No Arabic abstract
Sequences play an important role in many engineering applications and systems. Searching sequences with desired properties has long been an interesting but also challenging research topic. This article proposes a novel method, called HpGAN, to search desired sequences algorithmically using generative adversarial networks (GAN). HpGAN is based on the idea of zero-sum game to train a generative model, which can generate sequences with characteristics similar to the training sequences. In HpGAN, we design the Hopfield network as an encoder to avoid the limitations of GAN in generating discrete data. Compared with traditional sequence construction by algebraic tools, HpGAN is particularly suitable for intractable problems with complex objectives which prevent mathematical analysis. We demonstrate the search capabilities of HpGAN in two applications: 1) HpGAN successfully found many different mutually orthogonal complementary code sets (MOCCS) and optimal odd-length Z-complementary pairs (OB-ZCPs) which are not part of the training set. In the literature, both MOCSSs and OB-ZCPs have found wide applications in wireless communications. 2) HpGAN found new sequences which achieve four-times increase of signal-to-interference ratio--benchmarked against the well-known Legendre sequence--of a mismatched filter (MMF) estimator in pulse compression radar systems. These sequences outperform those found by AlphaSeq.
We investigate the use of parametrized 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, called least $k$th-order GAN (L$k$GAN), is first introduced, generalizing the least squares GANs (LSGANs) by using a $k$th order absolute error distortion measure with $k geq 1$ (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 $k$th-order Pearson-Vajda divergence. Another novel GAN generator loss function is next proposed in terms of R{e}nyi cross-entropy functionals with order $alpha >0$, $alpha eq 1$. It is demonstrated that this R{e}nyi-centric generalized loss function, which provably reduces to the original GAN loss function as $alphato1$, preserves the equilibrium point satisfied by the original GAN based on the Jensen-R{e}nyi divergence, a natural extension of the Jensen-Shannon divergence. Experimental results indicate that the proposed loss functions, applied to the MNIST and CelebA datasets, under both DCGAN and StyleGAN architectures, confer performance benefits by virtue of the extra degrees of freedom provided by the parameters $k$ and $alpha$, respectively. More specifically, experiments show improvements with regard to the quality of the generated images as measured by the Frechet Inception Distance (FID) 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, e.g., the issues of fairness or privacy in artificial intelligence.
We propose to extend the concept of private information retrieval by allowing for distortion in the retrieval process and relaxing the perfect privacy requirement at the same time. In particular, we study the tradeoff between download rate, distortion, and user privacy leakage, and show that in the limit of large file sizes this trade-off can be captured via a novel information-theoretical formulation for datasets with a known distribution. Moreover, for scenarios where the statistics of the dataset is unknown, we propose a new deep learning framework by leveraging a generative adversarial network approach, which allows the user to learn efficient schemes from the data itself, minimizing the download cost. We evaluate the performance of the scheme on a synthetic Gaussian dataset as well as on both the MNIST and CIFAR-10 datasets. For the MNIST dataset, the data-driven approach significantly outperforms a non-learning based scheme which combines source coding with multiple file download, while the CIFAR-10 performance is notably better.
We propose a unified game-theoretical framework to perform classification and conditional image generation given limited supervision. It is formulated as a three-player minimax game consisting of a generator, a classifier and a discriminator, and therefore is referred to as Triple Generative Adversarial Network (Triple-GAN). The generator and the classifier characterize the conditional distributions between images and labels to perform conditional generation and classification, respectively. The discriminator solely focuses on identifying fake image-label pairs. Under a nonparametric assumption, we prove the unique equilibrium of the game is that the distributions characterized by the generator and the classifier converge to the data distribution. As a byproduct of the three-player mechanism, Triple-GAN is flexible to incorporate different semi-supervised classifiers and GAN architectures. We evaluate Triple-GAN in two challenging settings, namely, semi-supervised learning and the extreme low data regime. In both settings, Triple-GAN can achieve excellent classification results and generate meaningful samples in a specific class simultaneously. In particular, using a commonly adopted 13-layer CNN classifier, Triple-GAN outperforms extensive semi-supervised learning methods substantially on more than 10 benchmarks no matter data augmentation is applied or not.
A Triangle Generative Adversarial Network ($Delta$-GAN) is developed for semi-supervised cross-domain joint distribution matching, where the training data consists of samples from each domain, and supervision of domain correspondence is provided by only a few paired samples. $Delta$-GAN consists of four neural networks, two generators and two discriminators. The generators are designed to learn the two-way conditional distributions between the two domains, while the discriminators implicitly define a ternary discriminative function, which is trained to distinguish real data pairs and two kinds of fake data pairs. The generators and discriminators are trained together using adversarial learning. Under mild assumptions, in theory the joint distributions characterized by the two generators concentrate to the data distribution. In experiments, three different kinds of domain pairs are considered, image-label, image-image and image-attribute pairs. Experiments on semi-supervised image classification, image-to-image translation and attribute-based image generation demonstrate the superiority of the proposed approach.
Generative adversarial networks (GANs) have achieved remarkable progress in recent years, but the continuously growing scale of models makes them challenging to deploy widely in practical applications. In particular, for real-time generation tasks, different devices require generators of different sizes due to varying computing power. In this paper, we introduce slimmable GANs (SlimGANs), which can flexibly switch the width of the generator to accommodate various quality-efficiency trade-offs at runtime. Specifically, we leverage multiple discriminators that share partial parameters to train the slimmable generator. To facilitate the textit{consistency} between generators of different widths, we present a stepwise inplace distillation technique that encourages narrow generators to learn from wide ones. As for class-conditional generation, we propose a sliceable conditional batch normalization that incorporates the label information into different widths. Our methods are validated, both quantitatively and qualitatively, by extensive experiments and a detailed ablation study.