Understanding Overparameterization in Generative Adversarial Networks

Abstract

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. 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). 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.

Accepted in ICLR 2021

References in corpus (16)

• Auto-Encoding Variational Bayes
• GANs Trained by a Two Time-Scale Update Rule Converge to a Local Nash Equilibrium
• Large Scale GAN Training for High Fidelity Natural Image Synthesis
• A Convergence Theory for Deep Learning via Over-Parameterization
• On Lazy Training in Differentiable Programming
• The Numerics of GANs
• Compressed Sensing with Deep Image Prior and Learned Regularization
• Adversarial Video Generation on Complex Datasets
• Overparameterized Nonlinear Learning: Gradient Descent Takes the Shortest Path?
• Generalization Guarantees for Neural Networks via Harnessing the Low-rank Structure of the Jacobian
• Understanding GANs: the LQG Setting
• Towards GAN Benchmarks Which Require Generalization
• A Closer Look at the Optimization Landscapes of Generative Adversarial Networks
• GANs May Have No Nash Equilibria
• SGD Learns One-Layer Networks in WGANs
• Understanding and Stabilizing GANs' Training Dynamics with Control Theory

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