Stabilizing Training of Generative Adversarial Networks through Regularization (1705.09367v2)

Abstract: Deep generative models based on Generative Adversarial Networks (GANs) have demonstrated impressive sample quality but in order to work they require a careful choice of architecture, parameter initialization, and selection of hyper-parameters. This fragility is in part due to a dimensional mismatch or non-overlapping support between the model distribution and the data distribution, causing their density ratio and the associated f-divergence to be undefined. We overcome this fundamental limitation and propose a new regularization approach with low computational cost that yields a stable GAN training procedure. We demonstrate the effectiveness of this regularizer across several architectures trained on common benchmark image generation tasks. Our regularization turns GAN models into reliable building blocks for deep learning.

• The paper introduces a Tikhonov regularizer that stabilizes GAN training by mitigating distributional mismatches.
• It employs Gaussian noise convolution to achieve well-defined f-divergences and prevent mode collapse.
• Empirical results on benchmarks like CelebA and CIFAR-10 demonstrate enhanced GAN reliability and output quality.

Overview of "Stabilizing Training of Generative Adversarial Networks through Regularization"

This paper addresses the inherent instability in training Generative Adversarial Networks (GANs), a class of deep generative models known for producing high-quality synthetic data. GANs, while innovative, are challenging to train due to their sensitivity to architectural design, initializations, and hyper-parameters. This instability mainly arises from issues like dimensional mismatch or non-overlapping support between the model distribution and the data distribution, leading to undefined density ratios and associated $f$-divergences.

Key Contributions

The paper introduces a novel regularization technique aimed at stabilizing GAN training, thus improving their reliability as a deep learning component. The authors propose an efficient regularization method that compensates for dimensional mismatches between the model and the data distribution. Using an analytical approach akin to training-with-noise, the authors develop a Tikhonov regularizer, which, when convolved with Gaussian noise, modifies the $f$-divergence objective, rendering a robust mechanism against distributional discrepancies.

This regularization technique, by ensuring well-defined $f$-divergences even under dimensional misspecifications, sidesteps the computational and performance issues associated with earlier methods such as explicit noise addition during training. The regularization inherently penalizes the discriminator's gradient norm and is claimed to be of low computational cost, making it feasible for practical application across various GAN architectures.

Analytical and Empirical Justification

The regularization method relies on the theoretical underpinning that involves smoothing operations by convolution with Gaussian noise, thereby achieving a more stable discriminant function. Empirically, the paper demonstrates the efficacy of this approach through experiments on multiple benchmark image datasets including CelebA, CIFAR-10, and LSUN, as well as various GAN architectures like DCGAN and ResNet GANs.

A particularly notable experiment involved training a GAN on a dataset constructed as a 2D submanifold mixture of Gaussians embedded in 3D space, a scenario rife with dimensional misspecification challenges. The regularization method successfully stabilized training, preventing the mode collapse common to unregularized GANs and yielding higher visual quality in the generated outputs.

Moreover, a cross-testing protocol is introduced, utilizing the discriminator’s classification ability to compare the outputs of regularized versus unregularized models, further validating the superior generalization capabilities facilitated by regularization.

Implications and Future Work

The implications of this research are both practical and theoretical. Practically, it paves the way for more reliable and stable GAN training processes, crucial for their adoption in sensitive applications like medical imaging and autonomous systems where stability and robustness are paramount. Theoretically, it opens avenues for further probing into the convergence properties and optimization landscapes of GANs under regularization.

Future work could delve into optimizing the annealing schedule of the regularizer's variance, further theoretical exploration of regularization effects in varying high-dimensional scenarios, and extending this framework to other types of generative models. The code repository linked within provides an avenue for practitioners to explore and apply these methodologies, potentially leading to innovations within the domain of generative modeling.

In summary, the paper makes strides in addressing longstanding issues with GAN training, proposing a theoretically sound yet computationally practical approach that significantly enhances the robustness of GANs and positions them as dependable components in the deep learning toolkit.