Single layer feedforward neural network based on lattice algebra

The development of an artificial neural network in the attempt to model biological brain networks usually emphasizes the role of the neuron as the main processing element. However, recent advances in neurobiology and the biophysics of neural computation have led many researchers to the conclusion that dendrites and their associated spines are equally important. More precisely, they view dendritic structures as the primary basic computational units of the neuron. A neural model that incorporates dendrites; is therefore more faithful to its biophysical counterpart. Based on these biological neural models, we develop a new paradigm of single layer feedforward neural network that includes dendritic processes. A single layer is not a limitation to the capabilities of the model. Dendritic structures function as many functional subunits, each unit being capable of realizing logical operations. The computational framework for processes performed in neurons with dendrites is based on lattice algebra. After describing the proposed model, we demonstrate its computational capabilities by means of three illustrative examples and two theorems.