Deep neural networks (DNNs) have shown to perform very well on large scale object recognition problems and lead to widespread use for real-world applications, including situations where DNN are implemented as "black boxes". A promising approach to secure their use is to accept decisions that are likely to be correct while discarding the others. In this work, we propose DOCTOR, a simple method that aims to identify whether the prediction of a DNN classifier should (or should not) be trusted so that, consequently, it would be possible to accept it or to reject it. Two scenarios are investigated: Totally Black Box (TBB) where only the soft-predictions are available and Partially Black Box (PBB) where gradient-propagation to perform input pre-processing is allowed. Empirically, we show that DOCTOR outperforms all state-of-the-art methods on various well-known images and sentiment analysis datasets. In particular, we observe a reduction of up to 4% of the false rejection rate (FRR) in the PBB scenario. DOCTOR can be applied to any pre-trained model, it does not require prior information about the underlying dataset and is as simple as the simplest available methods in the literature.

Following Reviewer #3, we clarify the motivation behind NC. General changes to the manuscript Following Reviewer's #1 suggestion, we included in the Appendix our experi-5 Our intent was to reason about optimal discriminators. Following Reviewer's #1 and #3 remarks, we replace the Donsker-V aradhan lower We thank the reviewers for their careful reading. We then use Jensen's inequality with uniform We follow Reviewer's #1 suggestion to

Dual discriminator generative adversarial networks (D2 GANs) were introduced to mitigate the problem of mode collapse in generative adversarial networks. In D2 GANs, two discriminators are employed alongside a generator: one discriminator rewards high scores for samples from the true data distribution, while the other favors samples from the generator. In this work, we first introduce dual discriminator $α$-GANs (D2 $α$-GANs), which combines the strengths of dual discriminators with the flexibility of a tunable loss function, $α$-loss. We further generalize this approach to arbitrary functions defined on positive reals, leading to a broader class of models we refer to as generalized dual discriminator generative adversarial networks. For each of these proposed models, we provide theoretical analysis and show that the associated min-max optimization reduces to the minimization of a linear combination of an $f$-divergence and a reverse $f$-divergence. This generalizes the known simplification for D2-GANs, where the objective reduces to a linear combination of the KL-divergence and the reverse KL-divergence. Finally, we perform experiments on 2D synthetic data and use multiple performance metrics to capture various advantages of our GANs.

Generative adversarial networks (GANs) comprise a generator, trained to learn the underlying distribution of the desired data, and a discriminator, trained to distinguish real samples from those output by the generator. A majority of GAN literature focuses on understanding the optimality of the discriminator through integral probability metric (IPM) or divergence based analysis. In this paper, we propose a unified approach to analyzing the generator optimization through variational approach. In $f$-divergence-minimizing GANs, we show that the optimal generator is the one that matches the score of its output distribution with that of the data distribution, while in IPM GANs, we show that this optimal generator matches score-like functions, involving the flow-field of the kernel associated with a chosen IPM constraint space. Further, the IPM-GAN optimization can be seen as one of smoothed score-matching, where the scores of the data and the generator distributions are convolved with the kernel associated with the constraint. The proposed approach serves to unify score-based training and existing GAN flavors, leveraging results from normalizing flows, while also providing explanations for empirical phenomena such as the stability of non-saturating GAN losses. Based on these results, we propose novel alternatives to $f$-GAN and IPM-GAN training based on score and flow matching, and discriminator-guided Langevin sampling.

We consider the problem of optimizing the discriminator in generative adversarial networks (GANs) subject to higher-order gradient regularization. We show analytically, via the least-squares (LSGAN) and Wasserstein (WGAN) GAN variants, that the discriminator optimization problem is one of interpolation in $n$-dimensions. The optimal discriminator, derived using variational Calculus, turns out to be the solution to a partial differential equation involving the iterated Laplacian or the polyharmonic operator. The solution is implementable in closed-form via polyharmonic radial basis function (RBF) interpolation. In view of the polyharmonic connection, we refer to the corresponding GANs as Poly-LSGAN and Poly-WGAN. Through experimental validation on multivariate Gaussians, we show that implementing the optimal RBF discriminator in closed-form, with penalty orders $m \approx\lceil \frac{n}{2} \rceil $, results in superior performance, compared to training GAN with arbitrarily chosen discriminator architectures. We employ the Poly-WGAN discriminator to model the latent space distribution of the data with encoder-decoder-based GAN flavors such as Wasserstein autoencoders.

In this paper, we propose ComGAN(ComparativeGAN) which allows the generator in GANs to refer to the semantics of comparative samples(e.g. real data) by comparison. ComGAN generalizes relativistic GANs by using arbitrary architecture and mostly outperforms relativistic GANs in simple input-concatenation architecture. To train the discriminator in ComGAN, we also propose equality regularization, which fits the discriminator to a neutral label for equally real or fake samples. Equality regularization highly boosts the performance of ComGAN including WGAN while being exceptionally simple compared to existing regularizations. Finally, we generalize comparative samples fixed to real data in relativistic GANs toward fake data and show that such objectives are sound in both theory and practice. Our experiments demonstrate superior performances of ComGAN and equality regularization, achieving the best FIDs in 7 out of 8 cases of different losses and data against ordinary GANs and relativistic GANs.

Generative adversarial networks (GANs) are known for their strong abilities on capturing the underlying distribution of training instances. Since the seminal work of GAN, many variants of GAN have been proposed. However, existing GANs are almost established on the assumption that the training dataset is clean. But in many real-world applications, this may not hold, that is, the training dataset may be contaminated by a proportion of undesired instances. When training on such datasets, existing GANs will learn a mixture distribution of desired and contaminated instances, rather than the desired distribution of desired data only (target distribution). To learn the target distribution from contaminated datasets, two purified generative adversarial networks (PuriGAN) are developed, in which the discriminators are augmented with the capability to distinguish between target and contaminated instances by leveraging an extra dataset solely composed of contamination instances. We prove that under some mild conditions, the proposed PuriGANs are guaranteed to converge to the distribution of desired instances. Experimental results on several datasets demonstrate that the proposed PuriGANs are able to generate much better images from the desired distribution than comparable baselines when trained on contaminated datasets. In addition, we also demonstrate the usefulness of PuriGAN on downstream applications by applying it to the tasks of semi-supervised anomaly detection on contaminated datasets and PU-learning. Experimental results show that PuriGAN is able to deliver the best performance over comparable baselines on both tasks.

Wasserstein GANs are based on the idea of minimising the Wasserstein distance between a real and a generated distribution. We provide an in-depth mathematical analysis of differences between the theoretical setup and the reality of training Wasserstein GANs. In this work, we gather both theoretical and empirical evidence that the WGAN loss is not a meaningful approximation of the Wasserstein distance. Moreover, we argue that the Wasserstein distance is not even a desirable loss function for deep generative models, and conclude that the success of Wasserstein GANs can in truth be attributed to a failure to approximate the Wasserstein distance.