Adding One Neuron Can Eliminate All Bad Local Minima

• DOI: 10.48550/arxiv.1805.08671
• Publication Date: 2018-01-01
• Authors: Shiyu Liang; Ruoyu Sun; Jason D. Lee; R. Srikant
• Keywords: Maxima and minima; Convexity

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