Recently, a series of theoretical studies have conjectured that synaptic nonlinearities in a dendritic tree could make individual neurons act more powerfully in complex computational operations. Each of the neurons has quite distinct morphologies of synapses and dendrites to determine what signals a neuron receives and how these signals are integrated. However, there is no effective model that can captures the nonlinearities among excitatory and inhibitory inputs while predicting the morphology and its evolution of synapses and dendrites. In this paper, we propose a new single neuron model with synaptic nonlinearities in a dendritic tree. The computation on neuron has a neuron-pruning function that can reduce dimension by removing useless synapses and dendrites during learning, forming a precise synaptic and dendritic morphology. The nonlinear interactions in a dendrite tree are expressed using the Boolean logic AND (conjunction), OR (disjunction) and NOT (negation). An error back propagation algorithm is used to train the neuron model. Furthermore, we apply the new model to the Exclusive OR (XOR) problem and it can solve the problem perfectly with the help of inhibitory synapses which demonstrate synaptic nonlinear computation and the neuron's ability to learn.
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