# Training GANs with Centripetal Acceleration

arXiv: https://arxiv.org/abs/1902.08949 · HTML: https://mlsanity.com/paper/1902.08949/

## Key facts

- Cited by 13 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 24 Feb 2019.

## Built on by (most cited first, 13 of 13)

- [Accelerated Single-Call Methods for Constrained Min-Max Optimization](https://mlsanity.com/paper/2210.03096/) (2022)
- [No-Regret Dynamics in the Fenchel Game: A Unified Framework for Algorithmic Convex Optimization](https://mlsanity.com/paper/2111.11309/) (2021)
- [Tight Last-Iterate Convergence of the Extragradient and the Optimistic Gradient Descent-Ascent Algorithm for Constrained Monotone Variational Inequalities](https://mlsanity.com/paper/2204.09228/) (2022)
- [Generalized Optimistic Methods for Convex-Concave Saddle Point Problems](https://mlsanity.com/paper/2202.09674/) (2022)
- [Optimal Algorithms for Decentralized Stochastic Variational Inequalities](https://mlsanity.com/paper/2202.02771/) (2022)
- [First Order Methods with Markovian Noise: from Acceleration to Variational Inequalities](https://mlsanity.com/paper/2305.15938/) (2023)
- [Complex Momentum for Optimization in Games](https://mlsanity.com/paper/2102.08431/) (2021)
- [Compression and Data Similarity: Combination of Two Techniques for Communication-Efficient Solving of Distributed Variational Inequalities](https://mlsanity.com/paper/2206.09446/) (2022)
- [Similarity, Compression and Local Steps: Three Pillars of Efficient Communications for Distributed Variational Inequalities](https://mlsanity.com/paper/2302.07615/) (2023)
- [On Scaled Methods for Saddle Point Problems](https://mlsanity.com/paper/2206.08303/) (2022)
- [Training Generative Adversarial Networks with Adaptive Composite Gradient](https://mlsanity.com/paper/2111.05508/) (2021)
- [Layer-wise Quantization for Quantized Optimistic Dual Averaging](https://mlsanity.com/paper/2505.14371/) (2025)
- [Shuffling Heuristic in Variational Inequalities: Establishing New Convergence Guarantees](https://mlsanity.com/paper/2509.04133/) (2025)

## Abstract (arXiv)

Training generative adversarial networks (GANs) often suffers from cyclic behaviors of iterates. Based on a simple intuition that the direction of centripetal acceleration of an object moving in uniform circular motion is toward the center of the circle, we present the Simultaneous Centripetal Acceleration (SCA) method and the Alternating Centripetal Acceleration (ACA) method to alleviate the cyclic behaviors. Under suitable conditions, gradient descent methods with either SCA or ACA are shown to be linearly convergent for bilinear games. Numerical experiments are conducted by applying ACA to existing gradient-based algorithms in a GAN setup scenario, which demonstrate the superiority of ACA.