In plain words: Adding one special neuron—wired straight to the output, or one in each layer—makes a binary classifier's loss free of bad local minima. Under mild assumptions, every local minimum becomes the best possible, unlike ordinary networks that can get stuck in worse ones.
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.
Shiyu Liang, Ruoyu Sun, Jason D. Lee, R. Srikant
arXiv:1805.08671 · stat.ML, cs.LG · submitted May 22, 2018
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