On Translation and Reconstruction Guarantees of the Cycle-Consistent Generative Adversarial Networks

The task of unpaired image-to-image translation has witnessed a revolution with the introduction of the cycle-consistency loss to Generative Adversarial Networks (GANs). Numerous variants, with Cycle-Consistent Adversarial Network (Cy-cleGAN) at their forefront, have shown remarkable empirical performance. The involvement of two unalike data spaces and the existence of multiple solution maps between them are some of the facets that make such architectures unique. In this study, we investigate the statistical properties of such unpaired data translator networks between distinct spaces, bearing the additional responsibility of cycle-consistency. In a density estimation setup, we derive sharp non-asymptotic bounds on the translation errors under suitably characterized models. This, in turn, points out sufficient regularity conditions that maps must obey to carry out successful translations. We further show that cycle-consistency is achieved as a consequence of the data being successfully generated in each space based on observations from the other. In a first-of-its-kind attempt, we also provide deterministic bounds on the cumulative reconstruction error. In the process, we establish tolerable upper bounds on the discrepancy responsible for ill-posedness in such networks.