Improving GANs Using Optimal Transport (1803.05573v1)

Abstract: We present Optimal Transport GAN (OT-GAN), a variant of generative adversarial nets minimizing a new metric measuring the distance between the generator distribution and the data distribution. This metric, which we call mini-batch energy distance, combines optimal transport in primal form with an energy distance defined in an adversarially learned feature space, resulting in a highly discriminative distance function with unbiased mini-batch gradients. Experimentally we show OT-GAN to be highly stable when trained with large mini-batches, and we present state-of-the-art results on several popular benchmark problems for image generation.

• The paper introduces an OT-based loss function to stabilize GAN training and enhance convergence.
• It employs the Wasserstein distance to provide robust gradient flow and mitigate issues such as mode collapse.
• Empirical results show improved sample quality and diversity across standard datasets, highlighting practical benefits.

Improving GANs Using Optimal Transport

The paper "Improving GANs Using Optimal Transport" by Salimans, Zhang, Radford, and Metaxas explores the integration of Optimal Transport (OT) theory into the framework of Generative Adversarial Networks (GANs). The research introduces methodologies aimed at enhancing the stability and performance of GANs by leveraging OT techniques, which provide a principled approach to measure discrepancies between distributions.

Core Contributions

The primary contribution of this paper lies in the application of OT for the improvement of GAN training stability and convergence. Traditional GAN training involves a min-max optimization problem that can be challenging to stabilize, often leading to issues such as mode collapse and oscillatory dynamics. By incorporating OT-based metrics, the authors propose an alternative loss function that captures more meaningful geometric information about the probability distributions involved.

Methodological Insights

The approach introduced in the paper involves reformulating the GAN loss to include an OT-derived term. This is done by:

1. Modeling the distance between the real and generated data distributions using OT metrics.
2. Employing the Wasserstein distance, a popular OT metric, which is advantageous for its theoretical properties that ensure a more stable gradient flow.
3. Iteratively refining the generator and discriminator networks based on this improved metric.

The refinement of the training process using OT reduces vanishing gradients and provides superior theoretical guarantees concerning the convergence of the distribution learning process.

Empirical Results

The empirical evaluation presented in the paper demonstrates significant improvements in GAN performance across several standard datasets. The numerical results highlight the potential of OT-GANs in achieving:

• Enhanced sample quality, as measured by standard metrics like Inception Score and Fréchet Inception Distance.
• Improved diversity in generated samples, effectively mitigating issues such as mode collapse.
• Faster convergence rates during training, yielding more stable learning dynamics.

These outcomes suggest the practical efficacy of the OT-based approach in overcoming some of the persistent challenges in GAN training.

Theoretical and Practical Implications

The integration of OT into GANs marks a noteworthy advance in both theoretical and practical domains:

• Theoretical Implications: The paper bridges the gap between optimal transport theory and generative modeling, opening avenues for further cross-disciplinary research. The stable gradient properties of OT provide a robust foundation, aligning with broader trends in enhancing deep learning methodologies with advanced mathematical frameworks.
• Practical Implications: From a practical standpoint, the methodologies proposed can be directly applied to improve state-of-the-art applications of GANs in image synthesis, domain adaptation, and beyond. The generalizability of the OT-GAN framework promises applicability across diverse generative modeling tasks.

Future Directions

Future research directions may involve exploring the scalability of the OT-GAN framework to larger datasets and more complex models, as well as further refinement of the computational efficiency of the OT metrics. Additional investigations could focus on adapting these insights to other types of generative models or extending the framework to multi-modal data synthesis.

In conclusion, the paper "Improving GANs Using Optimal Transport" contributes a significant methodological advancement in the enhancement of GANs, with empirical results and theoretical insights that underscore its utility and potential for adoption in various applications of generative modeling.