Generalization and Equilibrium in Generative Adversarial Nets (GANs) (1703.00573v5)

Abstract: We show that training of generative adversarial network (GAN) may not have good generalization properties; e.g., training may appear successful but the trained distribution may be far from target distribution in standard metrics. However, generalization does occur for a weaker metric called neural net distance. It is also shown that an approximate pure equilibrium exists in the discriminator/generator game for a special class of generators with natural training objectives when generator capacity and training set sizes are moderate. This existence of equilibrium inspires MIX+GAN protocol, which can be combined with any existing GAN training, and empirically shown to improve some of them.

• The paper demonstrates that traditional metrics like JS divergence fail to generalize, introducing neural net distance as a more effective measure.
• The paper establishes that a finite mixture of generators can approximate an equilibrium in GAN training, ensuring stability in discriminator-generator games.
• The paper introduces the MIX+GAN protocol, which leverages mixtures of generators and discriminators to improve generative performance and stabilize training.

Overview of Generalization and Equilibrium in Generative Adversarial Nets (GANs)

The paper "Generalization and Equilibrium in Generative Adversarial Nets (GANs)" offers a comprehensive analysis of the generalization properties and equilibrium conditions within GANs. Authored by Sanjeev Arora et al., this work highlights the potential limitations of GANs regarding their capacity to generate distributions that closely approximate target distributions, as well as presents strategies to ensure approximate equilibrium in GAN games.

Generalization in GANs

The authors investigate whether the trained distribution in GANs is close to the target distribution using traditional metrics such as Jensen-Shannon (JS) divergence or Wasserstein distance. They reveal that GANs may not generalize well using these metrics. Instead, they propose a weaker metric called neural net distance, showing that generalization does occur with this metric provided moderate generator capacity and reasonable training set sizes.

Key insights include:

• Generalization Limitations: The paper demonstrates that both JS divergence and Wasserstein distance can fail to generalize, leading to overfitting on finite samples and failing to capture the true distribution.
• Neural Net Distance: Unlike traditional metrics, neural net distance achieves generalization with reasonable sample sizes, maintaining a closer alignment between empirical and real distributions.

Existence of Equilibrium

A critical discussion in the paper centers on the equilibrium in GAN training. The authors establish that an approximate pure equilibrium exists in the discriminator-generator game, even when moderate generator capacities and natural training objectives are employed. This extends prior results that were limited to Wasserstein GANs.

• Infinite Mixtures: By considering an infinite mixture of generators, the authors argue that such mixtures can closely approximate any target distribution, leading to equilibrium.
• Finite Mixture Strategy: They provide a theorem showing that a finite mixture of generators can suffice to approximate the performance of infinite mixtures, ensuring equilibrium in practice.

Contribution: MIX+GAN Protocol

This theoretical foundation leads to the introduction of the MIX+GAN protocol, an innovative training framework that utilizes mixtures of generators and discriminators. The empirical results demonstrate that MIX+GAN can stabilize GAN training and improve generative performance.

Implications and Speculations for Future AI

1. Practical Improvements: By addressing GAN training instability through mixing strategies, the work has immediate practical implications for developing more robust generative models.
2. Theoretical Foundations: The insights on generalization extend our understanding of how learning in high-dimensional spaces might require weaker, more adaptable metrics.
3. Future AI Research: The observed need for balance between expressiveness and overfitting in GANs could guide future model architecture designs and training algorithms, highlighting an ongoing interplay between theory and empirical observation.

This paper thus advances the discourse on GANs by elucidating both theoretical and practical facets of training challenges, offering a detailed perspective that can inform future innovations in AI-driven generative modeling.