{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/on-the-performance-analysis-of-momentum","title":"On the Performance Analysis of Momentum Method: A Frequency Domain Perspective","arxiv_id":"2411.19671","date":"2024-11-29","proceeding":null,"authors":["Xianliang Li","Jun Luo","Zhiwei Zheng","Hanxiao Wang","Li Luo","Lingkun Wen","Linlong Wu","Sheng Xu"],"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.","url_abs":"https://arxiv.org/abs/2411.19671v6","url_pdf":"https://arxiv.org/pdf/2411.19671v6.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"abstracts"},"code_links":[{"paper_slug":"on-the-performance-analysis-of-momentum","repo_url":"https://github.com/yinleung/FSGDM","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":0,"framework":"pytorch","reach":null}],"tasks":[{"task_slug":"image-classification","task_name":"Image Classification"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[{"leaderboard":"/sota/image-classification-on-cifar-10","task":"Image Classification","dataset":"CIFAR-10","model":"ResNet18 (FSGDM)","rank_in_archive_order":127,"of":265,"metrics":{"Percentage correct":"95.66"},"uses_additional_data":false},{"leaderboard":"/sota/image-classification-on-cifar-100","task":"Image Classification","dataset":"CIFAR-100","model":"ResNet50 (FSGDM)","rank_in_archive_order":120,"of":211,"metrics":{"Percentage correct":"81.44"},"uses_additional_data":false},{"leaderboard":"/sota/image-classification-on-imagenet","task":"Image Classification","dataset":"ImageNet","model":"ResNet50 (FSGDM)","rank_in_archive_order":894,"of":1060,"metrics":{"Top 1 Accuracy":"76.91%"},"uses_additional_data":false},{"leaderboard":"/sota/image-classification-on-imagenet","task":"Image Classification","dataset":"ImageNet","model":"ResNet34 (FSGDM)","rank_in_archive_order":1037,"of":1060,"metrics":{"Top 1 Accuracy":"67.74%"},"uses_additional_data":false}],"syntology":{"syntology_url":"https://syntology.ai/paper/2411.19671","atlas_url":"https://app.syntology.ai/?focus=2411.19671","mcp":{"get_harvested_code_for_paper":{"arxiv_id":"2411.19671"}},"developers":"https://syntology.ai/developers","read_at":"2026-09-25T09:33:49+00:00","read_at_is":"when the build read Syntology's graph, not when any sample ran","claim":"Per-sample execution status on synthesized fixtures; not a correctness claim about the paper. 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