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1. InfoGAN-CR and ModelCentrality: Self-supervised Model Training and Selection for Disentangling GANs

   Zinan Lin, Kiran Thekumparampil (January 2020, International Conference on Machine Learning)

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   Disentangled generative models map a latent code vector to a target space, while enforcing that a subset of the learned latent codes are interpretable and associated with distinct properties of the target distribution. Recent advances have been dominated by Variational AutoEncoder (VAE)-based methods, while training disentangled generative adversarial networks (GANs) remains challenging. In this work, we show that the dominant challenges facing disentangled GANs can be mitigated through the use of self-supervision. We make two main contributions: first, we design a novel approach for training disentangled GANs with self-supervision. We propose contrastive regularizer, which is inspired by a natural notion of disentanglement: latent traversal. This achieves higher disentanglement scores than state-of-the-art VAE- and GAN-based approaches. Second, we propose an unsupervised model selection scheme called ModelCentrality, which uses generated synthetic samples to compute the medoid (multi-dimensional generalization of median) of a collection of models. The current common practice of hyper-parameter tuning requires using ground-truths samples, each labelled with known perfect disentangled latent codes. As real datasets are not equipped with such labels, we propose an unsupervised model selection scheme and show that it finds a model close to the best one, for both VAEs and GANs. Combining contrastive regularization with ModelCentrality, we improve upon the state-of-the-art disentanglement scores significantly, without accessing the supervised data. 

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2. 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)

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   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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3. Subspace Fitting Meets Regression: The Effects of Supervision and Orthonormality Constraints on Double Descent of Generalization Errors

   Dar, Yehuda; Mayer, Paul; Luzi, Lorenzo; Baraniuk, Richard G. (July 2020, Proceedings of Machine Learning Research)

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   We study the linear subspace fitting problem in the overparameterized setting, where the estimated subspace can perfectly interpolate the training examples. Our scope includes the least-squares solutions to subspace fitting tasks with varying levels of supervision in the training data (i.e., the proportion of input-output examples of the desired low-dimensional mapping) and orthonormality of the vectors defining the learned operator. This flexible family of problems connects standard, unsupervised subspace fitting that enforces strict orthonormality with a corresponding regression task that is fully supervised and does not constrain the linear operator structure. This class of problems is defined over a supervision-orthonormality plane, where each coordinate induces a problem instance with a unique pair of supervision level and softness of orthonormality constraints. We explore this plane and show that the generalization errors of the corresponding subspace fitting problems follow double descent trends as the settings become more supervised and less orthonormally constrained. 

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4. Adaptive Learning of the Latent Space of Wasserstein Generative AdversarialNetworks

   Qiu, Y; Gao, Q; Wang, X (November 2024, Journal of the American Statistical Association)

   Generative models based on latent variables, such as generative adversarial networks (GANs) and variationalauto-encoders (VAEs), have gained lots of interests due to their impressive performance in many fields.However, many data such as natural images usually do not populate the ambient Euclidean space but insteadreside in a lower-dimensional manifold. Thus an inappropriate choice of the latent dimension fails to uncoverthe structure of the data, possibly resulting in mismatch of latent representations and poor generativequalities. Toward addressing these problems, we propose a novel framework called the latent WassersteinGAN (LWGAN) that fuses the Wasserstein auto-encoder and the Wasserstein GAN so that the intrinsicdimension of the data manifold can be adaptively learned by a modified informative latent distribution. Weprove that there exist an encoder network and a generator network in such a way that the intrinsic dimensionof the learned encoding distribution is equal to the dimension of the data manifold. We theoreticallyestablish that our estimated intrinsic dimension is a consistent estimate of the true dimension of the datamanifold. Meanwhile, we provide an upper bound on the generalization error of LWGAN, implying that weforce the synthetic data distribution to be similar to the real data distribution from a population perspective.Comprehensive empirical experiments verify our framework and show that LWGAN is able to identify thecorrect intrinsic dimension under several scenarios, and simultaneously generate high-quality syntheticdata by sampling from the learned latent distribution. Supplementary materials for this article are availableonline, including a standardized description of the materials available for reproducing the work. 

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5. Towards Sample-efficient Overparameterized Meta-learning

   Sun, Yue; Narang, Adhyyan; Gulluk, Ibrahim; Oymak, Samet; Fazel, Maryam (December 2021, Advances in neural information processing systems)

   An overarching goal in machine learning is to build a generalizable model with few samples. To this end, overparameterization has been the subject of immense interest to explain the generalization ability of deep nets even when the size of the dataset is smaller than that of the model. While the prior literature focuses on the classical supervised setting, this paper aims to demystify overparameterization for meta-learning. Here we have a sequence of linear-regression tasks and we ask: (1) Given earlier tasks, what is the optimal linear representation of features for a new downstream task? and (2) How many samples do we need to build this representation? This work shows that surprisingly, overparameterization arises as a natural answer to these fundamental meta-learning questions. Specifically, for (1), we first show that learning the optimal representation coincides with the problem of designing a task-aware regularization to promote inductive bias. We leverage this inductive bias to explain how the downstream task actually benefits from overparameterization, in contrast to prior works on few-shot learning. For (2), we develop a theory to explain how feature covariance can implicitly help reduce the sample complexity well below the degrees of freedom and lead to small estimation error. We then integrate these findings to obtain an overall performance guarantee for our meta-learning algorithm. Numerical experiments on real and synthetic data verify our insights on overparameterized meta-learning. 

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