Name
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. |
Year | Venue | Field |
|---|---|---|
2017 | arXiv: Machine Learning | Finite set,Local optimum,Stochastic neural network,Types of artificial neural networks,Artificial intelligence,Deep learning,Artificial neural network,Mathematics,Machine learning |
DocType | Volume | Citations |
Journal | abs/1710.02196 | 5 |
PageRank | References | Authors |
0.47 | 20 | 4 |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Soheil Feizi | 1 | 113 | 24.65 |
| Hamid Javadi | 2 | 7 | 1.84 |
| Jesse Zhang | 3 | 10 | 4.58 |
| David N. C. Tse | 4 | 2078 | 246.17 |