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Neurons with Multiplicative Interactions of Nonlinear Synapses

Neurons are the fundamental units of the brain and nervous system. Developing a good modeling of human neurons is very important not only to neurobiology but also to computer science and many other fields. The McCulloch and Pitts neuron model is the most widely used neuron model, but has long been criticized as being oversimplified in view of properties of real neuron and the computations they perform. On the other hand, it has become widely accepted that dendrites play a key role in the overall computation performed by a neuron. However, the modeling of the dendritic computations and the assignment of the right synapses to the right dendrite remain open problems in the field. Here, we propose a novel dendritic neural model (DNM) that mimics the essence of known nonlinear interaction among inputs to the dendrites. In the model, each input is connected to branches through a distance-dependent nonlinear synapse, and each branch performs a simple multiplication on the inputs. The soma then sums the weighted products from all branches and produces the neuron's output signal. We show that the rich nonlinear dendritic response and the powerful nonlinear neural computational capability, as well as many known neurobiological phenomena of neurons and dendrites, may be understood and explained by the DNM. Furthermore, we show that the model is capable of learning and developing an internal structure, such as the location of synapses in the dendritic branch and the type of synapses, that is appropriate for a particular task - for example, the linearly nonseparable problem, a real-world benchmark problem - Glass classification and the directional selectivity problem.