arXiv:2606. 16883v1 Announce Type: cross Abstract: Generalization is a critical property of data-driven models, particularly deep learning models deployed in safety-critical applications.
By Abdul-Rauf Nuhu, Parham M. Kebria, Vahid Hemmati, Mahmoud N. Mahmoud, Edward Tunstel, Abdollah Homaifar
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: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:2211. 14966v2 Announce Type: replace Abstract: Deep neural networks (DNNs) are highly vulnerable to adversarial attacks.
By Jiancong Xiao, Yanbo Fan, Ruoyu Sun, Zhi-Quan Luo
arXiv:2602. 23128v2 Announce Type: replace Abstract: Generalization bounds for deep learning models are typically vacuous, not computable or restricted to specific model classes.
By Mathieu Bazinet, Valentina Zantedeschi, Pascal Germain
Over the past decade, deep neural networks (DNNs) have achieved remarkable success on complex machine-learning tasks, yet the theoretical foundations of their performance remain incomplete. From a statistical viewpoint, a natural question is: can DNNs attain feature-learning and prediction consistency comparable to that of classical models?