Understanding GANs: the LQG Setting

Abstract

Generative Adversarial Networks (GANs) have become a popular method to learn a probability model from data. In this paper, we aim to provide an understanding of some of the basic issues surrounding GANs including their formulation, generalization and stability on a simple benchmark where the data has a high-dimensional Gaussian distribution. Even in this simple benchmark, the GAN problem has not been well-understood as we observe that existing state-of-the-art GAN architectures may fail to learn a proper generative distribution owing to (1) stability issues (i.e., convergence to bad local solutions or not converging at all), (2) approximation issues (i.e., having improper global GAN optimizers caused by inappropriate GAN's loss functions), and (3) generalizability issues (i.e., requiring large number of samples for training). In this setup, we propose a GAN architecture which recovers the maximum-likelihood solution and demonstrates fast generalization. Moreover, we analyze global stability of different computational approaches for the proposed GAN optimization and highlight their pros and cons. Finally, we outline an extension of our model-based approach to design GANs in more complex setups than the considered Gaussian benchmark.

References in corpus (5)

• Spectral Normalization for Generative Adversarial Networks
• Generative Moment Matching Networks
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• 2-Wasserstein Approximation via Restricted Convex Potentials with Application to Improved Training for GANs
• SGD Learns One-Layer Networks in WGANs
• Understanding Overparameterization in Generative Adversarial Networks
• The Inductive Bias of Restricted f-GANs
• Generative Adversarial Nets for Robust Scatter Estimation: A Proper Scoring Rule Perspective
• Particle Optimization in Stochastic Gradient MCMC
• Understanding and Stabilizing GANs' Training Dynamics with Control Theory
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• Universality Theorems for Generative Models
• Forward Super-Resolution: How Can GANs Learn Hierarchical Generative Models for Real-World Distributions
• Deconstructing Generative Adversarial Networks
• GANs with Conditional Independence Graphs: On Subadditivity of Probability Divergences
• Convergence and Sample Complexity of SGD in GANs
• Making Method of Moments Great Again? -- How can GANs learn distributions
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• Performance Analysis of Plug-and-Play ADMM: A Graph Signal Processing Perspective
• Understanding Entropic Regularization in GANs
• On the Optimization Landscape of Maximum Mean Discrepancy