206 citations · 808 across the 40 of their papers we have counts for
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math.OC2016
Gradient Descent Finds the Cubic-Regularized Non-Convex Newton Step
Yair Carmon, John C. Duchi
We consider the minimization of non-convex quadratic forms regularized by a cubic term, which exhibit multiple saddle points and poor local minima. Nonetheless, we prove that, unde…
math.OC2016★ 53 cited
Accelerated Methods for Non-Convex Optimization
Yair Carmon, John C. Duchi, Oliver Hinder +1
We present an accelerated gradient method for non-convex optimization problems with Lipschitz continuous first and second derivatives. The method requires time $O(ε^{-7/4} \log(1/…
stat.ML2016★ 143 cited
No bad local minima: Data independent training error guarantees for multilayer neural networks
Daniel Soudry, Yair Carmon
We use smoothed analysis techniques to provide guarantees on the training loss of Multilayer Neural Networks (MNNs) at differentiable local minima. Specifically, we examine MNNs wi…