PacGAN: The power of two samples in generative adversarial networks (1712.04086v3)

Abstract: Generative adversarial networks (GANs) are innovative techniques for learning generative models of complex data distributions from samples. Despite remarkable recent improvements in generating realistic images, one of their major shortcomings is the fact that in practice, they tend to produce samples with little diversity, even when trained on diverse datasets. This phenomenon, known as mode collapse, has been the main focus of several recent advances in GANs. Yet there is little understanding of why mode collapse happens and why existing approaches are able to mitigate mode collapse. We propose a principled approach to handling mode collapse, which we call packing. The main idea is to modify the discriminator to make decisions based on multiple samples from the same class, either real or artificially generated. We borrow analysis tools from binary hypothesis testing---in particular the seminal result of Blackwell [Bla53]---to prove a fundamental connection between packing and mode collapse. We show that packing naturally penalizes generators with mode collapse, thereby favoring generator distributions with less mode collapse during the training process. Numerical experiments on benchmark datasets suggests that packing provides significant improvements in practice as well.

PacGAN: Addressing Mode Collapse in GANs Through Sample Packing

The paper "PacGAN: The power of two samples in generative adversarial networks" introduces a novel approach to mitigating mode collapse in Generative Adversarial Networks (GANs) by utilizing a concept termed "packing." The authors focus on understanding and resolving the mode collapse problem, where GANs generate outputs with limited diversity, thereby failing to capture the full variability of the input data distribution.

Core Ideas and Contributions

GANs, since their inception, have made significant strides in generating realistic images and other high-dimensional data. However, one of the persistent issues with GANs is mode collapse, where the generator fails to produce diverse samples representative of the entire input distribution. This paper tackles mode collapse by altering the discriminator's structure to consider multiple samples simultaneously—a concept the authors call "packing." Unlike traditional GANs, which consider individual samples, PacGAN forms a single input to the discriminator from multiple data points, thus evaluating on product distributions.

The introduction of packing is grounded in hypothesis testing principles, drawing specifically from binary hypothesis testing and leveraging results like those of Blackwell. This theoretical framework allows for a rigorous understanding of how packing penalizes mode collapse during training.

1. Mathematical Formulation of Mode Collapse: The paper posits a formal definition of mode collapse, which is used to frame the relationship between lack of sample diversity and the generator's performance. This theoretical underpinning is expressed through a two-dimensional representation known as the mode collapse region, providing a fundamental basis for understanding discriminator behavior.
2. Analytic Insights on Product Distributions: By extending analysis to product distributions via packing, the work provides insights into how such distributions naturally penalize generators that exhibit mode collapse. The analytical results demonstrate that the total variation distance increases under packing at different rates, dependent on the presence of mode collapse.
3. Extensive Empirical Validation and Practical Implications: Through experiments on standard datasets like MNIST and CelebA, the authors empirically validate PacGAN's efficacy. The results demonstrate significant improvements over several state-of-the-art methods, highlighting PacGAN's robustness and effectiveness. Importantly, the packing method requires minimal architectural changes and no hyperparameter tuning, making it a versatile enhancement applicable across various GAN architectures.

Theoretical Implications and Future Directions

The theoretical implications of this work suggest that optimizing for less mode collapse is achievable by modifying how discriminators process data. By viewing the discriminator through the lens of binary hypothesis testing, the analysis elucidates mechanistic insights into sampling robustness intrinsic to the packing approach. Moreover, the connection with classical hypothesis testing offers avenues to explore other discriminator modifications that might further enhance GAN training stability and output diversity.

Speculatively, future work might extend this approach by exploring alternative discriminator architectures that incorporate packing in more sophisticated ways, such as permutation-invariant models or attention-based architectures. Additionally, investigating the generalization of packing to other types of generative models beyond GANs could also yield valuable insights, potentially offering solutions to similar challenges in those domains.

Conclusion

PacGAN presents a concise yet compelling approach to addressing mode collapse—a long-standing challenge in GAN training. By leveraging multiple samples in a discriminator decision, the method enhances the diversity of generated samples without significant overhead. This contribution underscores the power of incorporating well-understood statistical principles into machine learning model design, suggesting a broader applicability of classical theory to modern AI systems.