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

Researchers propose a new nonasymptotic generalization theory for multilayer neural networks using path regularization, proving near-minimax optimal error bounds without requiring unbounded loss functions or infinite network dimensions. The theory notably explains the double descent phenomenon and solves an open problem in approximation theory for neural networks.