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arXiv · 1710.02196

Porcupine Neural Networks: (Almost) All Local Optima are Global

Soheil Feizi·Hamid Javadi·Jesse Zhang·David Tse
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Abstract

Neural networks have been used prominently in several machine learning and statistics applications. In general, the underlying optimization of neural networks is non-convex which makes their performance analysis challenging. In this paper, we take a novel approach to this problem by asking whether one can constrain neural network weights to make its optimization landscape have good theoretical properties while at the same time, be a good approximation for the unconstrained one. For two-layer neural networks, we provide affirmative answers to these questions by introducing Porcupine Neural Networks (PNNs) whose weight vectors are constrained to lie over a finite set of lines. We show that most local optima of PNN optimizations are global while we have a characterization of regions where bad local optimizers may exist. Moreover, our theoretical and empirical results suggest that an unconstrained neural network can be approximated using a polynomially-large PNN.

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Soheil Feizi, Hamid Javadi, Jesse Zhang, David Tse. 2017-10-05. Porcupine Neural Networks: (Almost) All Local Optima are Global. https://arxiv.org/abs/1710.02196

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