We provide theoretical convergence bounds for the variational Monte Carlo (VMC) method as applied to optimize neural network wave functions for the electronic structure problem. We study both the energy minimization phase and the supervised pre-training phase that is commonly used prior to energy minimization. For the energy minimization phase, the standard algorithm is scale-invariant by design, and we provide a proof of convergence for this algorithm without modifications. The pre-training stage typically does not feature such scale-invariance. We propose using a scale-invariant loss for the pretraining phase and demonstrate empirically that it leads to faster pre-training.

翻译：我们针对变分蒙特卡罗（VMC）方法在优化电子结构问题的神经网络波函数时提供了理论上的收敛界。同时研究了能量最小化阶段以及该阶段前常用的有监督预训练阶段。对于能量最小化阶段，标准算法在设计上具有尺度不变性，我们对此算法在不做修改的情况下给出了收敛性证明。而预训练阶段通常不具备这种尺度不变性。为此，我们提出在预训练阶段使用尺度不变损失，并通过实验表明该损失能实现更快的预训练速度。