Algebraic geometrical methods for hierarchical learning machines

@article{Watanabe2001AlgebraicGM,
  title={Algebraic geometrical methods for hierarchical learning machines},
  author={Sumio Watanabe},
  journal={Neural networks : the official journal of the International Neural Network Society},
  year={2001},
  volume={14 8},
  pages={1049-60}
}
Hierarchical learning machines such as layered perceptrons, radial basis functions, Gaussian mixtures are non-identifiable learning machines, whose Fisher information matrices are not positive definite. This fact shows that conventional statistical asymptotic theory cannot be applied to neural network learning theory, for example either the Bayesian a posteriori probability distribution does not converge to the Gaussian distribution, or the generalization error is not in proportion to the… CONTINUE READING
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