Group-Equivariant Diffusion Models for Lattice Field Theory
Octavio Vega, Javad Komijani, Aida El-Khadra, Marina Marinkovic
在临界点附近，格点量子场论(LQFT)的马尔可夫链蒙特卡洛(MCMC)模拟由于临界减速而变得越来越低效。在这项工作中，我们研究了基于分数的对称性保持扩散模型作为采样二维ϕ^4和U(1)格点场论的替代策略。我们开发了对一系列群变换具有等变性的分数网络，包括全局ℤ_2反射、局部U(1)旋转和周期平移𝕋。这些分数网络使用增强的训练方案进行训练，显著提高了模拟场论中的样本质量。我们还通过实验证明，我们的对称性感知模型在样本质量、表达能力和有效样本大小方面优于通用分数网络。
Near the critical point, Markov Chain Monte Carlo (MCMC) simulations of lattice quantum field theories (LQFT) become increasingly inefficient due to critical slowing down. In this work, we investigate score-based symmetry-preserving diffusion models as an alternative strategy to sample two-dimensional ϕ^4 and U(1) lattice field theories. We develop score networks that are equivariant to a range of group transformations, including global ℤ_2 reflections, local U(1) rotations, and periodic transla...