  In neural networks, developing regularization algorithms to settle
overfitting is one of the major study areas. We propose a new approach for the
regularization of neural networks by the local Rademacher complexity called
LocalDrop. A new regularization function for both fully-connected networks
(FCNs) and convolutional neural networks (CNNs), including drop rates and
weight matrices, has been developed based on the proposed upper bound of the
local Rademacher complexity by the strict mathematical deduction. The analyses
of dropout in FCNs and DropBlock in CNNs with keep rate matrices in different
layers are also included in the complexity analyses. With the new
regularization function, we establish a two-stage procedure to obtain the
optimal keep rate matrix and weight matrix to realize the whole training model.
Extensive experiments have been conducted to demonstrate the effectiveness of
LocalDrop in different models by comparing it with several algorithms and the
effects of different hyperparameters on the final performances.
