Adding One Neuron Can Eliminate All Bad Local Minima

Authors:
SHIYU LIANG UIUC
Ruoyu Sun University of Illinois at Urbana-Champaign
Jason Lee University of Southern California
R. Srikant University of Illinois at Urbana-Champaign

Introduction:

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, the authors study the landscape of neural networks for binary classification tasks.

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.

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