Adding One Neuron Can Eliminate All Bad Local Minima

Part of Advances in Neural Information Processing Systems 31 (NeurIPS 2018)

Authors

SHIYU LIANG, Ruoyu Sun, Jason D. Lee, R. Srikant

Abstract

One of the main difficulties in analyzing neural networks is the non-convexity of the loss function which may have many bad local minima. In this paper, we study the landscape of neural networks for binary classification tasks. Under mild assumptions, we prove that after adding one special neuron with a skip connection to the output, or one special neuron per layer, every local minimum is a global minimum.