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The paper demonstrates that gradient descent, with random initialization and a sufficiently small constant step size, almost surely converges to a local minimizer for twice continuously differentiable functions that satisfy the strict saddle property. This conclusion is supported by applying the Stable Manifold Theorem from dynamical systems theory, indicating that saddle points are not a significant concern for gradient descent methods. The authors also discuss related work and the implications of their fi

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291023379

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EN