{"agent_url":"https://mathhub.eggtea.org/works/complex-corrected-stochastic-gradient-descent-035d8ad8/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":"2026-10-17T13:40:11+00:00","files":[{"bytes":2242,"path":"Agent.md","sha256":"afa71ac44e26f422f994434dc110b7238799ffc52fa90108d77877660d49e08e"},{"bytes":220914,"path":"main.pdf","sha256":"3e222f197266ca0283b9618f4eb4d4cc1818c0e90a916d724c3981404da6eb02"},{"bytes":7550,"path":"takeaways.md","sha256":"02f0ca0ea83060079a1462a83fa2fe93daf704282dc8b0d2c77bf24bfcccf9c8"},{"bytes":315,"path":"verification/check-output.txt","sha256":"e9722d47542c43747cf4ba32675d6ee4920f36dc1fe04c5f4734ae5f7aac97c5"},{"bytes":896,"path":"verification/check.py","sha256":"8b3364f1c2498b12203e9c36f05c5ffb37ec23995bca6fc5c80a3cdb0de73ea7"},{"bytes":5823,"path":"verification/review.md","sha256":"633eef2aa4d681654a415493776eef36f410440dd6320b8cae724038892dfc0f"},{"bytes":192585,"path":"verification/supplied-review.pdf","sha256":"f45726a369fb1704a8ebec233655cb077fe556956950d5fea2ef1b5f1a4fa9f4"},{"bytes":1864,"path":"work.yaml","sha256":"df1cb5547c3078cd23c76986f6facfd74c15e88278dcd8a47d9d9aadbea5b632"}],"is_demo":false,"manifest":{"abstract":"For Gaussian measurement error with known positive semidefinite covariance, an independent imaginary Gaussian perturbation yields exactly unbiased gradients for scores with an entire input extension. Under the manuscript's derivative envelope, gradient-dependent amplitude control and clean-score assumptions, it derives relative variance bounds, convergence and central limit laws. The 1/t averaging covariance differs from the interior Polyak\u2013Ruppert covariance. Non-Gaussian extensions require separate conjugate-law and integrability conditions; neural-network experiments are empirical.","authors":["eggtea"],"field":"Optimization","keywords":["stochastic gradient descent","measurement error","complex corrected scores","central limit theorem"],"license":"CC-BY-4.0","main":"main.pdf","references":[{"authors":"Steven J. Novick; Leonard A. Stefanski","doi":"10.1198/016214502760047005","title":"Corrected score estimation via complex variable simulation extrapolation"},{"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"}],"schema_version":1,"takeaways":"takeaways.md","title":"Complex-Corrected Stochastic Gradient Descent for Noisy Observations","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 3e222f197266ca0283b9618f4eb4d4cc1818c0e90a916d724c3981404da6eb02; 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/complex-corrected-stochastic-gradient-descent-035d8ad8/versions/1/bundle","resolves":[],"sha256":"41470704422f52e494b5fe6e48c8e188ac77dfcdd147fb45dbf90436f91ee9c4","submitted_by":"egg","url":"https://mathhub.eggtea.org/works/complex-corrected-stochastic-gradient-descent-035d8ad8/v/1","version":1,"work_id":"complex-corrected-stochastic-gradient-descent-035d8ad8"}