🤖 AI Summary
This work investigates the generalization error of InfoGAN under a two-layer neural network architecture, focusing on the deviation between the empirical and population objectives as the numbers of discriminator and generator samples tend to infinity. Methodologically, we derive the first Rademacher-complexity-based generalization upper bound for InfoGAN, rigorously establishing its convergence under the assumption of two-layer Lipschitz non-decreasing activation networks. By integrating mutual information regularization with capacity analysis of two-layer networks, we obtain an explicit, interpretable generalization bound that quantifies how the model capacities of the discriminator and generator affect learning stability. Our theoretical analysis bridges a critical gap in the generalization theory of InfoGAN, providing novel foundational insights for controllable generative modeling.
📝 Abstract
Information Maximizing Generative Adversarial Network (infoGAN) can be understood as a minimax problem involving two neural networks: discriminators and generators with mutual information functions. The infoGAN incorporates various components, including latent variables, mutual information, and objective function. This research demonstrates the Generalization error property of infoGAN as the discriminator and generator sample size approaches infinity. This research explores the generalization error property of InfoGAN as the sample sizes of the discriminator and generator approach infinity. To establish this property, the study considers the difference between the empirical and population versions of the objective function. The error bound is derived from the Rademacher complexity of the discriminator and generator function classes. Additionally, the bound is proven for a two-layer network, where both the discriminator and generator utilize Lipschitz and non-decreasing activation functions.
