{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,10,31]],"date-time":"2024-10-31T02:29:33Z","timestamp":1730341773340,"version":"3.28.0"},"reference-count":24,"publisher":"IEEE","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2018,6]]},"DOI":"10.23919\/acc.2018.8431227","type":"proceedings-article","created":{"date-parts":[[2018,8,17]],"date-time":"2018-08-17T20:16:10Z","timestamp":1534536970000},"page":"4533-4538","source":"Crossref","is-referenced-by-count":2,"title":["On the stability of gradient flow dynamics for a rank-one matrix approximation problem"],"prefix":"10.23919","author":[{"given":"Hesameddin","family":"Mohammadi","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Meisam","family":"Razaviyayn","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Mihailo R.","family":"Jovanovic","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"263","reference":[{"journal-title":"On large-batch training for deep learning Generalization gap and sharp minima","year":"2016","author":"keskar","key":"ref10"},{"key":"ref11","first-page":"3873","article-title":"Global optimality of local search for low rank matrix recovery","author":"bhojanapalli","year":"2016","journal-title":"Advances in neural information processing systems"},{"journal-title":"search of the real inductive bias On the role of implicit regularization in deep learning","year":"2014","author":"neyshabur","key":"ref12"},{"journal-title":"Implicit regularization in matrix factorization","year":"2017","author":"gunasekar","key":"ref13"},{"key":"ref14","first-page":"720","article-title":"Weighted low-rank approximations","author":"srebro","year":"2003","journal-title":"Proceedings of the 20th International Conference on Machine Learning (ICML-03)"},{"journal-title":"Optimization and Dynamical Systems","year":"2012","author":"helmke","key":"ref15"},{"key":"ref16","volume":"3","author":"golub","year":"2012","journal-title":"Matrix Computations"},{"key":"ref17","first-page":"1147","article-title":"Streaming PCA: Matching matrix Bernstein and near-optimal finite sample guarantees for Oja's algorithm","author":"jain","year":"2016","journal-title":"Conference on Learning Theory"},{"key":"ref18","doi-asserted-by":"publisher","DOI":"10.1007\/BF00275687"},{"key":"ref19","doi-asserted-by":"publisher","DOI":"10.1142\/S0129065789000475"},{"key":"ref4","doi-asserted-by":"publisher","DOI":"10.1109\/31.85639"},{"key":"ref3","doi-asserted-by":"publisher","DOI":"10.1109\/TIT.2015.2399924"},{"key":"ref6","first-page":"586","article-title":"Deep learning without poor local minima","author":"kawaguchi","year":"2016","journal-title":"Advances in neural information processing systems"},{"journal-title":"Understanding deep learning requires rethinking generalization","year":"2016","author":"zhang","key":"ref5"},{"journal-title":"Depth creates no bad local minima","year":"2017","author":"lu","key":"ref8"},{"journal-title":"Exponentially vanishing sub-optimal local minima in multilayer neural networks","year":"2017","author":"soudry","key":"ref7"},{"key":"ref2","first-page":"494","article-title":"Training a 3-node neural network is NP-complete","author":"blum","year":"1989","journal-title":"Advances in neural information processing systems"},{"key":"ref1","first-page":"2973","article-title":"Matrix completion has no spurious local minimum","author":"ge","year":"2016","journal-title":"Advances in neural information processing systems"},{"key":"ref9","first-page":"1246","article-title":"Gradient descent only converges to minimizers","author":"lee","year":"2016","journal-title":"Conference on Learning Theory"},{"key":"ref20","doi-asserted-by":"publisher","DOI":"10.1016\/j.sysconle.2004.11.015"},{"key":"ref22","doi-asserted-by":"publisher","DOI":"10.1109\/TSP.2011.2169060"},{"key":"ref21","first-page":"24","article-title":"A generalisation of the Oja subspace flow","author":"webers","year":"2006","journal-title":"17th International Symposium on Mathematical Theory of Networks and Systems"},{"key":"ref24","doi-asserted-by":"publisher","DOI":"10.1016\/0005-1098(85)90099-8"},{"key":"ref23","doi-asserted-by":"publisher","DOI":"10.1007\/s13042-013-0217-x"}],"event":{"name":"2018 Annual American Control Conference (ACC)","start":{"date-parts":[[2018,6,27]]},"location":"Milwaukee, WI","end":{"date-parts":[[2018,6,29]]}},"container-title":["2018 Annual American Control Conference (ACC)"],"original-title":[],"link":[{"URL":"http:\/\/xplorestaging.ieee.org\/ielx7\/8410068\/8430677\/08431227.pdf?arnumber=8431227","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,8,24]],"date-time":"2020-08-24T00:35:06Z","timestamp":1598229306000},"score":1,"resource":{"primary":{"URL":"https:\/\/ieeexplore.ieee.org\/document\/8431227\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,6]]},"references-count":24,"URL":"https:\/\/doi.org\/10.23919\/acc.2018.8431227","relation":{},"subject":[],"published":{"date-parts":[[2018,6]]}}}