Time coded neurons, geometric networks, and homomorphic learning

Regina Bernhaupt, Jochen Pfalzgraf

Research output: Chapter in Book/Report/Conference proceedingChapterAcademicpeer-review

1 Citation (Scopus)


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 languageEnglish
Title of host publicationAdvances in Neural Networks and Applications
PublisherWorld Scientific and Engineering Academy and Society (WSEAS)
Number of pages6
ISBN (Print)9608052262
Publication statusPublished - 1 Dec 2001
Externally publishedYes


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


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