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[Submitted on 12 Aug 2026] Title:Why Clipping Matters in AdaGrad? Toward a High-Probability Theory under Generalized Smoothness View a PDF of the paper titled Why Clipping Matters in AdaGrad? Toward a High-Probability Theory under Generalized Smoothness, by Alokendu Mazumder and 5 other authors View PDF HTML (experimental) Abstract:We analyze the original same-step coordinate-wise AdaGrad under generalized smoothness and heavy-tailed noise with bounded variance. In this setting, local curvature may grow sub-quadratically with the gradient norm, and stochastic gradients are assumed to have only bounded conditional second moments. We show that unclipped AdaGrad can become \emph{anisotropically miscalibrated}: under heavy-tailed noise, the adaptive denominator can learn the geometry of rare noise shocks rather than the local curvature of the objective, leading to a persistent directional distortion that blocks finite-horizon Euclidean progress. We then prove that clipping repairs this failure mode. Our main result is a finite-horizon high-probability guarantee for the original non-lagged AdaGrad update, yielding $\frac1T\sum_{t=0}^{T-1}\|\nabla f(x_t)\|^2=\mathcal{O}\left(\frac{d\big(\sqrt{\log T} + \log \frac{1}{\delta}\big)}{\sqrt{T}}\right),$ and hence $\widetilde{\mathcal O}(\varepsilon^{-2})$ complexity. This shows that, for AdaGrad under heavy-tailed noise, clipping is a structural stabilizer of the adaptive geometry rather than merely a robustness heuristic. Subjects: Machine Learning (cs.LG); Systems and Control (eess.SY) Cite as: arXiv:2609.30276 [cs.LG] (or arXiv:2609.30276v1 [cs.LG] for this version) https://doi.org/10.48550/arXiv.2609.30276 arXiv-issued DOI via DataCite Submission history From: Alokendu Mazumder [view email] [v1] Wed, 12 Aug 2026 12:16:48 UTC (59 KB) Full-text links: Access Paper: View a PDF of the paper titled Why Clipping Matters in AdaGrad? Toward a High-Probability Theory under Generalized Smoothness, by Alokendu Mazumder and 5 other authors View PDF HTML (experimental) TeX Source view license Current browse context: cs.LG new | recent | 2026-09 Change to browse by: cs cs.SY eess 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?)