Reducing Mode Collapse With Monge-Kantorovich Optimal Transport for Generative Adversarial Networks

Area of Science:

• Artificial Intelligence
• Machine Learning
• Computer Vision

Background:

• Mode collapse is a significant challenge in Generative Adversarial Networks (GANs), limiting their practical applications.
• Existing solutions for mode collapse, such as optimal transport (OT) strategies and modifications to generator numbers or loss functions, have notable limitations including gradient issues and mode redundancy.

Purpose of the Study:

• To propose a novel method, Monge GAN, to effectively reduce mode collapse in generative adversarial networks.
• To address the limitations of existing approaches in mitigating mode collapse.

Main Methods:

• Formulating mode collapse as a Monge problem within optimal transport (OT).
• Transforming the Monge problem into a distribution transformation problem suitable for GANs.
• Utilizing a rectified affine neural network as a measurable function for distribution transformation.
• Employing the Kantorovich formulation to compute the optimal transport (OT) cost as the distance between distributions.

Main Results:

• Monge GAN successfully transforms the generated data distribution towards the original data distribution.
• Extensive experiments on image and numerical datasets demonstrate the efficacy of Monge GAN in reducing mode collapse.

Conclusions:

• Monge GAN offers a promising solution to the persistent challenge of mode collapse in generative adversarial networks.
• The proposed method, grounded in optimal transport theory, provides a robust framework for improving GAN stability and performance.