Exact Stochastic Second Order Deep Learning

• URL: http://arxiv.org/abs/2104.03804v1
• Date: Thu, 8 Apr 2021 14:29:31 GMT
• Title: Exact Stochastic Second Order Deep Learning
• Authors: Fares B. Mehouachi, Chaouki Kasmi
• Abstract summary: Deep Learning is mainly dominated by first-order methods which are built around the central concept of backpropagation. Second-order methods, take into account second-order derivatives less used than first-order methods.
• Score: 0.0
• License: http://creativecommons.org/licenses/by-nc-sa/4.0/
• Abstract: Optimization in Deep Learning is mainly dominated by first-order methods which are built around the central concept of backpropagation. Second-order optimization methods, which take into account the second-order derivatives are far less used despite superior theoretical properties. This inadequacy of second-order methods stems from its exorbitant computational cost, poor performance, and the ineluctable non-convex nature of Deep Learning. Several attempts were made to resolve the inadequacy of second-order optimization without reaching a cost-effective solution, much less an exact solution. In this work, we show that this long-standing problem in Deep Learning could be solved in the stochastic case, given a suitable regularization of the neural network. Interestingly, we provide an expression of the stochastic Hessian and its exact eigenvalues. We provide a closed-form formula for the exact stochastic second-order Newton direction, we solve the non-convexity issue and adjust our exact solution to favor flat minima through regularization and spectral adjustment. We test our exact stochastic second-order method on popular datasets and reveal its adequacy for Deep Learning.

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