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

Fuente: arXiv
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Main Authors: Li, Xianliang, Luo, Jun, Zheng, Zhiwei, Wang, Hanxiao, Luo, Li, Wen, Lingkun, Wu, Linlong, Xu, Sheng
Format: Preprint
Published: 2024
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_version_ 1866916748800819200
author Li, Xianliang
Luo, Jun
Zheng, Zhiwei
Wang, Hanxiao
Luo, Li
Wen, Lingkun
Wu, Linlong
Xu, Sheng
author_facet Li, Xianliang
Luo, Jun
Zheng, Zhiwei
Wang, Hanxiao
Luo, Li
Wen, Lingkun
Wu, Linlong
Xu, Sheng
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2411_19671
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle On the Performance Analysis of Momentum Method: A Frequency Domain Perspective
Li, Xianliang
Luo, Jun
Zheng, Zhiwei
Wang, Hanxiao
Luo, Li
Wen, Lingkun
Wu, Linlong
Xu, Sheng
Machine Learning
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.
title On the Performance Analysis of Momentum Method: A Frequency Domain Perspective
topic Machine Learning
url https://arxiv.org/abs/2411.19671