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Abstract. Nonconvex optimization methods are widely applied to problems arising in various fields of since and engineering, such as machine learning, statistics, signal processing, and data science. However, the efficacy and reliability of nonconvex optimization approaches are usually questionable due to potentially many local optima. In this talk, the speaker will introduce some theoretical frameworks under certain stochastic setups to explain the empirical successes of nonconvex optimization methods for phase retrieval and low-rank recovery.