Beta-Scheduling: Momentum from Critical Damping as a Diagnostic and Correction Tool for Neural Network Training
arXiv:2603.28921v1 Announce Type: new Abstract: Standard neural network training uses constant momentum (typically 0.9), a convention dating to 1964 with limited theoretical justification for its optimality. We derive a time-varying momentum schedule from the critically damped harmonic oscillator: mu(t) = 1 - 2*sqrt(alpha(t)), where alpha(t) is the current learning rate. This beta-schedule requires zero free parameters beyond the existing learning rate schedule. On ResNet-18/CIFAR-10, beta-scheduling delivers 1.9x faster convergence to 90% accuracy compared to constant momentum. More importantly, the per-layer gradient attribution under this schedule produces a cross-optimizer invariant diagnostic: the same three problem layers are identified regardless of whether the model was trained wit
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Abstract:Standard neural network training uses constant momentum (typically 0.9), a convention dating to 1964 with limited theoretical justification for its optimality. We derive a time-varying momentum schedule from the critically damped harmonic oscillator: mu(t) = 1 - 2sqrt(alpha(t)), where alpha(t) is the current learning rate. This beta-schedule requires zero free parameters beyond the existing learning rate schedule. On ResNet-18/CIFAR-10, beta-scheduling delivers 1.9x faster convergence to 90% accuracy compared to constant momentum. More importantly, the per-layer gradient attribution under this schedule produces a cross-optimizer invariant diagnostic: the same three problem layers are identified regardless of whether the model was trained with SGD or Adam (100% overlap). Surgical correction of only these layers fixes 62 misclassifications while retraining only 18% of parameters. A hybrid schedule -- physics momentum for fast early convergence, then constant momentum for the final refinement -- reaches 95% accuracy fastest among five methods tested. The main contribution is not an accuracy improvement but a principled, parameter-free tool for localizing and correcting specific failure modes in trained networks.
Comments: 18 pages, 3 figures, 5 tables. Code available on Kaggle
Subjects:
Machine Learning (cs.LG); Artificial Intelligence (cs.AI)
Cite as: arXiv:2603.28921 [cs.LG]
(or arXiv:2603.28921v1 [cs.LG] for this version)
https://doi.org/10.48550/arXiv.2603.28921
arXiv-issued DOI via DataCite (pending registration)
Submission history
From: Ivan Pasichnyk [view email] [v1] Mon, 30 Mar 2026 18:53:03 UTC (44 KB)
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