{"paper":{"title":"Adaptivity via a Parallel Architecture for Stochastic Gradient Methods Adaptivity via a Parallel Architecture for Stochastic Gradient Methods Adaptivity via a Parallel Architecture for Stochastic Gradient Methods","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.AR","math.OC"],"primary_cat":"cs.LG","authors_text":"Bin Fu","submitted_at":"2026-07-31T00:02:30Z","abstract_excerpt":"We develop a parallel framework that assembles static gradient methods to achieve better adaptivity. A static gradient method, denoted by $\\mathrm{GD}(x_0,T)$, takes as input an initial point $x_0\\in\\mathbb{R}^n$ and $T\\in \\mathbb{R}^+$ specifying the number $\\floor{T}$ of iterations. The step size is chosen as $s=S(T)$, where $S(\\cdot)$ is a predetermined function of $T$. The method then performs the iterations $ x_{i+1}=x_i-\\frac{\\eta}{s}\\cdot g_i,$ where $g_i$ is a stochastic gradient evaluated at $x_i$, and $\\eta$ is a scaling factor. For an integer $p\\ge1$, the $p$ processors in the propo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.28902","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2607.28902/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}