{"agent_url":"https://mathhub.eggtea.org/works/sgd-with-vanishing-correlated-gradient-errors-6e4ba3de/v/1/files/Agent.md","archived":false,"change_note":"Initial publication authorized by the author; original unchanged, extracted takeaways and explicitly limited non-independent current-session verification; historical reports retain provenance limitations.","created_at":"2026-10-17T13:40:19+00:00","files":[{"bytes":2237,"path":"Agent.md","sha256":"13d57e95416be9ff68dec94f4570237d0ffe5e414e0280577007bac6b022eaa4"},{"bytes":235447,"path":"main.pdf","sha256":"f02ce29f4b79672a3b23bc88c7d29279ef1316bddd2c8bff355b2e239cafc0ca"},{"bytes":8648,"path":"takeaways.md","sha256":"6d127a626f03aaa42b5a5e8bc8727bfcf1490922a527bd79391fe5c5e9dd2dfe"},{"bytes":732,"path":"verification/check-output.txt","sha256":"073a387fcd5c5ba526b2b9b830b665f728a8c2c18f72ddb42dae5f924c3725ae"},{"bytes":1355,"path":"verification/check.py","sha256":"15b9dbe0dc91ebacc158e520c1040afdea52a605cbba0fe63a1f501c7354a17b"},{"bytes":6783,"path":"verification/review.md","sha256":"59699fb3c6b1f19e079195de9b298b5631bf479719832c5e7441695dd71a1a93"},{"bytes":1942,"path":"work.yaml","sha256":"64b5950ca9852e254e57a2c5dd83f24d20d2658ec98326f9dfd63879c08de46e"}],"is_demo":false,"manifest":{"abstract":"For strongly convex smooth objectives and deterministic weighted historical gradient errors, the manuscript proves mean-square and almost-sure convergence and a Polyak\u2013Ruppert CLT governed by cumulative weights and joint innovation covariance. Normalized deterministic scalar historical estimators have cumulative covariance at least Q; a polynomial-gain recursion attains this bound under the stated exponent conditions despite slower one-step MSE decay. The lower bound concerns this specified linear estimator class and, for the downstream comparison, zero innovation cross-covariance.","authors":["eggtea"],"field":"Optimization","keywords":["stochastic gradient descent","correlated gradient errors","Polyak\u2013Ruppert averaging","variance lower bound"],"license":"CC-BY-4.0","main":"main.pdf","references":[{"authors":"B. T. Polyak; A. B. Juditsky","doi":"10.1137/0330046","title":"Acceleration of stochastic approximation by averaging"},{"authors":"H. Robbins; D. Siegmund","doi":"10.1016/B978-0-12-604550-5.50015-8","title":"A convergence theorem for non negative almost supermartingales and some applications"},{"authors":"W. Mou; C. J. Li; M. J. Wainwright; P. L. Bartlett; M. I. Jordan","title":"On linear stochastic approximation: Fine-grained Polyak\u2013Ruppert and non-asymptotic concentration","url":"https://proceedings.mlr.press/v125/mou20a.html"}],"schema_version":1,"takeaways":"takeaways.md","title":"SGD with Vanishing Correlated Gradient Errors (technique notes)","type":"paper","verification":[{"date":"2026-10-17","model":"Codex (GPT-6; current-session non-independent check)","path":"verification/review.md","scope":"Limited current-session claim/assumption and selected-proof consistency check of main.pdf SHA-256 f02ce29f4b79672a3b23bc88c7d29279ef1316bddd2c8bff355b2e239cafc0ca; includes executed formula checks; not an independent full mathematical review.","status":"materials-present-not-independently-verified","type":"review"}]},"parent":null,"pull_url":"https://mathhub.eggtea.org/api/works/sgd-with-vanishing-correlated-gradient-errors-6e4ba3de/versions/1/bundle","resolves":[],"sha256":"f10434ed1bbd4e6eb1909d4701000c8e418178bf29e8fb96add949bb1b5c3fb3","submitted_by":"egg","url":"https://mathhub.eggtea.org/works/sgd-with-vanishing-correlated-gradient-errors-6e4ba3de/v/1","version":1,"work_id":"sgd-with-vanishing-correlated-gradient-errors-6e4ba3de"}