{"url":"/method/qhm","slug":"qhm","name":"QHM","full_name":"QHM","full_name_withheld":false,"description_markdown":"**Quasi-Hyperbolic Momentum (QHM)** is a stochastic optimization technique that alters [momentum SGD](https://paperswithcode.com/method/sgd-with-momentum) with a momentum step, averaging an [SGD](https://paperswithcode.com/method/sgd) step with a momentum step:\r\n\r\n$$ g\\_{t+1} = \\beta{g\\_{t}} + \\left(1-\\beta\\right)\\cdot{\\nabla}\\hat{L}\\_{t}\\left(\\theta\\_{t}\\right) $$\r\n$$ \\theta\\_{t+1} = \\theta\\_{t} - \\alpha\\left[\\left(1-v\\right)\\cdot\\nabla\\hat{L}\\_{t}\\left(\\theta\\_{t}\\right) + v\\cdot{g\\_{t+1}}\\right]$$\r\n\r\nThe authors suggest a rule of thumb of $v = 0.7$ and $\\beta = 0.999$.","description_state":"present","introduced_year":null,"introduced_by":{"title":"Quasi-hyperbolic momentum and Adam for deep learning","paper":"/paper/quasi-hyperbolic-momentum-and-adam-for-deep","first_author":"Jerry Ma","n_authors":2,"url_abs":null,"archive_paper_url":"https://paperswithcode.com/paper/quasi-hyperbolic-momentum-and-adam-for-deep"},"source":{"url":"http://arxiv.org/abs/1810.06801v4","title":"Quasi-hyperbolic momentum and Adam for deep learning","url_on_a_paper_host":true},"code_snippet_url":"https://github.com/jettify/pytorch-optimizer/blob/155246597d66dd774156599be0f07a8c6f7758aa/torch_optimizer/qhm.py#L9","code_snippet_url_on_a_code_host":true,"categories":[{"area":"General","area_id":"general","collection":"Stochastic Optimization","url":"/methods/category/stochastic-optimization","pwc_aliases":[]}],"n_papers_tagged":2,"archive_num_papers":2,"papers_newest_first":[{"paper":"/paper/understanding-the-role-of-momentum-in","title":"Understanding the Role of Momentum in Stochastic Gradient Methods","date":"2019-10-30","arxiv_id":"1910.13962","n_code_links":1,"syntology":null},{"paper":"/paper/quasi-hyperbolic-momentum-and-adam-for-deep","title":"Quasi-hyperbolic momentum and Adam for deep learning","date":"2018-10-16","arxiv_id":"1810.06801","n_code_links":2,"syntology":{"ran":0,"of":7,"unverified":7,"pointer_only":7}}],"papers_shown":2,"tasks":[{"task":"/task/stochastic-optimization","name":"Stochastic Optimization","papers":2},{"task":"/task/deep-learning","name":"Deep Learning","papers":1}],"tasks_shown":2,"n_tasks":2,"usage_by_year":[{"year":"2018","papers":1},{"year":"2019","papers":1}],"row_source":"methods_table","archive":{"source":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","archive_url":"https://paperswithcode.com/method/qhm"},"syntology_read_at":"2026-09-24T18:15:14+00:00"}