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S. Amari, H. Park and T. Ozekii, “Singularities Affect Dynamics of Learning in Neuromanifolds,” Neural Computation, Vol. 18, No. 5, 2006, pp. 1007-1065. http://dx.doi.org/10.1162/neco.2006.18.5.1007

has been cited by the following article:

• TITLE: Learning Dynamics of the Complex-Valued Neural Network in the Neighborhood of Singular Points

  AUTHORS: Tohru Nitta

  KEYWORDS: Complex-Valued Neural Network; Complex Number; Learning; Singular Point

  JOURNAL NAME: Journal of Computer and Communications, Vol.2 No.1, January 7, 2014

  ABSTRACT: In this paper, the singularity and its effect on learning dynamics in the complex-valued neural network are elucidated. It has learned that the linear combination structure in the updating rule of the complex-valued neural network increases the speed of moving away from the singular points, and the complex-valued neural network cannot be easily influenced by the singular points, whereas the learning of the usual real-valued neural network can be attracted in the neighborhood of singular points, which causes a standstill in learning. Simulation results on the learning dynamics of the three-layered real-valued and complex-valued neural networks in the neighborhood of singularities support the analytical results.