mlsanityData to 7 Oct 2026

Graph-Informed Adversarial Modeling: Infimal Subadditivity of Interpolative Divergences

arXiv 2603.20025 ↗First posted 20 Mar 2026stat.ML cs.LG math.STcited by 0

Not on the map. Why?

Abstract (arXiv)

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.

Key facts. No citing papers in the map yet (data through 7 Oct 2026). Builds on 30 of its 53 references that are in the map. First posted on arXiv 20 Mar 2026.

Builds on

30 of 53 references.

References · 30

  1. 2017Improved Training of Wasserstein GANscited by 2,223
  2. 2018Spectral Normalization for Generative Adversarial Networkscited by 1,618
  3. 2019Normalizing Flows for Probabilistic Modeling and Inferencecited by 1,315
  4. 2021E(n) Equivariant Graph Neural Networkscited by 951
  5. 2018Free-Form Image Inpainting with Gated Convolutioncited by 594
  6. 2016f-GAN: Training Generative Neural Samplers using Variational Divergence Minimizationcited by 504
  7. 2018GraphRNN: Generating Realistic Graphs with Deep Auto-regressive Modelscited by 406
  8. 2017Real-valued (Medical) Time Series Generation with Recurrent Conditional GANscited by 329
  9. 2022Graph neural networks for materials science and chemistrycited by 181
  10. 2017CausalGAN: Learning Causal Implicit Generative Models with Adversarial Trainingcited by 152
  11. 2021DECAF: Generating Fair Synthetic Data Using Causally-Aware Generative Networkscited by 109
  12. 2019Free-form Video Inpainting with 3D Gated Convolution and Temporal PatchGANcited by 85
18 more
  1. 2019Normalized Wasserstein Distance for Mixture Distributions with Applications in Adversarial Learning and Domain Adaptationcited by 23
  2. 2022Structure-preserving GANscited by 17
  3. 2024Wasserstein Gradient Flows for Moreau Envelopes of f-Divergences in Reproducing Kernel Hilbert Spacescited by 15
  4. 2020Causal Adversarial Network for Learning Conditional and Interventional Distributionscited by 13
  5. 2017Understanding GANs: the LQG Settingcited by 12
  6. 2020GINNs: Graph-Informed Neural Networks for Multiscale Physicscited by 12
  7. 2023Conditional Generative Models are Provably Robust: Pointwise Guarantees for Bayesian Inverse Problemscited by 12
  8. 2025DenseGNN: universal and scalable deeper graph neural networks for high-performance property prediction in crystals and moleculescited by 12
  9. 2016Square Hellinger Subadditivity for Bayesian Networks and its Applications to Identity Testingcited by 11
  10. 2019Formulation and properties of a divergence used to compare probability measures without absolute continuitycited by 11
  11. 2022Lipschitz-regularized gradient flows and generative particle algorithms for high-dimensional scarce datacited by 8
  12. 2022Principled Knowledge Extrapolation with GANscited by 6
  13. 2024Paired Wasserstein Autoencoders for Conditional Samplingcited by 5
  14. 2020GAT-GMM: Generative Adversarial Training for Gaussian Mixture Modelscited by 4
  15. 2024Robust Generative Learning with Lipschitz-Regularized α-Divergences Allows Minimal Assumptions on Target Distributionscited by 4
  16. 2023Optimal Transport Regularized Divergences: Application to Adversarial Robustnesscited by 2
  17. 2024Learning conditional distributions on continuous spacescited by 2
  18. 2025Proximal optimal transport divergencescited by 2

Built on by

Not cited yet.