On the Number of Linear Regions of Deep Neural Networks

作者: Yoshua Bengio , Razvan Pascanu , Guido F Montufar , Kyunghyun Cho

DOI:

关键词: Artificial neural networkStructure (category theory)AlgorithmMathematical optimizationRectifier (neural networks)Layer (object-oriented design)Deep learningMathematicsComputationFeedforward neural networkPiecewise linear functionArtificial intelligence

摘要: … by deep feedforward neural networks with piecewise linear activations in terms of the symmetries and the number of linear regions that they have. Deep networks … deep neural networks …

参考文章(21)
Peter Bartlett, Martin M. Anthony, Learning in Neural Networks: Theoretical Foundations Cambridge University Press. ,(1999)
Martin Anthony, Peter L Bartlett, Peter L Bartlett, Neural Network Learning: Theoretical Foundations ,(1999)
Geoffrey E. Hinton, Vinod Nair, Rectified Linear Units Improve Restricted Boltzmann Machines international conference on machine learning. pp. 807- 814 ,(2010)
Yoshua Bengio, Razvan Pascanu, Guido Montufar, On the number of response regions of deep feed forward networks with piece-wise linear activations arXiv: Learning. ,(2013)
Yoshua Bengio, Razvan Pascanu, Guido Montufar, On the number of inference regions of deep feed forward networks with piece-wise linear activations international conference on learning representations. ,(2014)
Guido F. Montúfar, Universal approximation depth and errors of narrow belief networks with discrete units Neural Computation. ,vol. 26, pp. 1386- 1407 ,(2014) , 10.1162/NECO_A_00601
G. Cybenko, Approximation by superpositions of a sigmoidal function Mathematics of Control, Signals, and Systems. ,vol. 2, pp. 303- 314 ,(1989) , 10.1007/BF02551274
Dan Cireşan, Ueli Meier, Jonathan Masci, Jürgen Schmidhuber, 2012 Special Issue: Multi-column deep neural network for traffic sign classification Neural Networks. ,vol. 32, pp. 333- 338 ,(2012) , 10.1016/J.NEUNET.2012.02.023