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Banach Wasserstein GAN

arXiv 1806.06621 ↗First posted 18 Jun 2018cs.CV cs.LG math.FAcited by 56

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Abstract (arXiv)

Wasserstein Generative Adversarial Networks (WGANs) can be used to generate realistic samples from complicated image distributions. The Wasserstein metric used in WGANs is based on a notion of distance between individual images, which induces a notion of distance between probability distributions of images. So far the community has considered ℓ2 as the underlying distance. We generalize the theory of WGAN with gradient penalty to Banach spaces, allowing practitioners to select the features to emphasize in the generator. We further discuss the effect of some particular choices of underlying norms, focusing on Sobolev norms. Finally, we demonstrate a boost in performance for an appropriate choice of norm on CIFAR-10 and CelebA.

Key facts. Cited by 56 papers in the map (data through 7 Oct 2026). First posted on arXiv 18 Jun 2018.

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Citing papers per year: 2021: 8; 2022: 9; 2023: 13; 2024: 13; 2025: 9; 2026: 4.

56 papers.

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  1. 2022Deep Unsupervised Domain Adaptation: A Review of Recent Advances and Perspectivescited by 98
  2. 2022Generative Adversarial Neural Operatorscited by 51
  3. 2023Nearly Optimal VC-Dimension and Pseudo-Dimension Bounds for Deep Neural Network Derivativescited by 30
  4. 2022SOS: Score-based Oversampling for Tabular Datacited by 29
  5. 2022Invertible Tabular GANs: Killing Two Birds with OneStone for Tabular Data Synthesiscited by 24
  6. 2023EHRDiff: Exploring Realistic EHR Synthesis with Diffusion Modelscited by 18
  7. 2024Continuous-Multiple Image Outpainting in One-Step via Positional Query and A Diffusion-based Approachcited by 18
  8. 2021Wasserstein Proximal of GANscited by 15
  9. 2024Deeper or Wider: A Perspective from Optimal Generalization Error with Sobolev Losscited by 14
  10. 2021Self-Diagnosing GAN: Diagnosing Underrepresented Samples in Generative Adversarial Networkscited by 13
  11. 2024Latent Diffusion Model-Enabled Low-Latency Semantic Communication in the Presence of Semantic Ambiguities and Wireless Channel Noisescited by 13
  12. 2024Graph Edit Distance with General Costs Using Neural Set Divergencecited by 10
38 more
  1. 2021Robust W-GAN-Based Estimation Under Wasserstein Contaminationcited by 9
  2. 2023Adversarial Constrained Bidding via Minimax Regret Optimization with Causality-Aware Reinforcement Learningcited by 7
  3. 2026HIERAMP: Coarse-to-Fine Autoregressive Amplification for Generative Dataset Distillationcited by 7
  4. 2021Moreau-Yosida f-divergencescited by 5
  5. 2024AnyECG: Foundational Models for Multitask Cardiac Analysis in Real-World Settingscited by 5
  6. 2025Robust Distribution Alignment for Industrial Anomaly Detection under Distribution Shiftcited by 5
  7. 2024Dissipative Gradient Descent Ascent Method: A Control Theory Inspired Algorithm for Min-max Optimizationcited by 4
  8. 2025Straighten Viscous Rectified Flow via Noise Optimizationcited by 4
  9. 2022Generative Adversarial Networks for Image Augmentation in Agriculture: A Systematic Reviewcited by 3
  10. 2023Assessing Domain Gap for Continual Domain Adaptation in Object Detectioncited by 3
  11. 2023Adaptive Consensus Optimization Method for GANscited by 3
  12. 2025Style-Adaptive Detection Transformer for Single-Source Domain Generalized Object Detectioncited by 3
  13. 2021About exchanging expectation and supremum for conditional Wasserstein GANscited by 2
  14. 2022Refiner: Data Refining against Gradient Leakage Attacks in Federated Learningcited by 2
  15. 2023Meta-Learning Enabled Score-Based Generative Model for 1.5T-Like Image Reconstruction from 0.5T MRIcited by 2
  16. 2023Convex Latent-Optimized Adversarial Regularizers for Imaging Inverse Problemscited by 2
  17. 2024Socialized Learning: A Survey of the Paradigm Shift for Edge Intelligence in Networked Systemscited by 2
  18. 2026Semantic-aware Wasserstein Policy Regularization for Large Language Model Alignmentcited by 2
  19. 2021Quality Map Fusion for Adversarial Learningcited by 1
  20. 2022HessianFR: An Efficient Hessian-based Follow-the-Ridge Algorithm for Minimax Optimizationcited by 1
  21. 2023Elastic Interaction Energy-Based Generative Model: Approximation in Feature Spacecited by 1
  22. 2023Parameter Estimation in DAGs from Incomplete Data via Optimal Transportcited by 1
  23. 2023GAN-MPC: Training Model Predictive Controllers with Parameterized Cost Functions using Demonstrations from Non-identical Expertscited by 1
  24. 2023Text-to-feature diffusion for audio-visual few-shot learningcited by 1
  25. 2023Hoeffding's Inequality for Markov Chains under Generalized Concentrability Conditioncited by 1
  26. 2024S2-DMs:Skip-Step Diffusion Modelscited by 1
  27. 2024Novel Hybrid Integrated Pix2Pix and WGAN Model with Gradient Penalty for Binary Images Denoisingcited by 1
  28. 2024Struc2mapGAN: improving synthetic cryo-EM density maps with generative adversarial networkscited by 1
  29. 2025Neural Measures for learning distributions of Random PDEscited by 1
  30. 2025Generative AI Meets Wireless Sensing: Towards Wireless Foundation Modelcited by 1
  31. 2021Variational Autoencoders: A Harmonic Perspectivecited by 0
  32. 2021IE-GAN: An Improved Evolutionary Generative Adversarial Network Using a New Fitness Function and a Generic Crossover Operatorcited by 0
  33. 2022Robust SVM Optimization in Banach spacescited by 0
  34. 2022Deep Progressive Feature Aggregation Network for High Dynamic Range Imagingcited by 0
  35. 2023Insights into Closed-form IPM-GAN Discriminator Guidance for Diffusion Modelingcited by 0
  36. 2024Feynman-Kac Operator Expectation Estimatorcited by 0
  37. 2024Curvature Diversity-Driven Deformation and Domain Alignment for Point Cloudcited by 0
  38. 2024Scaling-based Data Augmentation for Generative Models and its Theoretical Extensioncited by 0

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