想理解VMC为何不稳定？这篇论文给出了严格的数学分析，还提出了一个实用的裁剪方法PS-Clip-VMC，对做量子化学模拟的朋友很有帮助。
该论文分析了变分蒙特卡洛（VMC）算法在电子结构优化中的鲁棒性，发现其局部能量和梯度估计量普遍呈现重尾分布，缺乏高阶矩。对于Slater-Jastrow等常见波函数类，估计量表现出重尾特性。作者提出PS-Clip-VMC方法，通过裁剪局部能量和梯度随机变量来提升稳定性。在FermiNet上对多达18个电子的原子进行初步实验，PS-Clip-VMC比标准方法更鲁棒。
Is Variational Monte Carlo Robust? Sharp Moment Thresholds and Heavy-tailed Stochastic Optimization
Variational Monte Carlo (VMC) is a central algorithm in electronic structure theory and has gained renewed importance through modern neural-network ansätze such as FermiNet. At its core, VMC seeks ground states by minimizing the Rayleigh quotient by stochastic optimization. In this work, we show that the resulting stochastic optimization problem is intrinsically governed by the nodal geometry of the underlying wave function. More precisely, we establish that properties of the nodal set determine the integrability of the local energy and gradient estimators that drive VMC. For broad and practically relevant ansatz classes, including Slater-Jastrow wave functions with variable-exponent Slater-type orbitals, we prove that these estimators are generically heavy-tailed and fail to admit higher moments. At the same time, for general analytic ansätze, we prove weak moment bounds for the relevant estimators and identify precise low-moment regimes, showing how generic and degenerate nodal structures lead to different integrability thresholds. Building on this analysis, we introduce a new robust variant of VMC $\unicode{x2013}$ coined PS-Clip-VMC $\unicode{x2013}$ which is based on clipping both the local energy and the gradient random variable. We prove that PS-Clip-VMC converges both in expectation and with high probability in the weak moment regime of VMC. Preliminary experiments for training FermiNet on Atoms with up to 18 electrons suggest that PS-Clip-VMC is significantly more robust than standard methods.