# Asymmetric regularization mechanism for GAN training with Variational Inequalities

arXiv: https://arxiv.org/abs/2601.13920 · HTML: https://mlsanity.com/paper/2601.13920/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 11 of its 20 references that are in the map.
- First posted on arXiv 20 Jan 2026.

## Builds on (most cited first, 11 of 11)

- [Generative Adversarial Networks](https://mlsanity.com/paper/2203.00667/) (2022)
- [Improved Training of Wasserstein GANs](https://mlsanity.com/paper/1704.00028/) (2017)
- [Which Training Methods for GANs do actually Converge?](https://mlsanity.com/paper/1801.04406/) (2018)
- [The relativistic discriminator: a key element missing from standard GAN](https://mlsanity.com/paper/1807.00734/) (2018)
- [A Variational Inequality Perspective on Generative Adversarial Networks](https://mlsanity.com/paper/1802.10551/) (2018)
- [The Numerics of GANs](https://mlsanity.com/paper/1705.10461/) (2017)
- [Gradient descent GAN optimization is locally stable](https://mlsanity.com/paper/1706.04156/) (2017)
- [A Unified Distributed Method for Constrained Networked Optimization via Saddle-Point Dynamics](https://mlsanity.com/paper/2307.07318/) (2023)
- [A stochastic generalized Nash equilibrium model for platforms competition in the ride-hail market](https://mlsanity.com/paper/2203.15412/) (2022)
- [Forward-Backward algorithms for stochastic Nash equilibrium seeking in restricted strongly and strictly monotone games](https://mlsanity.com/paper/2103.03593/) (2021)
- [Primal-dual Accelerated Mirror-Descent Method for Constrained Bilinear Saddle-Point Problems](https://mlsanity.com/paper/2409.18285/) (2024)

## Abstract (arXiv)

We formulate the training of generative adversarial networks (GANs) as a Nash equilibrium seeking problem. To stabilize the training process and find a Nash equilibrium, we propose an asymmetric regularization mechanism based on the classic Tikhonov step and on a novel zero-centered gradient penalty. Under smoothness and a local identifiability condition induced by a Gauss-Newton Gramian, we obtain explicit Lipschitz and (strong)-monotonicity constants for the regularized operator. These constants ensure last-iterate linear convergence of a single-call Extrapolation-from-the-Past (EFTP) method. Empirical simulations on an academic example show that, even when strong monotonicity cannot be achieved, the asymmetric regularization is enough to converge to an equilibrium and stabilize the trajectory.