Decoupled Weight Decay for Any p Norm

With the success of deep neural networks (NNs) in a variety of domains, the computational and storage requirements for training and deploying large NNs have become a bottleneck for further improvements. Sparsification has consequently emerged as a leading approach to tackle these issues. In this work, we consider a simple yet effective approach to sparsification, based on the Bridge, or Lₚ regularization during training. We introduce a novel weight decay scheme, which generalizes the standard L₂ weight decay to any p norm. We show that this scheme is compatible with adaptive optimizers, and avoids the gradient divergence associated with $0<p<1$ norms. We empirically demonstrate that it leads to highly sparse networks, while maintaining generalization performance comparable to standard L₂ regularization.