f-GAN: Training Generative Neural Samplers using Variational Divergence Minimization (1606.00709v1)

Abstract: Generative neural samplers are probabilistic models that implement sampling using feedforward neural networks: they take a random input vector and produce a sample from a probability distribution defined by the network weights. These models are expressive and allow efficient computation of samples and derivatives, but cannot be used for computing likelihoods or for marginalization. The generative-adversarial training method allows to train such models through the use of an auxiliary discriminative neural network. We show that the generative-adversarial approach is a special case of an existing more general variational divergence estimation approach. We show that any f-divergence can be used for training generative neural samplers. We discuss the benefits of various choices of divergence functions on training complexity and the quality of the obtained generative models.

• The paper generalizes GAN training by integrating any f-divergence within a variational divergence minimization framework.
• It introduces a simplified single-step gradient method that streamlines saddle-point optimization under strong convexity and concavity conditions.
• Experimental results on MNIST and LSUN highlight how different divergence measures impact training stability and sample quality.

$f$-GAN: Training Generative Neural Samplers using Variational Divergence Minimization

The paper "f-GAN: Training Generative Neural Samplers using Variational Divergence Minimization" by Nowozin, Cseke, and Tomioka presents an extended framework for training generative adversarial networks (GANs) using a general family of divergences, the $f$-divergences. This work provides a theoretical and practical foundation for broadening the scope of GAN training, enabling the use of various divergence measures beyond the commonly used Jensen-Shannon divergence.

Overview

Generative neural samplers are probabilistic models that use feedforward neural networks to generate samples from a certain probability distribution. These models excel in generating diverse data types, such as images, text, and audio. However, traditional methods like likelihood evaluation and marginalization are not feasible for these models. The original GAN framework introduced by Goodfellow et al. (2014) enables the training of these generative models by introducing an auxiliary discriminative network, thus reformulating the problem into an adversarial setting.

This paper demonstrates that the GAN training approach is a specific instance of a more general framework known as variational divergence minimization (VDM), which itself is rooted in estimating $f$-divergences—a broad class of statistical divergences. By extending VDM to generative model estimation, the authors show that one can employ any $f$-divergence for training generative neural samplers. They provide a thorough analysis of the computational trade-offs and benefits associated with different choices of divergence functions.

Key Contributions

1. Generalization to $f$-divergences: The authors extend the generative-adversarial training method by showing that any $f$-divergence can be used within the VDM framework for training generative neural samplers. This unifies various divergence measures under a single training paradigm and opens the door to leveraging different statistical properties of $f$-divergences for specific tasks.
2. Simplified Saddle-point Optimization Procedure: The paper simplifies the original saddle-point optimization procedure proposed by Goodfellow et al. by providing a theoretical justification and introducing a direct, single-step gradient method. This method ensures convergence to a saddle point under mild conditions—namely, strong convexity in the generator's parameters and strong concavity in the discriminator's parameters.
3. Experimental Insights: The paper offers detailed experimental insights gained from applying different $f$-divergences on natural image datasets, particularly MNIST and LSUN. These experiments underscore the strengths and weaknesses of each divergence measure concerning the training stability and quality of the generated samples.

Experimental Results

The authors empirically validate their methodology by training generative models on the MNIST and LSUN datasets. For MNIST, they evaluate their models using kernel density estimation (KDE) of the log-likelihood on the test data. They find that models trained using Kullback-Leibler divergence and Pearson $\chi^2$ divergence perform comparably to Variational Autoencoders (VAEs) in terms of log-likelihood, emphasizing that different divergences offer varied empirical benefits.

The LSUN dataset experiments involve generating natural images using the architecture proposed in DCGAN. The results demonstrate that models trained with different divergences, including the standard GAN (Jensen-Shannon based) and Kullback-Leibler divergence, produce visually compelling and diverse samples.

Implications and Future Work

This paper's findings have both theoretical and practical implications:

1. Theoretical implications: The generalization of GAN training to $f$-divergences provides a new perspective on how divergence measures influence the learning dynamics and quality of generative models. This framework offers a principled way to choose a divergence based on the specific requirements of the generative task at hand.
2. Practical implications: The single-step gradient method for saddle-point optimization simplifies the implementation and enhances the convergence properties of GANs. Practitioners can leverage this method to stabilize and speed up the training process of GANs applied to various applications, from image synthesis to data augmentation.

Future Directions

The extension to $f$-divergences invites several avenues for further research:

1. Conditional Models: Future work could explore the application of this framework to conditional generative models, where additional input variables help condition the generation process, as seen in conditional GANs.
2. Combination with VAEs: Combining the $f$-GAN framework with VAEs, as suggested by recent studies (e.g., adversarial autoencoders), could enhance the capabilities of both generative modeling approaches, combining the strengths of explicit likelihood modeling and adversarial training.
3. Robustness and Generalization: Analysis of how different $f$-divergences affect the robustness and generalization capabilities of generative models across varied and complex datasets would be valuable for improving their practical utility in real-world scenarios.

In summary, the paper "f-GAN: Training Generative Neural Samplers using Variational Divergence Minimization" significantly advances the understanding and application of GANs by introducing a broader training framework using $f$-divergences, simplifying optimization methods, and offering concrete experimental validations. This framework holds promise for creating more nuanced and capable generative models across diverse domains.