arXiv:2606. 28242v1 Announce Type: cross Abstract: Understanding how performance scales jointly with model size and data is a central problem in modern machine learning.
By Julius Girardin, Emanuele Troiani, Yizhou Xu, Vittorio Erba, Florent Krzakala, Lenka Zdeborov\'a
arXiv:2607. 21005v1 Announce Type: new Abstract: Most explanations of training instability focus on \emph{learning-rate criticality}, typically characterized by the Edge of Stability, beyond which optimization becomes unstable.
By Xiaolong Li, Zhangchen Zhou, Zhi-Qin John Xu
arXiv:2506. 13139v3 Announce Type: replace-cross Abstract: Modern Machine Learning (ML) and Deep Neural Networks (DNNs) often operate on high-dimensional data and rely on overparameterized models, where classical low-dimensional intuitions break down.
By Zhenyu Liao, Michael W. Mahoney
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:2605. 31244v2 Announce Type: replace Abstract: Neural scaling laws describe predictable power-law relationships between model size, dataset size, compute, and performance.
By Konstantin Nikolaou, Jonas Scheunemann, Sven Krippendorf, Samuel Tovey, Christian Holm
arXiv:2505. 22578v2 Announce Type: replace Abstract: The optimization of neural networks under weight decay remains poorly understood from a theoretical standpoint.
By Etienne Boursier, Matthew Bowditch, Matthias Englert, Ranko Lazic