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1. Effective Dynamics of Generative Adversarial Networks

   https://doi.org/10.1103/PhysRevX.13.041004  

   Durr, Steven; Mroueh, Youssef; Tu, Yuhai; Wang, Shenshen (October 2023, Physical Review X)

   Generative adversarial networks (GANs) are a class of machine-learning models that use adversarial training to generate new samples with the same (potentially very complex) statistics as the training samples. One major form of training failure, known as mode collapse, involves the generator failing to reproduce the full diversity of modes in the target probability distribution. Here, we present an effective model of GAN training, which captures the learning dynamics by replacing the generator neural network with a collection of particles in the output space; particles are coupled by a universal kernel valid for certain wide neural networks and high-dimensional inputs. The generality of our simplified model allows us to study the conditions under which mode collapse occurs. Indeed, experiments which vary the effective kernel of the generator reveal a mode collapse transition, the shape of which can be related to the type of discriminator through the frequency principle. Further, we find that gradient regularizers of intermediate strengths can optimally yield convergence through critical damping of the generator dynamics. Our effective GAN model thus provides an interpretable physical framework for understanding and improving adversarial training. 

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2. Bootstrapping Conditional GANs for Video Game Level Generation

   https://doi.org/10.1109/CoG47356.2020.9231576  

   Rodriguez Torrado, Ruben; Khalifa, Ahmed; Cerny Green, Michael; Justesen, Niels; Risi, Sebastian; Togelius, Julian (August 2020, IEEE Conference on Games)

   null (Ed.)

   Generative Adversarial Networks (GANs) have shown impressive results for image generation. However, GANs face challenges in generating contents with certain types of constraints, such as game levels. Specifically, it is difficult to generate levels that have aesthetic appeal and are playable at the same time. Additionally, because training data usually is limited, it is challenging to generate unique levels with current GANs. In this paper, we propose a new GAN architecture named Conditional Embedding Self-Attention Generative Adversarial Net- work (CESAGAN) and a new bootstrapping training procedure. The CESAGAN is a modification of the self-attention GAN that incorporates an embedding feature vector input to condition the training of the discriminator and generator. This allows the network to model non-local dependency between game objects, and to count objects. Additionally, to reduce the number of levels necessary to train the GAN, we propose a bootstrapping mechanism in which playable generated levels are added to the training set. The results demonstrate that the new approach does not only generate a larger number of levels that are playable but also generates fewer duplicate levels compared to a standard GAN. 

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3. Training Faster by Separating Modes of Variation in Batch-normalized Models

   https://doi.org/10.1109/TPAMI.2019.2895781  

   Kalayeh, Mahdi M.; Shah, Mubarak (January 2019, IEEE Transactions on Pattern Analysis and Machine Intelligence)

   Batch Normalization (BN) is essential to effectively train state-of-the-art deep Convolutional Neural Networks (CNN). It normalizes the layer outputs during training using the statistics of each mini-batch. BN accelerates training procedure by allowing to safely utilize large learning rates and alleviates the need for careful initialization of the parameters. In this work, we study BN from the viewpoint of Fisher kernels that arise from generative probability models. We show that assuming samples within a mini-batch are from the same probability density function, then BN is identical to the Fisher vector of a Gaussian distribution. That means batch normalizing transform can be explained in terms of kernels that naturally emerge from the probability density function that models the generative process of the underlying data distribution. Consequently, it promises higher discrimination power for the batch-normalized mini-batch. However, given the rectifying non-linearities employed in CNN architectures, distribution of the layer outputs show an asymmetric characteristic. Therefore, in order for BN to fully benefit from the aforementioned properties, we propose approximating underlying data distribution not with one, but a mixture of Gaussian densities. Deriving Fisher vector for a Gaussian Mixture Model (GMM), reveals that batch normalization can be improved by independently normalizing with respect to the statistics of disentangled sub-populations. We refer to our proposed soft piecewise version of batch normalization as Mixture Normalization (MN). Through extensive set of experiments on CIFAR-10 and CIFAR-100, using both a 5-layers deep CNN and modern Inception-V3 architecture, we show that mixture normalization reduces required number of gradient updates to reach the maximum test accuracy of the batch normalized model by ∼31%-47% across a variety of training scenarios. Replacing even a few BN modules with MN in the 48-layers deep Inception-V3 architecture is sufficient to not only obtain considerable training acceleration but also better final test accuracy. We show that similar observations are valid for 40 and 100-layers deep DenseNet architectures as well. We complement our study by evaluating the application of mixture normalization to the Generative Adversarial Networks (GANs), where "mode collapse" hinders the training process. We solely replace a few batch normalization layers in the generator with our proposed mixture normalization. Our experiments using Deep Convolutional GAN (DCGAN) on CIFAR-10 show that mixture normalized DCGAN not only provides an acceleration of ∼58% but also reaches lower (better) "Fréchet Inception Distance" (FID) of 33.35 compared to 37.56 of its batch normalized counterpart. 

