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arXiv · 2411.19671

On the Performance Analysis of Momentum Method: A Frequency Domain Perspective

Xianliang Li·Jun Luo·Zhiwei Zheng·Hanxiao Wang·Li Luo·Lingkun Wen·Linlong Wu·Sheng Xu
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Abstract

Momentum-based optimizers are widely adopted for training neural networks. However, the optimal selection of momentum coefficients remains elusive. This uncertainty impedes a clear understanding of the role of momentum in stochastic gradient methods. In this paper, we present a frequency domain analysis framework that interprets the momentum method as a time-variant filter for gradients, where adjustments to momentum coefficients modify the filter characteristics. Our experiments support this perspective and provide a deeper understanding of the mechanism involved. Moreover, our analysis reveals the following significant findings: high-frequency gradient components are undesired in the late stages of training; preserving the original gradient in the early stages, and gradually amplifying low-frequency gradient components during training both enhance performance. Based on these insights, we propose Frequency Stochastic Gradient Descent with Momentum (FSGDM), a heuristic optimizer that dynamically adjusts the momentum filtering characteristic with an empirically effective dynamic magnitude response. Experimental results demonstrate the superiority of FSGDM over conventional momentum optimizers.

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Xianliang Li, Jun Luo, Zhiwei Zheng, Hanxiao Wang, Li Luo, Lingkun Wen, Linlong Wu, Sheng Xu. 2024-11-29. On the Performance Analysis of Momentum Method: A Frequency Domain Perspective. https://arxiv.org/abs/2411.19671

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