翻訳待ち：A Trust-region Framework for Moment Estimation
AI サービスが一時的に利用できないため、復旧後に翻訳を補完します。ソース概要：arXiv:2608.04026v1 Announce Type: new Abstract: In this paper, we develop a trust-region framework for understanding the behavior of adaptive moment estimation mechanisms, such as \textsc{Adam}, in stochastic gradient optimization. Specifically, in this framework, the magnitude of the update step for each individual weight is constrained within a trust-region governed by a moment constraint of order $p\in[2,4]$. The resulting derivation then leads to a family of learning-rate mechanisms based on second-moment estimation and a normalized $p$-th moment estimation. When $p=4$, this involves kurtosis-like estimation. The general mechanism, referred to as \textsc{Gmake}, provides a unified interpretation of normalization by moment estimation, learning-rate scheduling, spectral lowpass filtering as momentum, and operator-level spectral normalization within a common trust-region framework. Experiments on GPT2-124M trained on FineWeb-Edu and TinyStories suggest that the fourth-moment realization provides its greatest benefit when trust-region constraints are weak. As progressively stronger trust-region controls are introduced, the second-moment realization becomes increasingly competitive, often achieving slightly lower validation loss than its corresponding fourth-moment realization.
AI サービスが一時的に利用できないため、復旧後に翻訳を補完します。
--> [Submitted on 26 Jul 2026] Title:A Trust-region Framework for Moment Estimation View a PDF of the paper titled A Trust-region Framework for Moment Estimation, by Oluwasegun A. Somefun View PDF HTML (experimental) Abstract:In this paper, we develop a trust-region framework for understanding the behavior of adaptive moment estimation mechanisms, such as \textsc{Adam}, in stochastic gradient optimization. Specifically, in this framework, the magnitude of the update step for each individual weight is constrained within a trust-region governed by a moment constraint of order $p\in[2,4]$. The resulting derivation then leads to a family of learning-rate mechanisms based on second-moment estimation and a normalized $p$-th moment estimation. When $p=4$, this involves kurtosis-like estimation. The general mechanism, referred to as \textsc{Gmake}, provides a unified interpretation of normalization by moment estimation, learning-rate scheduling, spectral lowpass filtering as momentum, and operator-level spectral normalization within a common trust-region framework. Experiments on GPT2-124M trained on FineWeb-Edu and TinyStories suggest that the fourth-moment realization provides its greatest benefit when trust-region constraints are weak. As progressively stronger trust-region controls are introduced, the second-moment realization becomes increasingly competitive, often achieving slightly lower validation loss than its corresponding fourth-moment realization. Comments: 20 pages, 5 figures. Submitted to TMLR Subjects: Machine Learning (cs.LG); Artificial Intelligence (cs.AI); Signal Processing (eess.SP); Systems and Control (eess.SY) Cite as: arXiv:2608.04026 [cs.LG] (or arXiv:2608.04026v1 [cs.LG] for this version) https://doi.org/10.48550/arXiv.2608.04026 arXiv-issued DOI via DataCite Submission history From: Oluwasegun Ayokunle Somefun [view email] [v1] Sun, 26 Jul 2026 20:46:45 UTC (1,302 KB) Full-text links: Access Paper: View a PDF of the paper titled A Trust-region Framework for Moment Estimation, by Oluwasegun A. Somefun View PDF HTML (experimental) TeX Source view license Current browse context: cs.LG new | recent | 2026-08 Change to browse by: cs cs.AI cs.SY eess eess.SP eess.SY References & Citations NASA ADS Google Scholar Semantic Scholar Loading... Data provided by: Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer (What is the Explorer?) Connected Papers Toggle Connected Papers (What is Connected Papers?) Litmaps Toggle Litmaps (What is Litmaps?) scite.ai Toggle scite Smart Citations (What are Smart Citations?) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv (What is alphaXiv?) Links to Code Toggle CatalyzeX Code Finder for Papers (What is CatalyzeX?) DagsHub Toggle DagsHub (What is DagsHub?) GotitPub Toggle Gotit.pub (What is GotitPub?) Huggingface Toggle Hugging Face (What is Huggingface?) ScienceCast Toggle ScienceCast (What is ScienceCast?) Demos Demos Replicate Toggle Replicate (What is Replicate?) Spaces Toggle Hugging Face Spaces (What is Spaces?) Spaces Toggle TXYZ.AI (What is TXYZ.AI?) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower (What are Influence Flowers?) Core recommender toggle CORE Recommender (What is CORE?) IArxiv recommender toggle IArxiv Recommender (What is IArxiv?) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs. Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)