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4. Games of GANs: Game-theoretical models for generative adversarial networks

   Monireh M. Moghadam, Bahar Boroomand (February 2023, Artificial intelligence review)

   Generative Adversarial Networks (GANs) have recently attracted considerable attention in the AI community due to their ability to generate high-quality data of significant statisti- cal resemblance to real data. Fundamentally, GAN is a game between two neural networks trained in an adversarial manner to reach a zero-sum Nash equilibrium profile. Despite the improvement accomplished in GANs in the last few years, several issues remain to be solved. This paper reviews the literature on the game-theoretic aspects of GANs and addresses how game theory models can address specific challenges of generative models and improve the GAN’s performance. We first present some preliminaries, including the basic GAN model and some game theory background. We then present a taxonomy to clas- sify state-of-the-art solutions into three main categories: modified game models, modified architectures, and modified learning methods. The classification is based on modifications made to the basic GAN model by proposed game-theoretic approaches in the literature. We then explore the objectives of each category and discuss recent works in each class. Finally, we discuss the remaining challenges in this field and present future research directions. 

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5. UNDERSTANDING OVERPARAMETERIZATION IN GENERATIVE ADVERSARIAL NETWORKS

   Balaji, Yogesh; Sajedi, Mohammadmahdi; Kalibhat, Neha Mukund; Ding, Mucong; Stoger, Dominik; Soltanolkotabi, Mahdi; Feizi, Soheil (April 2021, International Conference on Learning Representations)

   null (Ed.)

   A broad class of unsupervised deep learning methods such as Generative Adversarial Networks (GANs) involve training of overparameterized models where the number of parameters of the model exceeds a certain threshold. Indeed, most successful GANs used in practice are trained using overparameterized generator and discriminator networks, both in terms of depth and width. A large body of work in supervised learning have shown the importance of model overparameterization in the convergence of the gradient descent (GD) to globally optimal solutions. In contrast, the unsupervised setting and GANs in particular involve non-convex concave mini-max optimization problems that are often trained using Gradient Descent/Ascent (GDA). The role and benefits of model overparameterization in the convergence of GDA to a global saddle point in non-convex concave problems is far less understood. In this work, we present a comprehensive analysis of the importance of model overparameterization in GANs both theoretically and empirically. We theoretically show that in an overparameterized GAN model with a 1-layer neural network generator and a linear discriminator, GDA converges to a global saddle point of the underlying non-convex concave min-max problem. To the best of our knowledge, this is the first result for global convergence of GDA in such settings. Our theory is based on a more general result that holds for a broader class of nonlinear generators and discriminators that obey certain assumptions (including deeper generators and random feature discriminators). Our theory utilizes and builds upon a novel connection with the convergence analysis of linear timevarying dynamical systems which may have broader implications for understanding the convergence behavior of GDA for non-convex concave problems involving overparameterized models. We also empirically study the role of model overparameterization in GANs using several large-scale experiments on CIFAR-10 and Celeb-A datasets. Our experiments show that overparameterization improves the quality of generated samples across various model architectures and datasets. Remarkably, we observe that overparameterization leads to faster and more stable convergence behavior of GDA across the board. 

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