The past few years have seen a dramatic i ncrease in the performance of recognition systems thanks to the introducti on of deep networks for representation learning. However\, the mathematica l reasons for this success remain elusive. A key issue is that the neural network training problem is non-convex\, hence optimization algorithms may not return a global minima. In addition\, the regularization properties o f algorithms such as dropout remain poorly understood. Building on ideas f rom convex relaxations of matrix factorizations\, this work proposes a gen eral framework which allows for the analysis of a wide range of non-convex factorization problems – including matrix factorization\, tensor factoriz ation\, and deep neural network training. The talk will describe sufficien t conditions under which a local minimum of the non-convex optimization pr oblem is a global minimum and show that if the size of the factorized vari ables is large enough then from any initialization it is possible to find a global minimizer using a local descent algorithm. The talk will also pre sent an analysis of the optimization and regularization properties of drop out in the case of matrix factorization.

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< a href='https://www.bme.jhu.edu/faculty_staff/rene-vidal-phd/' target='_bl ank' rel='noopener'>René Vidal is the Herschel L. Seder Professor in t he Department of Biomedical Engineering. He joined Johns Hopkins in 2004. He holds joint appointments in the departments of Electrical and Computer Engineering\, Computer Science\, and Mechanical Engineering. He is the dir ector of the Mathematical Institute for Data Science and the Vision Dynamics and Learning Lab\, and is also a professor in the Institute for Computati onal Medicine\, the Center for Imaging Science\, and the Laboratory for Co mputational Sensing and Robotics.

\nVidal’s research focuses on the development of theory and algorithms for the analysis of complex high-dime nsional datasets such as images\, videos\, time-series and biomedical data . His lab creates new technologies for a variety of biomedical application s\, including detection\, classification\, and tracking of blood cells in holographic images\, classification of embryonic cardio-myocytes in optica l images\, and assessment of surgical skill in surgical videos.

DTSTART;TZID=America/New_York:20180706T090000 DTEND;TZID=America/New_York:20180706T100000 LOCATION:Hackerman Hall\, Room B17 SEQUENCE:0 SUMMARY:René Vidal (Johns Hopkins University): Mathematics of Deep Learning URL:https://www.clsp.jhu.edu/events/vidal-mathematics-deep-learning/ X-COST-TYPE:free X-TAGS;LANGUAGE=en-US:Deep Learning\,Rene Vidal END:VEVENT END:VCALENDAR