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Training neural networks is a challenging non-convex optimization problem,and backpropagation or gradient descent can get stuck in spurious local optima.We propose a novel algorithm based on tensor decomposition for guaranteedtraining of two-layer neural networks. We provide risk bounds for our proposedmethod, with a polynomial sample complexity in the relevant parameters, such asinput dimension and number of neurons. While learning arbitrary targetfunctions is NP-hard, we provide transparent conditions on the function and theinput for learnability. Our training method is based on tensor decomposition,which provably converges to the global optimum, under a set of mildnon-degeneracy conditions. It consists of simple embarrassingly parallel linearand multi-linear operations, and is competitive with standard stochasticgradient descent (SGD), in terms of computational complexity. Thus, we proposea computationally efficient method with guaranteed risk bounds for trainingneural networks with one hidden layer.

Beating the Perils of Non-Convexity: Guaranteed Training of Neural Networks using Tensor Methods