SHANG++: Robust Stochastic Acceleration under Multiplicative Noise

Fuente: arXiv
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Main Authors: Yu, Yaxin, Chen, Long, Feng, Minfu
Format: Preprint
Published: 2026
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author Yu, Yaxin
Chen, Long
Feng, Minfu
author_facet Yu, Yaxin
Chen, Long
Feng, Minfu
contents Under the multiplicative noise scaling (MNS) condition, original Nesterov acceleration is provably sensitive to noise and may diverge when gradient noise overwhelms the signal. In this paper, we develop two accelerated stochastic gradient descent methods by discretizing the Hessian-driven Nesterov accelerated gradient flow. We first derive SHANG, a direct Gauss-Seidel-type discretization that already improves stability under MNS. We then introduce SHANG++, which adds a damping correction and achieves faster convergence with stronger noise robustness. We establish convergence guarantees for both convex and strongly convex objectives under MNS, together with explicit parameter choices. In our experiments, SHANG++ performs consistently well across convex problems and applications in deep learning. In a dedicated noise experiment on ResNet-34, a single hyperparameter configuration attains accuracy within 1% of the noise-free setting. Across all experiments, SHANG++ outperforms existing accelerated methods in robustness and efficiency, with minimal parameter sensitivity.
format Preprint
id arxiv_https___arxiv_org_abs_2603_09355
institution arXiv
publishDate 2026
record_format arxiv
spellingShingle SHANG++: Robust Stochastic Acceleration under Multiplicative Noise
Yu, Yaxin
Chen, Long
Feng, Minfu
Optimization and Control
Machine Learning
Under the multiplicative noise scaling (MNS) condition, original Nesterov acceleration is provably sensitive to noise and may diverge when gradient noise overwhelms the signal. In this paper, we develop two accelerated stochastic gradient descent methods by discretizing the Hessian-driven Nesterov accelerated gradient flow. We first derive SHANG, a direct Gauss-Seidel-type discretization that already improves stability under MNS. We then introduce SHANG++, which adds a damping correction and achieves faster convergence with stronger noise robustness. We establish convergence guarantees for both convex and strongly convex objectives under MNS, together with explicit parameter choices. In our experiments, SHANG++ performs consistently well across convex problems and applications in deep learning. In a dedicated noise experiment on ResNet-34, a single hyperparameter configuration attains accuracy within 1% of the noise-free setting. Across all experiments, SHANG++ outperforms existing accelerated methods in robustness and efficiency, with minimal parameter sensitivity.
title SHANG++: Robust Stochastic Acceleration under Multiplicative Noise
topic Optimization and Control
Machine Learning
url https://arxiv.org/abs/2603.09355