Papers › On the Performance Analysis of Momentum Method: A Frequency Domain Perspective
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
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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Tasks
Results from the paper archive 2025-07-28
| Task | Dataset | Model | Metric | Value | Rank at snapshot | Leaderboard | Report |
|---|---|---|---|---|---|---|---|
| Image Classification | CIFAR-10 | ResNet18 (FSGDM) | Percentage correct | 95.66 | #127 of 265 | Archive leaderboard | report |
| Image Classification | CIFAR-100 | ResNet50 (FSGDM) | Percentage correct | 81.44 | #120 of 211 | Archive leaderboard | report |
| Image Classification | ImageNet | ResNet50 (FSGDM) | Top 1 Accuracy | 76.91% | #894 of 1060 | Archive leaderboard | report |
| Image Classification | ImageNet | ResNet34 (FSGDM) | Top 1 Accuracy | 67.74% | #1037 of 1060 | Archive leaderboard | report |
Ranks are positions in the archive's leaderboards as they stood at the 2025-07-28 snapshot. Results published since then are not among these rows, so a rank here is not a current standing.
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