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In this paper, we theoretically prove that the deep ReLU neural networks donot lie in spurious local minima in the loss landscape under the Neural TangentKernel (NTK) regime, that is, in the gradient descent training dynamics of thedeep ReLU neural networks whose parameters are initialized by a normaldistribution in the limit as the widths of the hidden layers tend to infinity.

Spurious Local Minima of Deep ReLU Neural Networks in the Neural Tangent Kernel Regime