We analyze stochastic gradient descent (SGD) type algorithms on a high-dimensional sphere which is parameterized by a neural network up to a normalization constant. We provide a new algorithm for the setting of supervised learning and show its convergence both theoretically and numerically. We also provide the first proof of convergence for the unsupervised setting, which corresponds to the widely used variational Monte Carlo (VMC) method in quantum physics.

翻译：我们分析了在高维球面上运行的随机梯度下降（SGD）类算法，该球面由神经网络参数化至一个归一化常数。我们针对监督学习场景提出了一种新算法，并从理论和数值上证明了其收敛性。我们还首次给出了无监督场景下的收敛性证明，该场景对应量子物理中广泛使用的变分蒙特卡洛（VMC）方法。