Graph-Informed Adversarial Modeling: Infimal Subadditivity of Interpolative Divergences

TL;DR

This paper develops a theoretical framework for graph-informed adversarial learning using interpolative divergences, enabling more stable and structurally aware generative models.

Contribution

It introduces a new infimal subadditivity principle for interpolative divergences, justifies graph-informed GANs with localized discriminators, and extends results to various divergence types.

Findings

Theoretical proof of infimal subadditivity for interpolative divergences.

Justification for replacing standard GANs with graph-informed GANs (GiGANs).

Experiments show improved stability and structural recovery with GiGANs.

Abstract

We study adversarial learning when the target distribution factorizes according to a known Bayesian network. For interpolative divergences, including $(f,\Gamma)$-divergences, we prove a new infimal subadditivity principle showing that, under suitable conditions, a global variational discrepancy is controlled by an average of family-level discrepancies aligned with the graph. In an additive regime, the surrogate is exact. This closes a theoretical gap in the literature; existing subadditivity results justify graph-informed adversarial learning for classical discrepancies, but not for interpolative divergences, where the usual factorization argument breaks down. In turn, we provide a justification for replacing a standard, graph-agnostic GAN with a monolithic discriminator by a graph-informed GAN (GiGAN) with localized family-level discriminators, without requiring the optimizer itself to factorize according to the graph. We also obtain parallel results for integral probability metrics and proximal optimal transport divergences, identify natural discriminator classes for which the theory applies, and present experiments showing improved stability and structural recovery relative to graph-agnostic baselines.