## Abstract

The state of a rotor neuron is constrained to live on the surface of a sphere in R^{n}. A rotor neural network is used to minimize an arbitrary cost function with respect to these 'spherical' states. One practical example of such a situation is optimal charge distribution on a sphere in electromagnetism. In this paper, I show that if the cost function is quadratic in the neuron states, the synchronous, iterated-map algorithm used to find the fixed-points of the network has a Lyapunov function. I also propose a continuous-time dynamical system for finding the fixed-points that is valid for any cost function. Moreover, I show that this continuous-time dynamics has a Lyapunov function. Finally, I show that a similar continuous-time algorithm and a similar Lyapunov function can be used for solving fixed-point equations more general than those of rotor neural networks.

Original language | British English |
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Pages (from-to) | 3355-3356 |

Number of pages | 2 |

Journal | Proceedings of the American Control Conference |

Volume | 3 |

State | Published - 1994 |

Event | Proceedings of the 1994 American Control Conference. Part 1 (of 3) - Baltimore, MD, USA Duration: 29 Jun 1994 → 1 Jul 1994 |