用对称Jeffreys散度改进生成模型，解决罕见事件采样中的模式坍塌问题
Jeffreys Flow: Robust Boltzmann Generators for Rare Event Sampling via Parallel Tempering Distillation
- 以并行温控轨迹数据为参考，通过对称Jeffreys散度蒸馏生成模型
- 在多模态非凸测试中实现无模式坍塌、高精度采样，加速量子热态计算
- 适合需要稳定多模态采样的分子模拟与量子系统研究者
在粗糙能量景观的物理系统采样中，罕见事件和亚稳态陷阱严重阻碍采样效率。尽管玻尔兹曼生成器已提供解决方案，但其依赖反向KL散度常导致灾难性模式坍塌，遗漏多模态分布中的特定模式。本文提出杰弗里斯流（Jeffreys Flow），一种鲁棒生成框架，通过并行温控轨迹的实测采样数据，利用对称杰弗里斯散度进行蒸馏。该方法有效平衡局部目标精确性与全局模式覆盖性。我们证明最小化杰弗里斯散度可抑制模式坍塌，并通过实测参考数据蒸馏结构化纠正固有误差。在高度非凸多维基准测试中验证了框架的可扩展性与准确性，包括在副本交换随机梯度朗之万动力学中系统修正随机梯度偏差，以及在路径积分蒙特卡洛中大幅加速量子热态的精确重要性采样。
原文摘要 · Abstract (English)
Sampling physical systems with rough energy landscapes is hindered by rare events and metastable trapping. While Boltzmann generators already offer a solution, their reliance on the reverse Kullback--Leibler divergence frequently induces catastrophic mode collapse, missing specific modes in multi-modal distributions. Here, we introduce the Jeffreys Flow, a robust generative framework that mitigates this failure by distilling empirical sampling data from Parallel Tempering trajectories using the symmetric Jeffreys divergence. This formulation effectively balances local target-seeking precision with global modes coverage. We show that minimizing Jeffreys divergence suppresses mode collapse and structurally corrects inherent inaccuracies via distillation of the empirical reference data. We demonstrate the framework's scalability and accuracy on highly non-convex multidimensional benchmarks, including the systematic correction of stochastic gradient biases in Replica Exchange Stochastic Gradient Langevin Dynamics and the massive acceleration of exact importance sampling in Path Integral Monte Carlo for quantum thermal states.
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