[Paper Review] Towards Principled Methods for Training Generative Adversarial Networks

Martín Arjovsky, Léon Bottou|arXiv (Cornell University)|Jan 17, 2017

Generative Adversarial Networks and Image Synthesis10 references355 citations

TL;DR

This paper analyzes the training dynamics of GANs, explains sources of instability and vanishing gradients, and proposes a principled route using softer metrics and noise to stabilize training. It provides theoretical results on discriminator behavior with low-dimensional supports and introduces noise-based strategies to improve gradient signals to the generator.

ABSTRACT

The goal of this paper is not to introduce a single algorithm or method, but to make theoretical steps towards fully understanding the training dynamics of generative adversarial networks. In order to substantiate our theoretical analysis, we perform targeted experiments to verify our assumptions, illustrate our claims, and quantify the phenomena. This paper is divided into three sections. The first section introduces the problem at hand. The second section is dedicated to studying and proving rigorously the problems including instability and saturation that arize when training generative adversarial networks. The third section examines a practical and theoretically grounded direction towards solving these problems, while introducing new tools to study them.

Motivation & Objective

• Explain why GAN training is unstable and why discriminator-driven updates degrade as the discriminator improves.
• Characterize the effects of using the original GAN objective and the -log D alternative on gradient behavior.
• Propose a principled direction to fix instability via softer divergences and noise-based regularization.
• Provide theoretical results and practical tools to study and improve GAN training dynamics.

Proposed method

• Model the discriminator optimality and its impact on generator gradients under disjoint or low-dimensional supports.
• Prove perfect discrimination theorems showing that an optimal D can have accuracy 1 and zero gradient on data/support regions.
• Analyze vanishing gradients under the original GAN objective and under the -log D alternative.
• Introduce noise to the inputs (and to generator samples) to smooth distributions and derive gradient expressions under noisy distributions.
• Show that noisy formulations align the generator updates with a softened divergence objective (JSD with noisy distributions).
• Propose a practical path toward stabilization by moving toward softer metrics and joint noise injection to smooth the optimization landscape.

Experimental results

Research questions

• RQ1 Why do GAN generator updates degrade as the discriminator becomes better?
• RQ2 Under what conditions do the original GAN objective and the -log D alternative produce vanishing or unstable gradients?
• RQ3 Can softer metrics or input/output noise stabilize GAN training and provide more reliable gradient signals to the generator?
• RQ4 How do low-dimensional supports and perfect discriminators influence the training dynamics and divergences used?
• RQ5 What theoretical tools can quantify and guide the stabilization of GAN training with noisier/discretized distributions?

Key findings

• Distributions in GANs often lie on low-dimensional manifolds, enabling a perfect discriminator with zero gradient on supports.
• Under disjoint or low-dimensional supports, the optimal discriminator can have accuracy 1 and zero gradient almost everywhere, causing vanishing gradients for the generator when using the original objective.
• Using the -log D objective yields unstable updates due to inverted relations with KL and JSD, and with a near-ideal discriminator gradients can explode due to noise.
• Adding continuous noise to inputs (and to generator samples) smooths the distributions, yielding non-degenerate gradients and aligning updates with a softened divergence between noisy distributions.
• The noisy discriminator framework leads to gradient updates that move samples toward the data manifold while discouraging overly probable generator samples, promoting stabilization.
• Annealing the noise level helps the generator and discriminator to progressively match the true data distribution through a softened JSD objective.