arXiv:2510.05606v2 Announce Type: replace
Abstract: Fundamental limits to predictability are central to our understanding of many physical and computational systems. In deep learning, training outcom...
By Andrew Ly, Pulin Gong
arXiv:2206. 04359v3 Announce Type: replace Abstract: One of the fundamental challenges in the deep learning community is to theoretically understand how well a deep neural network generalizes to unseen data.
By Chengli Tan, Jiangshe Zhang, Junmin Liu, Yihong Gong
arXiv:2505. 11766v4 Announce Type: replace Abstract: Neural Operators (NOs) are powerful architectures for learning mappings between function spaces.
By Haoze Song, Zhihao Li, Xiaobo Zhang, Zecheng Gan, Zhilu Lai, Wei Wang
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: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
arXiv:2606. 06772v1 Announce Type: cross Abstract: Understanding the generalization performance of over-parameterized neural networks has become a central topic in deep learning theory.
By Junyu Zhou, Puyu Wang, Yunwen Lei, Marius Kloft, Yiming Ying