mlsanityData to 14 Oct 2026

GANs Trained by a Two Time-Scale Update Rule Converge to a Local Nash Equilibrium

arXiv 1706.08500 ↗First posted 26 Jun 2017cs.LG stat.MLcited by 213

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Cited by 59 in Diffusion models, but placed by its own abstract, which didn’t fit.

Abstract (arXiv)

Generative Adversarial Networks (GANs) excel at creating realistic images with complex models for which maximum likelihood is infeasible. However, the convergence of GAN training has still not been proved. We propose a two time-scale update rule (TTUR) for training GANs with stochastic gradient descent on arbitrary GAN loss functions. TTUR has an individual learning rate for both the discriminator and the generator. Using the theory of stochastic approximation, we prove that the TTUR converges under mild assumptions to a stationary local Nash equilibrium. The convergence carries over to the popular Adam optimization, for which we prove that it follows the dynamics of a heavy ball with friction and thus prefers flat minima in the objective landscape. For the evaluation of the performance of GANs at image generation, we introduce the "Fr'echet Inception Distance" (FID) which captures the similarity of generated images to real ones better than the Inception Score. In experiments, TTUR improves learning for DCGANs and Improved Wasserstein GANs (WGAN-GP) outperforming conventional GAN training on CelebA, CIFAR-10, SVHN, LSUN Bedrooms, and the One Billion Word Benchmark.

Key facts. Cited by 213 papers in the map (data through 14 Oct 2026). First posted on arXiv 26 Jun 2017.

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Citing papers per year: 2020: 1; 2021: 29; 2022: 31; 2023: 34; 2024: 58; 2025: 32; 2026: 28.

213 papers.

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  9. 2021Text to Image Generation with Semantic-Spatial Aware GANcited by 53
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  11. 2024Multimodal Latent Language Modeling with Next-Token Diffusioncited by 48
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  13. 2022On Evaluation Metrics for Graph Generative Modelscited by 46
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  23. 2023Efficient Post-training Quantization with FP8 Formatscited by 29
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  28. 2021SAFA: Structure Aware Face Animationcited by 20
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  31. 2023InvertAvatar: Incremental GAN Inversion for Generalized Head Avatarscited by 19
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  33. 2025Learning Human-Perceived Fakeness in AI-Generated Videos via Multimodal LLMscited by 17
  34. 2024Towards Geographic Inclusion in the Evaluation of Text-to-Image Modelscited by 16
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  36. 2021MUGL: Large Scale Multi Person Conditional Action Generation with Locomotioncited by 14
  37. 2024A Practical Guide to Sample-based Statistical Distances for Evaluating Generative Models in Sciencecited by 14
  38. 2021Semantic Relation Preserving Knowledge Distillation for Image-to-Image Translationcited by 13

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