arXiv:2607.14576v2 Announce Type: replace-cross
Abstract: Whether a deep residual architecture trains stably is usually determined by training it, which is expensive and answers the question only for...
By Hyemin Gu, Michael Tyrrell, Tuhin Sahai, Markos A. Katsoulakis
arXiv:2605. 28983v2 Announce Type: replace-cross Abstract: In this paper, training a neural network is identified, exactly, as a search through Hamilton--Jacobi initial-value problems: each gradient step selects the initial data of a viscous Hamilton--Jacobi equation whose Hopf--Cole propagator best fits the observations; at inference, the input is the spatial point at which that solution is evaluated and the initial condition is already encoded in the weights.
By Jose Marie Antonio Mi\~noza, Erika Fille T. Legara, Christopher P. Monterola
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 introduces Anchored Neighborhood Optimization (ANO), a new policy‑optimization method that directly designs a smooth, bounded gain field for the probability‑ratio surrogate objective. ANO anchors the identity map at a ratio of one, peaks at a specified trust‑region boundary, and limits the influence of extreme off‑policy samples while providing a bounded, redescending pull on outliers. Empirical results show ANO consistently outperforms existing methods on Atari and MuJoCo benchmarks, and it remains robust under aggressive learning‑rate settings.
By Yiheng Zhang, Yiming Wang, Kaiyan Zhao, Zhenglin Wan, Jiayu Chen, Leong Hou U
arXiv:2602. 18849v2 Announce Type: replace-cross Abstract: We develop a sensitivity analysis for transformer attention in a geometry aligned with tokenwise computation.
By Seyed Morteza Emadi
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."