arXiv:2505. 13196v3 Announce Type: replace-cross Abstract: We introduce Velocity-Regularized Adam (VRAdam), a physics-inspired optimizer for training deep neural networks that draws on ideas from quartic terms for kinetic energy with its stabilizing effects on various system dynamics.
By Pranav Vaidhyanathan, Lucas Schorling, Natalia Ares, Maike Osborne
The paper investigates how Adam’s update rule relates to natural gradient descent (NGD) by treating Adam as a diagonal empirical Fisher approximation with additional factors such as diagonal truncation, empirical label substitution, and temporal lag. Using a scale‑invariant metric, the authors quantify Adam’s geometric deviation from true NGD across four loss landscapes—well‑conditioned and ill‑conditioned linear regression, logistic regression, and a small neural network—finding that deviation is low in well‑conditioned settings but can reach about 10³ in ill‑conditioned or non‑convex scenarios. Despite higher geometric drift correlating with slower early optimization, Adam still achieves low final loss, and the improved empirical Fisher (iEF) yields more stable trajectories than the standard empirical Fisher (EF).
By Vihaan Paka-Hegde
arXiv:2602. 00329v4 Announce Type: replace-cross Abstract: Reliable data attribution is essential for mitigating bias and reducing computational waste in modern machine learning, with the Shapley value serving as the theoretical gold standard.
By Meng Ding, Zeqing Zhang, Di Wang, Lijie Hu
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
arXiv:2605. 22432v2 Announce Type: replace Abstract: Modern deep learning commonly relies on AdamW with prescribed learning rate schedules, but recent works challenge both components: Schedule-Free optimization removes explicit schedules via iterate averaging, and Muon improves the update geometry by orthogonalizing momentum for matrix parameters.
By Jueun Kim, Baekrok Shin, Jihun Yun, Beomhan Baek, Minhak Song, Chulhee Yun
arXiv:2406. 14340v2 Announce Type: replace-cross Abstract: The standard stochastic gradient descent (SGD) optimization method, as well as adaptive methods such as the Adam optimizer fail to converge if the learning rates do not converge to zero (particularly, in the situation of constant learning rates).
By Steffen Dereich, Arnulf Jentzen, Adrian Riekert