Inducing Metrizability of Generative Adversarial Networks with Discriminative Normalized Linear Layer

핵심 개념

Generative adversarial networks (GANs) can be optimized to make the generator distribution close to the target distribution by satisfying metrizable conditions on the discriminator, including direction optimality, separability, and injectivity.

초록

The paper addresses the question of whether GAN optimization actually makes the generator distribution close to the target distribution. It derives metrizable conditions, sufficient conditions for the discriminator to serve as the distance between the distributions, by connecting the GAN formulation with the concept of sliced optimal transport.
The key insights are:

The authors introduce the Functional Mean Divergence (FM) and Functional Mean Divergence* (FM*) to analyze the metrizability of the discriminator.
They show that direction optimality, separability, and injectivity of the discriminator's feature mapping are sufficient conditions for the discriminator to be a metrizable distance.
Based on these theoretical results, the authors propose the Slicing Adversarial Network (SAN), which modifies the GAN training scheme to enforce direction optimality on the discriminator.
Experiments on synthetic and image datasets support the theoretical results and demonstrate the effectiveness of SAN compared to standard GANs.
SAN can be easily applied to existing GANs by simple modifications to the discriminator architecture and training objective.

통계

The target probability distribution is modeled as a mixture of 8 isotropic Gaussians in a 2D space.
The generator uses a 10-dimensional latent space.

인용구

None

핵심 통찰 요약

SAN

by Yuhta Takida... 게시일 arxiv.org 04-11-2024

https://arxiv.org/pdf/2301.12811.pdf

더 깊은 질문

How can the proposed metrizable conditions be extended to other generative models beyond GANs, such as variational autoencoders or diffusion models

The proposed metrizable conditions can be extended to other generative models beyond GANs by adapting the concepts to fit the specific characteristics of each model. For variational autoencoders (VAEs), one could consider the optimization objective, such as minimizing the Kullback-Leibler divergence or maximizing the evidence lower bound. By connecting the concept of sliced optimal transport to VAEs, one could derive metrizable conditions that ensure the encoder and decoder distributions are close in a meaningful way. Similarly, for diffusion models, which are optimized using denoising diffusion probabilistic models, one could explore how the discriminator can serve as a distance metric between the generated samples and the target distribution. By formulating the appropriate optimization objectives and conditions, one can establish metrizable criteria for these models as well.

What are the potential limitations or drawbacks of the SAN approach, and how can they be addressed

One potential limitation of the SAN approach is the additional computational complexity introduced by modifying the training scheme to enforce direction optimality and separability. This could lead to longer training times and increased resource requirements. To address this, one could explore optimization techniques to streamline the training process, such as adaptive learning rate schedules or regularization methods to prevent overfitting. Additionally, further research could focus on developing more efficient algorithms for enforcing the metrizable conditions without significantly increasing computational overhead.

What are the broader implications of ensuring that the discriminator in a GAN serves as a meaningful distance metric between the generator and target distributions

Ensuring that the discriminator in a GAN serves as a meaningful distance metric between the generator and target distributions has several broader implications. Firstly, it can lead to more stable and reliable training of GANs, as the discriminator provides valuable feedback to the generator on how to improve the generated samples. This can result in higher-quality outputs and better convergence during training. Additionally, having a discriminator that acts as a distance metric can enhance the interpretability of the GAN model, allowing for a clearer understanding of the learned representations and the relationship between the generator and target distributions. Overall, this approach can contribute to advancements in generative modeling and improve the performance of GANs in various applications.