arXiv:2311. 15365v3 Announce Type: replace Abstract: We study an idealized training process for deep neural networks in a continuous-depth, mean-field model in which each layer is parameterized by a probability measure on a Euclidean parameter space.
By Noboru Isobe
arXiv:2505. 12430v2 Announce Type: replace Abstract: Recently, innovative adaptations of the Ritz method incorporating deep learning have been developed, known as the Deep Ritz Method.
By Rafael Florencio, Julio Guerrero
arXiv:2608. 09523v1 Announce Type: new Abstract: Deep neural network (DNN) training with stochastic gradient descent (SGD) and its variants achieves strong empirical performance, yet classical optimization theory does not fully explain this success.
By Binchuan Qi
arXiv:2606. 14954v1 Announce Type: cross Abstract: We develop a general framework for analyzing representation costs of parametric data-fitting methods through their parameter-space regularizers.
By Greg Ongie, Rahul Parhi
The paper presents a near-complete, nonasymptotic generalization theory for multilayer neural networks using path regularization, applicable to broad Lipschitz loss functions without requiring bounded loss or extreme network hyperparameters. It provides an explicit upper bound that addresses approximation rates in generalized Barron spaces and demonstrates the double descent phenomenon for ReLU networks. The authors claim near-minimax optimality for regression problems and plan to establish matching lower bounds in future work.
By Hao Yu
arXiv:2501.14993v4 Announce Type: replace-cross
Abstract: The proximal algorithm is a powerful tool to minimize nonlinear and nonsmooth functionals in a general metric space. Motivated by the recent...
By Shuailong Zhu, Xiaohui Chen