
3
Covertype
116203
116202
44
10
7
Sensorless
46807
11702
0
48
11
B DETAIL RESULT
B.1 ADULT
REAL
ACGAN
WGAN
BWGAN
MMDGAN
BMMDGAN
DT (d=10)
83.6 (100.0)
80.8 (96.6)
80.3
(9.9
79.7 (95.3)
(9..1)
DT (d=20)
81.2 (100.0)
00.9
(9.9))
(9.94)))4
73.8
75.9 (93.5)
Linear SVM
81.2 (100.0)
80.9 (99.6)
(93.))
(98.4)
73.8
75.9 (93.5)
MIP (100)
84.4 (100.0)
81.8 (96.9)
83.1
(9.61
82.9 (98.2)
84.1 (99.7)
MLP (200x2)
84.4 (100.0)
(97.2)
83.15)
83.8 (99.3)
82.69
84.2 (99.8)
RF (n=10, d=10)
83.9 (100.0)
82.6 (98.4)
(9..4)
83.6 (99.6)
83.3 (99.3)
RF (n=10, d=20)
84.1 (100.0)
80.7 (96.0)
81.5 (96.9)
83.2 (99.0)
81.5 (96.9)
82.3 (97.8)
Avg.
100.0
97.8
96.6
98.8
95.7
97.2
B.2 CONNECT4
REAL
ACGAN
WGAN
BWGAN
MMDGAN
BMMDGAN
DT (d=10)
74.7 (100.0)
64.1 (85.8)
67.7 (90.7)
69.5 (93.1)
66.7 (89.3)
68.5 (91.7)
DT (d=20)
76.3 (100.0)
64.1 (83.9)
60.9 (79.8)
(8..1)
61.4 (80.4)
64.1 (84.0)
Linear SVM
(100.0)
64.1 (83.9)
67.98)9.8)
64.9
(80.4)
64.1 (84.0)
MLP (100)
84.2 (100.0)
(78.4)
74.7.88.77
73.7 (87.6)
72.2
72.8 (86.5)
MLP (200x2)
85.7 (100.0)
(77.77
78.5.86.9)
73.7 (86.0)
71.9 (83.8)
72.9 (85.0)
RF (n=10, d=10)
73.0 (100.0)
66.8 (91.6)
(97.8)
70.4 (96.4)
70.1 (96.0)
68.3 (93.6)
1n=10, d=20)
79.2 (100.0)
68.06)
70.7 (89.3)
70.8 (89.4)
69.8 (88.1)
68.9 (87.0)
Avg.
100.0
83.7
87.6
88.9
86.3
87.4
B.3 COVERTYPE
REAL
ACGAN
WGAN
BWGAN
MMDGAN
BMMDGAN
DT (d=10)
77.1 (100.0)
37.8 (49.1)
65.6 (85.1)
68.9 (89.4)
65.5
66.7 (86.5)
DT (d=20)
86.9 (100.0)
(45.3)
62.9
67.2
63.4 67.2
Linear SVM
86.9 (100.0)
39.434).3)
(7..3)
(77.3)
63.4 67.2
MLP (100)
80.6 (100.0)
54.0
(83.8)
69.9 (86.7)
(2.55)
66.2 (82.2)
MLP (200x2)
89.2 (100.0)
(60.))
66.5 (74.5)
68.3 (76.5)
58.8 (65.9)
65.1 (73.0)
RF (n=10, d=10)
73.8 (100.0)
38.6 (52.2)
67.2
69.5 (94.1)
68.0 (92.1)
67.8 (91.8)
RF (n=10, 10, d=20)
86.2 (100.0)
38.6 (44.8)
(7.99
69.7 (80.8)
65.9 (76.4)
68.3 (79.2)
Avg.
100.0
52.0
79.6
83.2
77.1
79.8
B.4 SENSORLESS
11

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Under review as a conference paper at ICLR 2020
REAL
ACGAN
WGAN
BWGAN
MMDGAN
BMMDGAN
DT (d=10)
96.3 (100.0)
75.8 (78.7)
77.9 (80.8)
87.2 (90.5)
82.3 (85.5)
82.6 (85.8)
DT (d=20)
98.4(100.0)
756.776.7)
89.6 (69.5)
81..
83.8 (85.2)
Linear SVM
(100.)))))
776.77
(9.61 (69.5)
882.6)
83.8 (85.2)
MLP (100)
93.6
72.8 (77.8)
87..8)
89.8 (96.0)
(8..0)
84.9 (90.6)
MIP (200x2)
98.7 (100.0)
76.8 (77.8)
(91.7)
93.7 (94.9)
85.4
87.7 (88.8)
RF (n=10, d=10)
98.4 (100.0)
76.2 (77.5)
92.1 (93.6)
92.5 (94.1)
87.9 (89.4)
88.7 (90.2)
RF (n=10, d=20)
99.8 (100.0)
77.1 (77.3)
93.3 (93.6)
95.6 (95.8)
89.2 (89.4)
90.8 (91.0)
Avg.
