mlsanityData to 7 Oct 2026

Learning disconnected manifolds: a no GANs land

arXiv 2006.04596 ↗First posted 8 Jun 2020stat.ML cs.LGcited by 25

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Abstract (arXiv)

Typical architectures of Generative AdversarialNetworks make use of a unimodal latent distribution transformed by a continuous generator. Consequently, the modeled distribution always has connected support which is cumbersome when learning a disconnected set of manifolds. We formalize this problem by establishing a no free lunch theorem for the disconnected manifold learning stating an upper bound on the precision of the targeted distribution. This is done by building on the necessary existence of a low-quality region where the generator continuously samples data between two disconnected modes. Finally, we derive a rejection sampling method based on the norm of generators Jacobian and show its efficiency on several generators including BigGAN.

Key facts. Cited by 25 papers in the map (data through 7 Oct 2026). First posted on arXiv 8 Jun 2020.

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Citing papers per year: 2021: 7; 2022: 12; 2023: 5; 2024: 0; 2025: 0; 2026: 1.

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  1. 2022Verifying the Union of Manifolds Hypothesis for Image Datacited by 62
  2. 2021MG-GAN: A Multi-Generator Model Preventing Out-of-Distribution Samples in Pedestrian Trajectory Predictioncited by 61
  3. 2022Can Push-forward Generative Models Fit Multimodal Distributions?cited by 41
  4. 2022Quo Vadis: Is Trajectory Forecasting the Key Towards Long-Term Multi-Object Tracking?cited by 28
  5. 2022Polarity Sampling: Quality and Diversity Control of Pre-Trained Generative Networks via Singular Valuescited by 21
  6. 2023Unifying GANs and Score-Based Diffusion as Generative Particle Modelscited by 21
  7. 2022FairStyle: Debiasing StyleGAN2 with Style Channel Manipulationscited by 20
  8. 2022Textual Manifold-based Defense Against Natural Language Adversarial Examplescited by 19
  9. 2021On the expressivity of bi-Lipschitz normalizing flowscited by 15
  10. 2022Out-of-Distribution Detection with Reconstruction Error and Typicality-based Penaltycited by 11
  11. 2021Partition-Guided GANscited by 9
  12. 2023Precision-Recall Divergence Optimization for Generative Modeling with GANs and Normalizing Flowscited by 9
13 more
  1. 2022Semi-Supervised Manifold Learning with Complexity Decoupled Chart Autoencoderscited by 8
  2. 2021Latent reweighting, an almost free improvement for GANscited by 6
  3. 2026Action Hallucination in Generative Vision-Language-Action Modelscited by 5
  4. 2021Fast Jacobian-Vector Product for Deep Networkscited by 4
  5. 2022Multi-level Latent Space Structuring for Generative Controlcited by 4
  6. 2022Optimal 1-Wasserstein Distance for WGANscited by 3
  7. 2022Unveiling the Latent Space Geometry of Push-Forward Generative Modelscited by 3
  8. 2023Convergence and Recovery Guarantees of Unsupervised Neural Networks for Inverse Problemscited by 3
  9. 2021Generalization of GANs and overparameterized models under Lipschitz continuitycited by 2
  10. 2022Smooth image-to-image translations with latent space interpolationscited by 2
  11. 2023Spider GAN: Leveraging Friendly Neighbors to Accelerate GAN Trainingcited by 2
  12. 2021Provably Valid and Diverse Mutations of Real-World Media Data for DNN Testingcited by 1
  13. 2023Training Normalizing Flows with the Precision-Recall Divergencecited by 0