Jason Lee (University of Southern California)
Deep Learning has had phenomenal empirical successes in many domains including computer vision, natural language processing, and speech recognition. To consolidate and boost the empirical success, we need to develop a more systematic and deeper understanding of the elusive principles of deep learning.
In this talk, I will provide analysis of several elements of deep learning including non-convex optimization, overparametrization, and generalization error. First, we show that gradient descent and many other algorithms are guaranteed to converge to a local minimizer of the loss. For several interesting problems including the matrix completion problem, this guarantees that we converge to a global minimum. Then we will show that gradient descent converges to a global minimizer for deep overparametrized networks. Finally, we analyze the generalization error by showing that a subtle combination of SGD, logistic loss, and architecture combine to promote large margin classifiers, which are guaranteed to have low generalization error.