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Lipschitz regularity of deep neural networks: analysis and efficient estimation

Neural Information Processing Systems

Deep neural networks are notorious for being sensitive to small well-chosen perturbations, and estimating the regularity of such architectures is of utmost importance for safe and robust practical applications. In this paper, we investigate one of the key characteristics to assess the regularity of such methods: the Lipschitz constant of deep learning architectures.






NEON2: Finding Local Minima via First-Order Oracles

Neural Information Processing Systems

It works both in the stochastic and the deterministic settings, without hurting the algorithm'sperformance. As applications, our reduction turns Natasha2 into a first-order method without hurting its theoretical performance. It also converts SGD, GD, SCSG, and SVRG into algorithms finding approximate local minima, outperforming some bestknownresults.