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Decoupled Weight Decay for Any $p$ Norm

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arXiv:2404.10824v2 Announce Type: replace
Abstract: 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 $L_p$ regularization during training. We introduce a novel weight decay scheme, which generalizes the standard $L_2$ weight decay to any $p$ norm. We show that this scheme is compatible with adaptive optimizers, and avoids the gradient divergence associated with $0

<1$ norms. We empirically demonstrate that it leads to highly sparse networks, while maintaining generalization performance comparable to standard $L_2$ regularization.

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