Singularities Affect Dynamics of Learning in Neuromanifolds

@article{Amari2006SingularitiesAD,
  title={Singularities Affect Dynamics of Learning in Neuromanifolds},
  author={Shun-ichi Amari and Hyeyoung Park and Tomoko Ozeki},
  journal={Neural Computation},
  year={2006},
  volume={18},
  pages={1007-1065}
}
The parameter spaces of hierarchical systems such as multilayer perceptrons include singularities due to the symmetry and degeneration of hidden units. A parameter space forms a geometrical manifold, called the neuromanifold in the case of neural networks. Such a model is identified with a statistical model, and a Riemannian metric is given by the Fisher information matrix. However, the matrix degenerates at singularities. Such a singular structure is ubiquitous not only in multilayer… CONTINUE READING
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