Shattering all sets of k points in "general position" requires (k - 1)/2 parameters

Neural Computation

Volumn 9, Issue 2, 1997, Pages 337-348

  Sontag, Eduardo D ^a  

^a RUTGERS UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0000428217     PISSN: 08997667     EISSN: None     Source Type: Journal    
DOI: 10.1162/neco.1997.9.2.337     Document Type: Article

References (10)

1. Cover, T. M. 1988. Capacity problems for linear machines. In Pattern Recognition, L. Kanal, ed., pp. 283-289. Thompson Book Co.
2. Karpinski, M., and Macintyre, A. in press. Polynomial bounds for VC dimension of sigmoidal and general Pfaffian neural networks. J. Computer Systems Sciences.
3. Koiran, P., and Sontag, E. D. in press. Neural networks with quadratic VC dimension. J. Computer Systems Sciences.
4. Kowalczyk, A. in press. Estimates of storage capacity of mutilayer perceptron with threshold logic units. Neural Networks.
5. Maass, M. 1994. Perspectives of current research about the complexity of learning in neural nets. In Theoretical Advances in Neural Computation and Learning, V. P. Roychowdhury, K. Y. Siu, and A. Orlitsky, eds., pp. 295-336. Kluwer, Boston.
6. Maass, W. 1996. Lower bounds for the computational power of networks of spiking neurons. Neural Computation 8, 1-40.
7. Maass, W. in press. The third generation of neural network models. In Proc. 7th Australian Conference on Neural Networks 1996, Canberra, Australia.
8. Macintyre, A., and Sontag, E. D. 1993. Finiteness results for sigmoidal "neural" networks. In Proc. 25th Annual Symp. Theory Computing, pp. 325-334, San Diego, CA.
9. Sontag, E. D. 1992. Feedforward nets for interpolation and classification. J. Comp. Syst. Sci. 45, 20-48.
10. Sontag, E. D. 1996. Critical points for least-squares problems involving certain analytic functions, with applications to sigmoidal nets. Advances in Computational Mathematics 5, 245-268.