{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,1]],"date-time":"2026-04-01T18:34:58Z","timestamp":1775068498983,"version":"3.50.1"},"reference-count":24,"publisher":"IEEE","license":[{"start":{"date-parts":[[2019,7,1]],"date-time":"2019-07-01T00:00:00Z","timestamp":1561939200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/ieeexplore.ieee.org\/Xplorehelp\/downloads\/license-information\/IEEE.html"},{"start":{"date-parts":[[2019,7,1]],"date-time":"2019-07-01T00:00:00Z","timestamp":1561939200000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-029"},{"start":{"date-parts":[[2019,7,1]],"date-time":"2019-07-01T00:00:00Z","timestamp":1561939200000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-037"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2019,7]]},"DOI":"10.1109\/ijcnn.2019.8852239","type":"proceedings-article","created":{"date-parts":[[2019,9,30]],"date-time":"2019-09-30T23:44:32Z","timestamp":1569887072000},"page":"1-8","source":"Crossref","is-referenced-by-count":256,"title":["A Proof of Local Convergence for the Adam Optimizer"],"prefix":"10.1109","author":[{"given":"Sebastian","family":"Bock","sequence":"first","affiliation":[]},{"given":"Martin","family":"Weis","sequence":"additional","affiliation":[]}],"member":"263","reference":[{"key":"ref10","first-page":"1097","author":"krizhevsky","year":"2012","journal-title":"Advances in Neural Information Processing Systems 25"},{"key":"ref11","author":"hinton","year":"2012","journal-title":"Overview of mini-batch gradient descent"},{"key":"ref12","doi-asserted-by":"publisher","DOI":"10.1109\/MSP.2012.2205597"},{"key":"ref13","author":"zou","year":"2018","journal-title":"A Sufficient Condition for Convergences of Adam and RMSProp"},{"key":"ref14","author":"da silva","year":"2018","journal-title":"A general system of differential equations to model first order adaptive algorithms"},{"key":"ref15","author":"krizhevsky","year":"2009","journal-title":"Learning multiple layers of features from tiny images"},{"key":"ref16","author":"bock","year":"2018","journal-title":"An improvement of the convergence proof of the ADAM-Optimizer"},{"key":"ref17","author":"barakat","year":"2018","journal-title":"Convergence of the ADAM algorithm from a Dynamical System Viewpoint"},{"key":"ref18","doi-asserted-by":"crossref","DOI":"10.1201\/9781420027020","author":"agarwal","year":"2000","journal-title":"Difference Equations and Inequalities Theory Methods and Applications"},{"key":"ref19","author":"kelley","year":"2001","journal-title":"Difference Equations An Introduction with Applications"},{"key":"ref4","article-title":"Adam: A Method for Stochastic Optimization","volume":"abs 1412 6980","author":"kingma","year":"2014","journal-title":"CoRR"},{"key":"ref3","first-page":"2121","article-title":"Adaptive subgradient methods for online learning and stochastic optimization","volume":"12","author":"duchi","year":"2011","journal-title":"J Mach Learn Res"},{"key":"ref6","article-title":"Convergence Analysis of an Adaptive Method of Gradient Descent","author":"rubio","year":"2017","journal-title":"University of Oxford Oxford M Sc thesis"},{"key":"ref5","article-title":"Rotationsermittlung von Bauteilen basierend auf neuronalen Netzen (unpublished)","author":"bock","year":"2017","journal-title":"Ostbayerische Technische Hochschule Regensburg M Sc thesis"},{"key":"ref8","author":"chen","year":"2018","journal-title":"On the Convergence of A Class of Adam-Type Algorithms for Non-Convex Optimization"},{"key":"ref7","article-title":"On the Convergence of Adam and Beyond","author":"reddi","year":"2018","journal-title":"International Conference on Learning Representations"},{"key":"ref2","author":"nocedal","year":"2006","journal-title":"Numerical Optimization"},{"key":"ref1","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4419-8853-9"},{"key":"ref9","doi-asserted-by":"publisher","DOI":"10.1214\/aoms\/1177729586"},{"key":"ref20","author":"freeman","year":"1965","journal-title":"Discrete-Time Systems An Introduction to the Theory"},{"key":"ref22","doi-asserted-by":"publisher","DOI":"10.1515\/9783110250398"},{"key":"ref21","author":"bof","year":"0","journal-title":"Lyapunov theory for discrete time systems"},{"key":"ref24","author":"silvester","year":"1999","journal-title":"Determinants Of Block Matrices"},{"key":"ref23","author":"de","year":"2018","journal-title":"Convergence guarantees for RMSProp and ADAM in non-convex optimization and an empirical comparison to Nesterov acceleration"}],"event":{"name":"2019 International Joint Conference on Neural Networks (IJCNN)","location":"Budapest, Hungary","start":{"date-parts":[[2019,7,14]]},"end":{"date-parts":[[2019,7,19]]}},"container-title":["2019 International Joint Conference on Neural Networks (IJCNN)"],"original-title":[],"link":[{"URL":"http:\/\/xplorestaging.ieee.org\/ielx7\/8840768\/8851681\/08852239.pdf?arnumber=8852239","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,7,17]],"date-time":"2022-07-17T17:54:56Z","timestamp":1658080496000},"score":1,"resource":{"primary":{"URL":"https:\/\/ieeexplore.ieee.org\/document\/8852239\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,7]]},"references-count":24,"URL":"https:\/\/doi.org\/10.1109\/ijcnn.2019.8852239","relation":{},"subject":[],"published":{"date-parts":[[2019,7]]}}}