天元讲堂：Partial Differential Equations, Nonconvex Optimizationand Deep Neural Nets
报告题目：
Partial Differential Equations, Nonconvex Optimizationand Deep Neural Nets
报告人：Stanley Osher 教授（加州大学洛杉矶分校；美国科学院、美国艺术与科学院、美国工程院院士）
时间：2018年5月24日（星期四）16：00—17：00
地点：苏州大学本部精正楼二楼学术报告厅
报告摘要：
Recently,links between partial differential equations (PDEs) and DNNs have been establishedin several interesting directions. We used ideas from Hamilton-Jacobi (HJ)equations and control and differential games to improve training time, modifyand improve the training algorithm, we propose a very simple modification ofgradient descent and stochastic gradient descent. We show that when applied toa variety of machine learning models including softmax regression,convolutional neural nets, generative adversarial nets, and deep reinforcementlearning, this very simple surrogate can dramatically reduce the variance andimprove the accuracy of the generalization. The new algorithm, (which dependson one nonnegative parameter) when applied to non convex minimization, tends toavoid sharp local minima. Instead it seeks somewhat flatter local (and oftenglobal) minima. Again, the programming changes needed to doing this is minimal,in cost, complexity and effort. We implement our algorithm into both PyTorchand Tensorflow platforms, which will be made publicly available.
报告人简介：
ProfessorStanley Osher has been elected to the USNational Academy of Science, the USNational Academy of Engineering, and the American Academy of Arts and Sciences. He was awarded the SIAM Pioneer Prize at the 2003 ICIAMconference and the Ralph E. KleinmanPrize in 2005. He was awarded honorary doctoral degrees by ENS Cachan,France, in 2006 and by Hong Kong Baptist University in 2009. He is a SIAM and AMS Fellow. He gave a one hour plenary address at the 2010 International Conference ofMathematicians. He also gave the John von Neumann Lecture at the SIAM 2013annual meeting. He is a Thomson-Reuters highly cited researcher-among the top1% from 2002-2016 in both Mathematics and Computer Science with an H index of111, more than 100,000 citations and an average of one new citation per hour inrecent years. In 2014, he received the CarlFriedrich Gauss Prize from the International Mathematics Union-this isregarded as the highest prize in applied mathematics. In 2016 he received the William Benter Prize. His currentinterests involve information science, which includes optimization, imageprocessing, compressed sensing and machine learning and applications of thesetechniques to the equations of medicine, physics, engineering and elsewhere.
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