  Overfitting is one of the critical problems in deep neural networks. Many
regularization schemes try to prevent overfitting blindly. However, they
decrease the convergence speed of training algorithms. Adaptive regularization
schemes can solve overfitting more intelligently. They usually do not affect
the entire network weights. This paper detects a subset of the weighting layers
that cause overfitting. The overfitting recognizes by matrix and tensor
condition numbers. An adaptive regularization scheme entitled Adaptive Low-Rank
(ALR) is proposed that converges a subset of the weighting layers to their
Low-Rank Factorization (LRF). It happens by minimizing a new Tikhonov-based
loss function. ALR also encourages lazy weights to contribute to the
regularization when epochs grow up. It uses a damping sequence to increment
layer selection likelihood in the last generations. Thus before falling the
training accuracy, ALR reduces the lazy weights and regularizes the network
substantially. The experimental results show that ALR regularizes the deep
networks well with high training speed and low resource usage.
