arXiv:2608.19021v2 Announce Type: replace
Abstract: Global Covariance Pooling (GCP) improves deep networks by capturing second-order feature statistics, and is especially effective for fine-grained r...
By Md Rifat Ur Rahman, Md Raihan Khan, Md Sakib Hossain Shovon, Pietro Li\`o, Mohammad Ali Moni
The paper derives an exact discrete‑time law that captures how learning‑rate schedules and weight decay interact in scale‑invariant neural networks, showing that a single scalar quantity governs the effective step size. It demonstrates that the balance point between contraction and expansion is intrinsically unstable, leading to recurrent dynamics when using constant learning rates with weight decay. The authors extend this analysis to various optimizers and datasets, confirming the law’s precision and showing that performance peaks sharply at the predicted boundary.
By Hasan Amin, Wei-Kai Chang, Rajiv Khanna
The paper investigates how normalization makes neural networks scale‑invariant, creating a feedback loop between learning‑rate schedules and weight decay that controls the effective step size of the optimizer. It derives an exact discrete‑time law showing that a single scalar quantity captures all schedule and decay effects, with norm growth providing a self‑quenching counter‑force that defines a sharp boundary between contraction‑ and expansion‑dominated regimes. Through exact analysis of a normalized regression model and experiments on MLPs, CNNs, GPT‑2, and various datasets, the authors demonstrate that constant learning rates with weight decay are intrinsically unstable, leading to recurrent dynamics, and that adaptive optimizers exhibit weaker stabilization under normalization.
"whyItMatters":"The study provides a precise, actionable rule for controlling training dynamics and schedule design in modern deep learning by isolating a single governing quantity for scale‑invariant optimization."
arXiv:2606. 15669v1 Announce Type: cross Abstract: Modern deep neural networks rely on Euclidean scalar activations (e.
By Sungwoo Goo, Hwi-yeol Yun, Sangkeun Jung
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: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