Path Regularization: A Near-Complete and Optimal Nonasymptotic Generalization Theory for Multilayer Neural Networks and Double Descent Phenomenon

ArXi:2503.02129v2 Announce Type: replace Path regularization has shown to be a very effective regularization to train neural networks, leading to a better generalization property than common regularizations i.e. weight decay, etc. We propose a first near-complete (as will be made explicit in the main text) nonasymptotic generalization theory for multilayer neural networks with path regularizations for general learning problems. In particular, it does not require the boundedness of the loss function, as is commonly assumed in the literature.