Kronecker-factored Quasi-Newton Methods for Convolutional Neural Networks

• URL: http://arxiv.org/abs/2102.06737v1
• Date: Fri, 12 Feb 2021 19:40:34 GMT
• Title: Kronecker-factored Quasi-Newton Methods for Convolutional Neural Networks
• Authors: Yi Ren, Donald Goldfarb
• Abstract summary: KF-QN-CNN is a new quasi-factored training convolutional neural networks (CNNs) KF-QN-CNN consistently exhibited superior performance in all of our tests.
• Score: 10.175972095073282
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Second-order methods have the capability of accelerating optimization by using much richer curvature information than first-order methods. However, most are impractical in a deep learning setting where the number of training parameters is huge. In this paper, we propose KF-QN-CNN, a new Kronecker-factored quasi-Newton method for training convolutional neural networks (CNNs), where the Hessian is approximated by a layer-wise block diagonal matrix and each layer's diagonal block is further approximated by a Kronecker product corresponding to the structure of the Hessian restricted to that layer. New damping and Hessian-action techniques for BFGS are designed to deal with the non-convexity and the particularly large size of Kronecker matrices in CNN models and convergence results are proved for a variant of KF-QN-CNN under relatively mild conditions. KF-QN-CNN has memory requirements comparable to first-order methods and much less per-iteration time complexity than traditional second-order methods. Compared with state-of-the-art first- and second-order methods on several CNN models, KF-QN-CNN consistently exhibited superior performance in all of our tests.

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