A Unifying Generator Loss Function for Generative Adversarial Networks.

A unifying α-parametrized generator loss function is introduced for a dual-objective generative adversarial network (GAN) that uses a canonical (or classical) discriminator loss function such as the one in the original GAN (VanillaGAN) system. The generator loss function is based on a symmetric class probability estimation type function, Lα, and the resulting GAN system is termed Lα-GAN. Under an optimal discriminator, it is shown that the generator's optimization problem consists of minimizing a Jensen-fα-divergence, a natural generalization of the Jensen-Shannon divergence, where fα is a convex function expressed in terms of the loss function Lα. It is also demonstrated that this Lα-GAN problem recovers as special cases a number of GAN problems in the literature, including VanillaGAN, least squares GAN (LSGAN), least kth-order GAN (LkGAN), and the recently introduced (αD,αG)-GAN with αD=1. Finally, experimental results are provided for three datasets-MNIST, CIFAR-10, and Stacked MNIST-to illustrate the performance of various examples of the Lα-GAN system.

On Decoder Ties for the Binary Symmetric Channel with Arbitrarily Distributed Input.

The error probability of block codes sent under a non-uniform input distribution over the memoryless binary symmetric channel (BSC) and decoded via the maximum a posteriori (MAP) decoding rule is investigated. It is proved that the ratio of the probability of MAP decoder ties to the probability of error grows most linearly in blocklength when no MAP decoding ties occur, thus showing that decoder ties do not affect the code's error exponent. This result generalizes a similar recent result shown for the case of block codes transmitted over the BSC under a uniform input distribution.

TARA: Training and Representation Alteration for AI Fairness and Domain Generalization.

We propose a novel method for enforcing AI fairness with respect to protected or sensitive factors. This method uses a dual strategy performing training and representation alteration (TARA) for the mitigation of prominent causes of AI bias. It includes the use of representation learning alteration via adversarial independence to suppress the bias-inducing dependence of the data representation from protected factors and training set alteration via intelligent augmentation to address bias-causing data imbalance by using generative models that allow the fine control of sensitive factors related to underrepresented populations via domain adaptation and latent space manipulation. When testing our methods on image analytics, experiments demonstrate that TARA significantly or fully debiases baseline models while outperforming competing debiasing methods that have the same amount of information-for example, with (% overall accuracy, % accuracy gap) = (78.8, 0.5) versus the baseline method's score of (71.8, 10.5) for Eye-PACS, and (73.7, 11.8) versus (69.1, 21.7) for CelebA. Furthermore, recognizing certain limitations in current metrics used for assessing debiasing performance, we propose novel conjunctive debiasing metrics. Our experiments also demonstrate the ability of these novel metrics in assessing the Pareto efficiency of the proposed methods.

Rényi Cross-Entropy Measures for Common Distributions and Processes with Memory.

Two Rényi-type generalizations of the Shannon cross-entropy, the Rényi cross-entropy and the Natural Rényi cross-entropy, were recently used as loss functions for the improved design of deep learning generative adversarial networks. In this work, we derive the Rényi and Natural Rényi differential cross-entropy measures in closed form for a wide class of common continuous distributions belonging to the exponential family, and we tabulate the results for ease of reference. We also summarise the Rényi-type cross-entropy rates between stationary Gaussian processes and between finite-alphabet time-invariant Markov sources.

Least kth-Order and Rényi Generative Adversarial Networks.

We investigate the use of parameterized families of information-theoretic measures to generalize the loss functions of generative adversarial networks (GANs) with the objective of improving performance. A new generator loss function, least kth-order GAN (LkGAN), is introduced, generalizing the least squares GANs (LSGANs) by using a kth-order absolute error distortion measure with k≥1 (which recovers the LSGAN loss function when k=2). It is shown that minimizing this generalized loss function under an (unconstrained) optimal discriminator is equivalent to minimizing the kth-order Pearson-Vajda divergence. Another novel GAN generator loss function is next proposed in terms of Rényi cross-entropy functionals with order α>0, α≠1. It is demonstrated that this Rényi-centric generalized loss function, which provably reduces to the original GAN loss function as α→1, preserves the equilibrium point satisfied by the original GAN based on the Jensen-Rényi divergence, a natural extension of the Jensen-Shannon divergence. Experimental results indicate that the proposed loss functions, applied to the MNIST and CelebA data sets, under both DCGAN and StyleGAN architectures, confer performance benefits by virtue of the extra degrees of freedom provided by the parameters k and α, respectively. More specifically, experiments show improvements with regard to the quality of the generated images as measured by the Fréchet inception distance score and training stability. While it was applied to GANs in this study, the proposed approach is generic and can be used in other applications of information theory to deep learning, for example, the issues of fairness or privacy in artificial intelligence.

Unsupervised Discovery, Control, and Disentanglement of Semantic Attributes With Applications to Anomaly Detection.

Our work focuses on unsupervised and generative methods that address the following goals: (1) learning unsupervised generative representations that discover latent factors controlling image semantic attributes, (2) studying how this ability to control attributes formally relates to the issue of latent factor disentanglement, clarifying related but dissimilar concepts that had been confounded in the past, and (3) developing anomaly detection methods that leverage representations learned in the first goal. For goal 1, we propose a network architecture that exploits the combination of multiscale generative models with mutual information (MI) maximization. For goal 2, we derive an analytical result, lemma 1, that brings clarity to two related but distinct concepts: the ability of generative networks to control semantic attributes of images they generate, resulting from MI maximization, and the ability to disentangle latent space representations, obtained via total correlation minimization. More specifically, we demonstrate that maximizing semantic attribute control encourages disentanglement of latent factors. Using lemma 1 and adopting MI in our loss function, we then show empirically that for image generation tasks, the proposed approach exhibits superior performance as measured in the quality and disentanglement of the generated images when compared to other state-of-the-art methods, with quality assessed via the Fréchet inception distance (FID) and disentanglement via mutual information gap. For goal 3, we design several systems for anomaly detection exploiting representations learned in goal 1 and demonstrate their performance benefits when compared to state-of-the-art generative and discriminative algorithms. Our contributions in representation learning have potential applications in addressing other important problems in computer vision, such as bias and privacy in AI.