100.0
77.5
84.6
93.3
86.3
88.1
12


Reviews:
[{"review_id": "HkgBnP1b2r", "reviewer": "AnonReviewer4", "summary": "", "questions": "", "limitations": "", "rating": 3, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "main_review": "", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "In this paper the authors propose a method for improving \"model compatibility\" in GANs. For this reason they add to the loss of the generation procedure a term that depends on the maximum mean discrepancy between the following datasets: (1) the output of a classifier with input the real dataset, (2) the output of the same classifier with input GAN-generated samples. They authors show that in essentially all the datasets they tried, the model compatibility of the produces generator is increased after adding the aforementioned cost, while the visual quality of the data is not decreased.\n\nStrengths:\n\n- The low model compatibility of GANs is a very important disadvantage and hence improving this aspect of GANs is a relevant problem.\n\nWeaknesses - Comments:\nA. The increase in the model compatibility is very mild. Especially in CIFAR-10, the increase in very small.\n\nB. In MNIST the increase is larger than CIFAR-10 but the initial model compatibility using vanilla GANs is smaller. The reason might be that for MNIST much simpler classification algorithms have been used. This maybe suggests that the proposed method affects more the model compatibility of methods that achieve lower model compatibility in before the addition of the extra cost term.\n\nMinor Comments:\n1. In equation (1) it looks strange that the summation is over A but A does not appear at all in the summand. I suggest you replace h and h' with A(D) and A(D') so that this is clear.\n2. In Theorem 2, \\hat{L}_G is used but for the proof the authors have replaces \\hat{M} with M. There should be a comment for that. In general I believe that Theorem 2 is almost trivial and does not add value to this clearly experimental paper.", "extra_scores": {"experience_assessment": "I have read many papers in this area.", "review_assessment:_checking_correctness_of_experiments": "I did not assess the experiments.", "review_assessment:_thoroughness_in_paper_reading": "I made a quick assessment of this paper.", "review_assessment:_checking_correctness_of_derivations_and_theory": "I assessed the sensibility of the derivations and theory."}, "extra_text": {}}, {"review_id": "HJlLQ8ERYH", "reviewer": "AnonReviewer2", "summary": "", "questions": "", "limitations": "", "rating": 3, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "main_review": "", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "This paper aims at training a GAN that can generate data matches the real data distribution well especially at the boundaries of the classifiers. A Boundary-Calibration loss (BC-loss) base on multi pretrained classifiers is introduced to match the statistics between the distributions of original data and generated data. The motivation is interesting. The story is clearly explained. However, the experiments part is weak.  \n\nThere are several typo and mistakes. The experiments only show that the proposed method got a good performance, but the analysis of the reason is not shown. The reason to name the loss as Boundary-Calibration loss (BC-loss) should be explained and the experiments should show some effect on the boundary areas. Some concerns are listed below,\n\n1.\tIf the generated dataset exhibits very good property as the real dataset, it means the data is to some extent perfectly foreseen, and there is little to no privacy, is it contrary to the aim of not leaking the real dataset?\n2.\tIt is more interesting to see the difference between the distribution of real data and the generated data, However the author only show a simple toy data distribution comparison, I would like to see more comprehensive results about the distribution differences on real dataset , e.g. the TSNE embedding? \n3.\tEquation (3) is not correct.\n4.\tThe author said that image quality of MNIST and CIFAR10 are not improved, then why the classification results are improved?  there should have some differences existed among different compared methods, it would be more convincing if you can show it out.\n5.\tWhat kind of  generator do you use for the UCI data?  How do you settle the output problem?  Since some of the data are continuous and some are discrete.\n", "extra_scores": {"experience_assessment": "I have published one or two papers in this area.", "review_assessment:_thoroughness_in_paper_reading": "I read the paper at least twice and used my best judgement in assessing the paper.", "review_assessment:_checking_correctness_of_experiments": "I assessed the sensibility of the experiments.", "review_assessment:_checking_correctness_of_derivations_and_theory": "I assessed the sensibility of the derivations and theory."}, "extra_text": {}}, {"review_id": "BJgUq9uoKH", "reviewer": "AnonReviewer1", "summary": "", "questions": "", "limitations": "", "rating": 3, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "main_review": "", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "In this work authors consider a problem of 'model compatibility' of GANs, i.e. usefullness of the generated samples for classification tasks. Proposed 'Boundary Calibration' GAN attempts to tackle this issue by adding non-adversarial terms to discriminator, obtained as outputs of the classifiers trained on the original data. For evaluation, it is proposed to compare accuracies obtained by classifiers trained on generated and on real data (termed 'relative acurracy'). Experiments show that the proposed methods improve such scores.