“…Recovery of low-rank matrices has a wide array of applications, including recommendation systems (Recht et al, 2010;Candès & Recht, 2009;Davenport & Romberg, 2016;Chandrasekaran et al, 2012;Chen & Chi, 2018;Candès & Plan, 2011), quantum state tomography (Recht et al, 2010;Kyrillidis et al, 2018;Flammia et al, 2012;Gross et al, 2010;Liu, 2011;Chen et al, 2015;Cai & Zhang, 2015), phase retrieval and blind deconvolution (Shechtman et al, 2015;Fienup, 1982;Candès et al, 2013;Chen et al, 2015;Cai & Zhang, 2015;Li et al, 2016;Segarra et al, 2017;Ling & Strohmer, 2015), neural word embeddings (Mikolov et al, 2013;Pennington et al, 2014), text classification (Joulin et al, 2017), convexified convolutional NNs (Zhang et al, 2017), and SDP instances (Burer & Monteiro, 2003;Bhojanapalli et al, 2018;Kyrillidis et al, 2018;Wang et al, 2017;Yurtsever et al, 2019;Goto et al, 2019). Because of its importance in practice, there has been a large push in the literature to develop efficient algorithms for this task (Davenport & Romberg, 2016).…”