检测并缓解格点场论基于流采样的模式坍塌
Detecting and Mitigating Mode-Collapse for Flow-based Sampling of Lattice Field Theories
AI总结：
本文揭示格点场论归一化流采样中的模式坍塌会将隧穿问题转移至训练阶段并造成显著偏差，提出量化指标、偏差界及面向热力学可观测量估计的缓解策略。
摘要：
我们在格点场论背景下研究了归一化流模式坍塌所带来的后果。归一化流允许进行独立采样。因此，人们希望它们能够避免局部更新 MCMC 算法在多模态分布中遇到的隧穿问题。在本工作中，我们首先指出，隧穿问题在归一化流中同样存在，只是从采样阶段转移到了算法的训练阶段。具体而言，归一化流经常受到模式坍塌的困扰，即在训练过程中，物理分布的相关模态被赋予趋近于零的概率质量。当该流被用作 Markov 链中的采样器，或与重要性采样结合使用时，这可能导致显著偏差。我们提出了一种用于量化模式坍塌程度的指标，并推导了由此产生偏差的界。此外，我们提出了多种缓解策略，尤其是在估计自由能等热力学可观测量的情境下。
英文摘要：
We study the consequences of mode-collapse of normalizing flows in the context of lattice field theory. Normalizing flows allow for independent sampling. For this reason, it is hoped that they can avoid the tunneling problem of local-update MCMC algorithms for multi-modal distributions. In this work, we first point out that the tunneling problem is also present for normalizing flows but is shifted from the sampling to the training phase of the algorithm. Specifically, normalizing flows often suffer from mode-collapse for which the training process assigns vanishingly low probability mass to relevant modes of the physical distribution. This may result in a significant bias when the flow is used as a sampler in a Markov-Chain or with Importance Sampling. We propose a metric to quantify the degree of mode-collapse and derive a bound on the resulting bias. Furthermore, we propose various mitigation strategies in particular in the context of estimating thermodynamic observables, such as the free energy.
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