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

Convergence of stochastic gradient descent on parameterized sphere with applications to variational Monte Carlo simulation