# Training GANs with Centripetal Acceleration

## TL;DR

This paper introduces the SCA and ACA methods to reduce cyclic behaviors in GAN training, demonstrating linear convergence in bilinear games and improved performance in experiments.

## Contribution

It proposes novel centripetal acceleration-based algorithms for stabilizing GAN training and proves their convergence under certain conditions.

## Key findings

- ACA outperforms existing gradient-based algorithms in GAN scenarios
- Gradient descent with SCA or ACA converges linearly in bilinear games
- Numerical experiments validate the effectiveness of ACA in practice

## Abstract

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.