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（该球面由神经网络参数化至归一化常数）的随机梯度下降（SGD）型算法。针对监督学习场景，我们提出了一种新算法，并从理论和数值两方面证明了其收敛性。此外，我们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学中广泛使用的变分蒙特卡洛（VMC）方法。