On regularization of gradient descent, layer imbalance and flat minima

• URL: http://arxiv.org/abs/2007.09286v1
• Date: Sat, 18 Jul 2020 00:09:14 GMT
• Title: On regularization of gradient descent, layer imbalance and flat minima
• Authors: Boris Ginsburg
• Abstract summary: We analyze the training dynamics for deep linear networks using a new metric - imbalance - which defines the flatness of a solution. We demonstrate that different regularization methods, such as weight decay or noise data augmentation, behave in a similar way.
• Score: 9.08659783613403
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We analyze the training dynamics for deep linear networks using a new metric - layer imbalance - which defines the flatness of a solution. We demonstrate that different regularization methods, such as weight decay or noise data augmentation, behave in a similar way. Training has two distinct phases: 1) optimization and 2) regularization. First, during the optimization phase, the loss function monotonically decreases, and the trajectory goes toward a minima manifold. Then, during the regularization phase, the layer imbalance decreases, and the trajectory goes along the minima manifold toward a flat area. Finally, we extend the analysis for stochastic gradient descent and show that SGD works similarly to noise regularization.

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