让生成模型自动学习对称性，提升物理模拟的采样精度。
SESaMo: Symmetry-Enforcing Stochastic Modulation for Normalizing Flows
- 通过随机调制机制将对称性嵌入流模型，增强归纳偏置。
- 在8个高斯混合与ϕ⁴理论等场景中实现更准确的概率建模。
- 适合需要精确对称性的物理系统建模与生成任务。
深度生成模型在物理、化学等领域受到广泛关注，其中从非归一化玻尔兹曼分布中采样是核心挑战。自回归模型和归一化流因其可计算概率密度而备受青睐。将对称性等先验知识融入神经网络可显著提升训练效果。本文提出对称性强制随机调制（SESaMo），通过新颖的随机调制技术，在归一化流中引入归纳偏置（如对称性），提升模型灵活性，有效学习精确与破缺对称性。数值实验在8个高斯混合模型及ϕ⁴理论、霍巴德模型等物理场论中验证了其性能。
原文摘要 · Abstract (English)
Deep generative models have recently garnered significant attention across various fields, from physics to chemistry, where sampling from unnormalized Boltzmann-like distributions represents a fundamental challenge. In particular, autoregressive models and normalizing flows have become prominent due to their appealing ability to yield closed-form probability densities. Moreover, it is well-established that incorporating prior knowledge - such as symmetries - into deep neural networks can substantially improve training performances. In this context, recent advances have focused on developing symmetry-equivariant generative models, achieving remarkable results. Building upon these foundations, this paper introduces Symmetry-Enforcing Stochastic Modulation (SESaMo). Similar to equivariant normalizing flows, SESaMo enables the incorporation of inductive biases (e.g., symmetries) into normalizing flows through a novel technique called stochastic modulation. This approach enhances the flexibility of the generative model, allowing to effectively learn a variety of exact and broken symmetries. Our numerical experiments benchmark SESaMo in different scenarios, including an 8-Gaussian mixture model and physically relevant field theories, such as the $ϕ^4$ theory and the Hubbard model.
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