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1. BourGAN: Generative Networks with Metric Embeddings

   Xiao, Chang; Zhong, Peilin; Zheng, Changxi (December 2018, 32nd Conference on Neural Information Processing Systems)

   This paper addresses the mode collapse for generative adversarial networks (GANs). We view modes as a geometric structure of data distribution in a metric space. Under this geometric lens, we embed subsamples of the dataset from an arbitrary metric space into the L2 space, while preserving their pairwise distance distribution. Not only does this metric embedding determine the dimensionality of the latent space automatically, it also enables us to construct a mixture of Gaussians to draw latent space random vectors. We use the Gaussian mixture model in tandem with a simple augmentation of the objective function to train GANs. Every major step of our method is supported by theoretical analysis, and our experiments on real and synthetic data confirm that the generator is able to produce samples spreading over most of the modes while avoiding unwanted samples, outperforming several recent GAN variants on a number of metrics and offering new features. 

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2. Double Descent and Other Interpolation Phenomena in GANs

   Luzi, Lorenzo; Dar, Yehuda; Baraniuk, Richard (June 2021, ArXivorg)

   null (Ed.)

   We study overparameterization in generative adversarial networks (GANs) that can interpolate the training data. We show that overparameterization can improve generalization performance and accelerate the training process. We study the generalization error as a function of latent space dimension and identify two main behaviors, depending on the learning setting. First, we show that overparameterized generative models that learn distributions by minimizing a metric or f-divergence do not exhibit double descent in generalization errors; specifically, all the interpolating solutions achieve the same generalization error. Second, we develop a new pseudo-supervised learning approach for GANs where the training utilizes pairs of fabricated (noise) inputs in conjunction with real output samples. Our pseudo-supervised setting exhibits double descent (and in some cases, triple descent) of generalization errors. We combine pseudo-supervision with overparameterization (i.e., overly large latent space dimension) to accelerate training while performing better, or close to, the generalization performance without pseudo-supervision. While our analysis focuses mostly on linear GANs, we also apply important insights for improving generalization of nonlinear, multilayer GANs. 

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

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

   null (Ed.)

   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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4. AE-OT-GAN: Training GANs from data specific latent distribution

   Dongsheng An, Yang Guo (January 2020, European Conference on Computer Vision (ECCV2020))

   Though generative adversarial networks (GANs) are prominent models to generate realistic and crisp images, they are unstable to train and suffer from the mode collapse problem. The problems of GANs come from approximating the intrinsic discontinuous distribution transform map with continuous DNNs. The recently proposed AE-OT model addresses the discontinuity problem by explicitly computing the discontinuous optimal transform map in the latent space of the autoencoder. Though have no mode collapse, the generated images by AE-OT are blurry. In this paper, we propose the AE-OT-GAN model to utilize the advantages of the both models: generate high quality images and at the same time overcome the mode collapse problems. Specifically, we firstly embed the low dimensional image manifold into the latent space by autoencoder (AE). Then the extended semi-discrete optimal transport (SDOT) map is used to generate new latent codes. Finally, our GAN model is trained to generate high quality images from the latent distribution induced by the extended SDOT map. The distribution transform map from this dataset related latent distribution to the data distribution will be continuous, and thus can be well approximated by the continuous DNNs. Additionally, the paired data between the latent codes and the real images gives us further restriction about the generator and stabilizes the training process. Experiments on simple MNIST dataset and complex datasets like CIFAR10 and CelebA show the advantages of the proposed method. 

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5. Implications of data topology for deep generative models

   https://doi.org/10.3389/fcomp.2024.1260604  

   Jin, Yinzhu; McDaniel, Rory; Tatro, N Joseph; Catanzaro, Michael J; Smith, Abraham D; Bendich, Paul; Dwyer, Matthew B; Fletcher, P Thomas (August 2024, Frontiers in Computer Science)

   Many deep generative models, such as variational autoencoders (VAEs) and generative adversarial networks (GANs), learn an immersion mapping from a standard normal distribution in a low-dimensional latent space into a higher-dimensional data space. As such, these mappings are only capable of producing simple data topologies, i.e., those equivalent to an immersion of Euclidean space. In this work, we demonstrate the limitations of such latent space generative models when trained on data distributions with non-trivial topologies. We do this by training these models on synthetic image datasets with known topologies (spheres, torii, etc.). We then show how this results in failures of both data generation as well as data interpolation. Next, we compare this behavior to two classes of deep generative models that in principle allow for more complex data topologies. First, we look at chart autoencoders (CAEs), which construct a smooth data manifold from multiple latent space chart mappings. Second, we explore score-based models, e.g., denoising diffusion probabilistic models, which estimate gradients of the data distribution without resorting to an explicit mapping to a latent space. Our results show that these models do demonstrate improved ability over latent space models in modeling data distributions with complex topologies, however, challenges still remain. 

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