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This paper presents the first sharp analysis that shows that perturbed gradient descent finds an approximate second order stationary point in at most polylog d iterations thus escaping all saddle

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Does gradient descent with a standard line search method avoid strict saddle points Surprisingly even this falls outside the scope of existing results We provide a positive answer for a

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In 1D A saddle point is a point where the function s slope is zero but it s not a local minimum or maximum Think of a horse saddle it s flat in one direction along the seat but curved upwards in

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Saddle points are points where the gradient is zero but the point is neither a minimum nor a maximum These are common in high dimensional non convex functions such as neural network

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Near a saddle point the gradients can become very small causing gradient descent to slow down significantly or even stall for a long time before potentially finding a direction to escape This slowing

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Building on a detailed examination of critical points of the square integral loss function for shallow ReLU and leaky ReLU networks relative to an affine target function we show that gradient descent

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Saddle points Dauphin et al 2014 Given that saddle points can cause gradient descent to get stuck at a highly suboptimal points methods to escape saddle points are highly usefu in non convex

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Can we escape saddle points via GD YES Lee Jason D et al Gradient descent only converges to minimizers COLT 2016 What is the time complexity of the escaping There exists a 0 such

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How to escape saddle points 1 For 2 3 1 For 2 3 Between two perturbations just run GD 3 Between two perturbations just run GD How can perturbation help How much is Vol Thank you