[Paper Review] BEGAN: Boundary Equilibrium Generative Adversarial Networks

David Berthelot, Thomas Schumm+1 more|arXiv (Cornell University)|Mar 31, 2017

Generative Adversarial Networks and Image Synthesis16 references744 citations

TL;DR

BEGAN introduces an auto-encoder discriminator with a boundary equilibrium mechanism to balance generator and discriminator, deriving a Wasserstein-based loss and a convergence measure for stable, high-quality image generation.

ABSTRACT

We propose a new equilibrium enforcing method paired with a loss derived from the Wasserstein distance for training auto-encoder based Generative Adversarial Networks. This method balances the generator and discriminator during training. Additionally, it provides a new approximate convergence measure, fast and stable training and high visual quality. We also derive a way of controlling the trade-off between image diversity and visual quality. We focus on the image generation task, setting a new milestone in visual quality, even at higher resolutions. This is achieved while using a relatively simple model architecture and a standard training procedure.

Motivation & Objective

• Motivate a stable GAN framework that mitigates training instability and mode collapse.
• Propose an equilibrium mechanism to balance generator and discriminator during training.
• Develop a loss based on a Wasserstein-distance lower bound applied to auto-encoder reconstruction errors.
• Introduce a convergence measure and analyze how to control image diversity versus visual quality.
• Demonstrate high-quality, high-resolution image generation with a simple architecture.

Proposed method

• Use an auto-encoder as the discriminator (EBGAN-style).
• Define an auto-encoder reconstruction loss L(v)=|v−D(v)|^η with η∈{1,2}.
• Derive a lower bound on the Wasserstein distance between auto-encoder loss distributions and maximize the bound w.r.t. the discriminator.
• Introduce an equilibrium term and a diversity ratio γ that balances real-image reconstruction and fake-image reconstruction.
• Implement a boundary equilibrium GAN (BEGAN) objective with a control variable k_t updated by k_{t+1}=k_t+λ_k(γL(x)−L(G(z))).
• Provide a global convergence measure M_global = L(x) + |γL(x) − L(G(z_G))| and discuss its use for monitoring training.

Experimental results

Research questions

• RQ1 Does an auto-encoder-based discriminator with an equilibrium controller yield stable and fast convergence for GANs?
• RQ2 How does balancing via γ and the k_t feedback influence image diversity and visual quality?
• RQ3 Can a Wasserstein-distance-based bound on auto-encoder losses serve as an effective convergence proxy for GAN training?
• RQ4 How does BEGAN perform across resolutions from 32×32 to 256×256 in terms of stability and realism?
• RQ5 What is the impact of maintaining equilibrium on avoiding mode collapse and improving sample quality?

Key findings

• BEGAN achieves stable and fast training without complex alternating procedures.
• The γ-diversity control allows explicit trade-offs between image diversity and visual quality.
• A convergence measure M_global correlates with image fidelity and rapid convergence is observed.
• Qualitative results show high-quality, coherent high-resolution images with varied poses and expressions on CelebA-like data.
• Experiments demonstrate robustness to unbalanced networks through equilibrium maintenance.
• Inception-score-like evaluation indicates competitive or favorable performance relative to several GAN variants (within the unsupervised setting).