论文信息 - Bounds on the number of samples needed for neural learning

Bounds on the number of samples needed for neural learning

The relationship between the number of hidden nodes in a neural network, the complexity of a multiclass discrimination problem, and the number of samples needed for effect learning are discussed. Bounds for the number of samples needed for effect learning are given. It is shown that Omega(min (d,n) M) boundary samples are required for successful classification of M clusters of samples using a two-hidden-layer neural network with d-dimensional inputs and n nodes in the first hidden layer.

[1] Thomas M. Cover,et al. Geometrical and Statistical Properties of Systems of Linear Inequalities with Applications in Pattern Recognition , 1965, IEEE Trans. Electron. Comput..

[2] Richard P. Lippmann,et al. An introduction to computing with neural nets , 1987 .

[3] R. Lippmann,et al. An introduction to computing with neural nets , 1987, IEEE ASSP Magazine.

[4] Eric B. Baum,et al. On the capabilities of multilayer perceptrons , 1988, J. Complex..

[5] Gerald Tesauro,et al. Scaling and Generalization in Neural Networks: A Case Study , 1988, NIPS.

[6] J. Makhoul,et al. Formation of disconnected decision regions with a single hidden layer , 1989, International 1989 Joint Conference on Neural Networks.

[7] David Haussler,et al. What Size Net Gives Valid Generalization? , 1989, Neural Computation.

[8] G. Mirchandani,et al. On hidden nodes for neural nets , 1989 .

[9] W. E. Engeler,et al. Neural network learning time: effects of network and training set size , 1989, International 1989 Joint Conference on Neural Networks.

[10] Patrick K. Simpson,et al. Artificial Neural Systems: Foundations, Paradigms, Applications, and Implementations , 1990 .