\n\nPros:\n- considered problem seems to be important GAN application which has not yet received too much attention.\n- proposed method seems to improve the accuracy of classifiers trained on generated data.\n\nCons:\n- the paper is poorly written, has multiple typos and often it is unclear what authors mean.\n- the proposed evaluation does not exactly measure the potential improvements from training classifiers with generated data. It would make sense to provide information if generated data can improve classifier's scores, if added to the training data (or small part of it).\n- it is unclear whether or not the proposed technique does not affect the sample quality, as no quantitative metrics are provided.\n\nDetails:\n1. Quantitative scores for quality of generated samples are not provided. Authors instead provide few samples and state that it is difficult to detect the difference. Although sample quality is not the main task here, it certainly is important - otherwise we could train generators solely against the classifier 'boundary calibration' loss terms - this, however would likely lead to adversarial examples. Combining two losses often leads to trade-offs, hence showing that we can improve 'model compatibility' without the loss of sample quality is actually crucial. Metrics such as Inception score [1], FID [2] or KID [3] are desired, especially given relatively poor quality of cifar and mnist samples from all models.\n2.The main metric used is the ratio between accurracies of classifiers (trained on real and generated data). It is hence difficult to tell if the classifiers that were used were trained reasonably and achieved reasonable scores.\n3. In the abstract, authors claim that 'GANs often prefer generating easier synthetic data that are far from boundaries of the classifiers'. Although for some GAN settings the generators might be biased to do so, in general this claim is unfounded, as GANs optimize divergences that are agnostic to classifier boundaries.\n4. It is unclear what kind of classifier-output is used as an input to MMD. Are these continuous logits, discrete class numbers, or one-hot-encoded class identities?\n5. Authors use WGAN and MMDGAN with gradient penalty. It is unclear how gradient penalty is applied to MMDGAN as what should be penalized is the witness function, which is different than in WGAN-GP [4], see e.g. [3].\n6. It is unclear how embeddings of class information are concatenated to discriminator inputs (p.5).\n7. It is unclear to what extent feature selection is deterministic. Authors argue in Section 5.4 that the intersection of top-k features selected from two models should be large. It would be good to provide the same statistics for features selected twice on the same sample.\n\nOverall, the paper currently does not match the quality requirements of ICLR, however it has potential for improvement if the mentioned issues are addressed.\n\nTypos/unclear expressions:\n[p1] 'may not willing' >> 'may not be willing'\n[p1]'with the property similar to the original data is demanding'  >> properties, demanded/in demand\n[p2] 'Although GANs are versatile as aforementioned' - strange wording\n[p2] 'The pioneered work' >> 'pioneering work'\n[p2] 'information of models' >> 'information from the models'\n[p2] effects >> affects\n[p3] related works >> related work\n[p3] distribution of label >> distribution of labels\n[p3] 'generated dataset adopt ' >> 'generated dataset will adopt '\n[p3] 'To known about the boundary' >> ' To know the boundary'/'To include the information about the boundary'\n[p3] 'the a distance'\n[p3] 'the problem to distinguish whether two sets of samples' \n[p4] 'If they are close the sets might be sampled from the same distribution' (?)\n[p4] tries to minimized the MMD\n[p4] would not leads to\n[p6, Table 2 caption] number of estimator used\n[p6] at Appendix\n[p6] depresses the model compatibility (?)\n[p6] can providing\n[p7] to known how\n[p8] our work open >> our work will open\n\n\n------------------------------------- Revision -------------------------------------\n\nAlthough some issue seem to have been clarified, two of my main concerns, i.e. the proposed evaluation and the text quality, have not been resolved. Additionally, as pointed out by reviewer #4, the results seem somewhat incremental. For these reasons, I decided to keep the rating unchanged.", "extra_scores": {"experience_assessment": "I have published one or two papers in this area.", "review_assessment:_checking_correctness_of_experiments": "I carefully checked the experiments.", "review_assessment:_thoroughness_in_paper_reading": "I read the paper thoroughly.", "review_assessment:_checking_correctness_of_derivations_and_theory": "I carefully checked the derivations and theory."}, "extra_text": {}}]

Author rebuttal:

Meta-review: The paper presents a method for increasing the "model compatibility" of Generative Adversarial Networks by adding a term to the loss function relating to classification boundaries. The reviewers recognized the importance of the problem, but several concerns were raised about the clarity of the paper, as well as the significance of the experimental results.
Decision: Reject