Generalization Bounds for a Generator-Regularized InfoGAN-Inspired Adversarial Objective

Mahmud Hasan^1*Mathias Nthiani Muia²Md Mahmudul Islam³

• ¹Virginia Commonwealth University, Richmond, United States
• ²University of South Alabama, Mobile, United States
• ³The University of Alabama at Birmingham, Birmingham, United States

The Information Maximizing Generative Adversarial Network (InfoGAN) can be formulated as a minimax problem involving two neural networks, namely a discriminator and a generator, together with an additional mutual information regularization term. In this paper, we study an InfoGAN-inspired adversarial framework obtained by removing the latent code component and introducing an explicit regularization term on the generator. This yields a generator-regularized adversarial objective that is analytically tractable for learning-theoretic analysis. We establish generalization error bounds by analyzing the difference between the empirical and population objective functions, with error bounds obtained via the Rademacher complexity of the discriminator, generator, and their composition. The resulting bounds reveal explicit n−1/2 and m−1/2 decay rates and quantify the role of the generator regularization parameter. The theory is specialized to two-layer networks with Lipschitz continuous and non-decreasing activation functions, where explicit entropy-based complexity bounds are derived. Experiments on the CIFAR-10 dataset validate the predicted scaling behavior and demonstrate that the generalization gap decreases systematically with sample size, further highlighting the stabilizing effect of generator regularization. Overall, this work provides a first rigorous generalization analysis for an InfoGAN-inspired adversarial objective with explicit generator regularization.