Dynamics of learning near singularities in radial basis function networks

Neural Networks - Tập 21 - Trang 989-1005 - 2008
Haikun Wei1,2,3, Shun-ichi Amari1
1Amari Research Unit, RIKEN Brain Science Institute, Saitama, 3510198, Japan
2School of Automation, Southeast University, Nanjing 210096, China
3Department of Brain Science and Engineering, Kyushu Institute of Technology, Kitakyushu 8080196, Japan

Tài liệu tham khảo

Amari, 1967, Theory of adaptive pattern classifiers, IEEE Transactions on Electronic Computers, EC-16, 299, 10.1109/PGEC.1967.264666 Amari, 2006, Singularities affect dynamics of learning in neuromanifolds, Neural Computation, 18, 1007, 10.1162/neco.2006.18.5.1007 Biehl, 1995, Learning by online gradient descent, Journal of Physics A-Mathematical and General, 28, 643, 10.1088/0305-4470/28/3/018 Cousseau, F., Ozeki, T., & Amari, S. (2007). Dynamics of learning in multilayer perceptrons near the singularity. IEEE Transactions on Neural Networks (in press) Freeman, 1997, Dynamics of on-line learning in radial basis function networks, Physical Review E, 56, 907, 10.1103/PhysRevE.56.907 Freeman, 1997, Online learning in radial basis function networks, Neural Computation, 9, 1601, 10.1162/neco.1997.9.7.1601 Fukumizu, 1996, A regularity condition of information matrix of a multilayer perceptron network, Neural Networks, 9, 871, 10.1016/0893-6080(95)00119-0 Fukumizu, 2000, Local minima and plateaus in hierarchical structure of multilayer perceptrons, Neural Networks, 13, 317, 10.1016/S0893-6080(00)00009-5 Geman, 1980, Some averaging and stability results for random differential equations, SIAM Journal of Applied Mathematics, 36, 86, 10.1137/0136009 Horn, 1985 Ostrowski, 1959, A quantitative formulation of Sylvester’s law of inertia, Proceedings of the National Academy of Sciences, 45, 740, 10.1073/pnas.45.5.740 Park, 2005, Slow dynamics due to singularities of hierarchical learning machines, Progress of Theoretical Physics Supplement, 157, 275, 10.1143/PTPS.157.275 Saad, 1995, On-line learning in soft committee machines, Physical Review E, 52, 4225, 10.1103/PhysRevE.52.4225 Wei, 2008, Dynamics of learning near singularities in layered networks, Neural Computation, 20, 813, 10.1162/neco.2007.12-06-414