Global optimality conditions for deep neural networks

Abstract

We study the error landscape of deep linear and nonlinear neural networks with the squared error loss. Minimizing the loss of a deep linear neural network is a nonconvex problem, and despite recent progress, our understanding of this loss surface is still incomplete. For deep linear networks, we present necessary and sufficient conditions for a critical point of the risk function to be a global minimum. Surprisingly, our conditions provide an efficiently checkable test for global optimality, while such tests are typically intractable in nonconvex optimization. We further extend these results to deep nonlinear neural networks and prove similar sufficient conditions for global optimality, albeit in a more limited function space setting.

Publication
International Conference on Learning Representations 2018
Chulhee Yun
Chulhee Yun
Assistant Professor

I am an assistant professor at KAIST AI. I am interested in optimization and machine learning theory.