## Abstract

A paradigm of artificial neural networks (ANN), introduced by II.Geiger, is presented. The design of the network structure and the neurons is of physiological relevance. We concentrate on two neuron types, the conductivity coupled model (CCM) and the single spike model (SSM). The introduction of the time parameter (in SSM) is motivated on basis of the functionality of CCM. Passing from CCM to SSM is described. It turned out that the typical network structures can be mathematically modeled in a natural way. Geometric and categorical methods can be used. A so-called geometric net can be associated to an originally designed ANN. Such networks form a category. A morphism in that category can be interpreted as a learning step ("homomorphic learning"). Learning in an ANN corresponds to a sequence of morphisms. The mathematical model results in an economic effect in (industrial) applications as considerable performance improvements in network simulations demonstrate. The networks of Geiger's paradigm have been very successful in industrial applications since many years.

Original language | English |
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Title of host publication | Advances in Neural Networks and Applications |

Publisher | World Scientific and Engineering Academy and Society (WSEAS) |

Pages | 268-273 |

Number of pages | 6 |

ISBN (Print) | 9608052262 |

Publication status | Published - 1 Dec 2001 |

Externally published | Yes |

## Keywords

- Category theory
- Geometric net
- Homomorphic learning
- Optical quality control
- Synchronization
- Time coded neuron