arXiv：cs.LG（机器学习，全量分类）· Nikolaos Makras, Sotirios Sabanis·· 14 小时前AI 评分33
Muon 遇上 Tamed Langevin：超越凸性与梯度-Lipschitz 势的动量预条件方法
Muon meets Tamed Langevin: Momentum Preconditioning beyond Convex and gradient-Lipschitz Potentials
AI 导读
研究者提出一族非二次动能函数，构建出带动量预条件的新型欠阻尼 Langevin 系统，其动能梯度对动量起到平滑的谱 taming 作用。在势能既非凸也非全局梯度-Lipschitz 的条件下，该动力学保持目标 Gibbs 分布不变，并在加权全变差距离下实现指数收敛。对应的 Euler-Maruyama 离散化无需修改势能梯度即可获得时间一致矩界，保证采样算法稳定。
正文
Abstract:We consider the problem of sampling from Gibbs distributions on matrix spaces whose potential energies are neither convex nor globally gradient-Lipschitz. We introduce a family of non-quadratic kinetic energies that lead to a new underdamped Langevin system with momentum preconditioning, in which the gradient of the kinetic energy acts as a smooth spectral taming of the momentum. We prove that, under these relaxed assumptions on the potential, the resulting dynamics leaves the target Gibbs measure invariant, and we establish exponential convergence to equilibrium in a weighted total variation distance. Finally, we show that the corresponding Euler-Maruyama discretization admits moment bounds that are uniform in time, without any modification of the potential gradient, which ensures the stability of the resulting sampling algorithm.
| Comments: | 26pages |
| Subjects: | Machine Learning (cs.LG); Optimization and Control (math.OC); Probability (math.PR); Machine Learning (stat.ML) |
| Cite as: | arXiv:2610.02158 [cs.LG] |
| (or arXiv:2610.02158v1 [cs.LG] for this version) | |
| https://doi.org/10.48550/arXiv.2610.02158 arXiv-issued DOI via DataCite (pending registration) |
Submission history
From: Nikos Makras [view email]
[v1]
Thu, 1 Oct 2026 17:52:36 UTC (36 KB)
来源：arXiv：cs.LG（机器学习，全量分类） · arxiv.org