arXiv:2503. 07325v2 Announce Type: replace Abstract: Understanding and certifying the behavior of modern deep neural networks remains a fundamental challenge in reliable machine learning.
By Khoat Than, Dat Phan
arXiv:2606. 06772v2 Announce Type: replace-cross Abstract: Characterizing the optimization dynamics and statistical performance of over-parameterized deep neural networks (DNNs) remains a central challenge in understanding the remarkable success of deep learning.
By Junyu Zhou, Puyu Wang, Dennis Wagner, Yunwen Lei, Marius Kloft, Yiming Ying
The paper introduces a pointwise generalization theory for fully connected deep neural networks, using a pointwise Riemannian Dimension derived from eigenvalues of learned feature representations across layers. This framework provides hypothesis-dependent, representation-aware generalization bounds that are significantly tighter than traditional size- or norm-based approaches, both theoretically and experimentally. The authors analytically identify structural properties that explain deep networks’ tractability and empirically show that the pointwise Riemannian Dimension captures feature compression, over‑parameterization effects, and optimizer bias.
By Shaojie Li, Yunbei Xu
arXiv:2510. 02779v4 Announce Type: replace Abstract: Recent advances have significantly improved our understanding of the generalization performance of gradient descent (GD) methods in deep neural networks.
By Yuanfan Li, Yunwen Lei, Zheng-Chu Guo, Yiming Ying
arXiv:2609.21422v1 Announce Type: cross
Abstract: Deep representation learning often selects hidden features and fits the final predictor on the same sample, so fixed-feature analysis performed after...
By Mahdi Mohammadigohari, Nicole M\"ucke
arXiv:2606. 08308v1 Announce Type: new Abstract: Predicting the generalization performance of deep neural networks without relying on hold-out validation data is a fundamental challenge in machine learning.
By Joao B. Florindo, Davi Wanderley Misturini