Abstract
Based on existing work where categorical and geometrical methods were used to establish a mathematical model of neural net structures, we develop a new very general model for artificial neural networks (ANN), where all basic components of a network are described abstractly. This mathematical model serves as a guideline for design and implementation of a new ANN-simulator. The proposed model of neuron types will be illustrated by the discussion of an example, using the Single Spiking Neuron Model (SSM). The main building blocks of the simulation tool, a new construction principle for ANN, and abstract modeling of connection weights are presented.
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Bernhaupt, R., Pfalzgraf, J. (2002). On Mathematical Modeling of Networks and Implementation Aspects. In: Calmet, J., Benhamou, B., Caprotti, O., Henocque, L., Sorge, V. (eds) Artificial Intelligence, Automated Reasoning, and Symbolic Computation. AISC Calculemus 2002 2002. Lecture Notes in Computer Science(), vol 2385. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45470-5_17
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DOI: https://doi.org/10.1007/3-540-45470-5_17
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