Multibranch Formal Neuron: An Internally Nonlinear Learning Unit

The transformation of synaptic input into action potential in nerve cells is strongly influenced by the morphology of the dendritic arbor as well as the synaptic efficacy map. The multiplicity of dendritic branches strikingly enables a single cell to act as a highly nonlinear processing element. Studies have also found functional synaptic clustering whereby synapses that encode a common sensory feature are spatially clustered together on the branches. Motivated by these findings, here we introduce a multibranch formal model of the neuron that can integrate synaptic inputs nonlinearly through collective action of its dendritic branches and yields synaptic clustering. An analysis in support of its use as a computational building block is offered. Also offered is an accompanying gradient descent-based learning algorithm. The model unit spans a wide spectrum of nonlinearities, including the parity problem, and can outperform the multilayer perceptron in generalizing to unseen data. The occurrence of synaptic clustering boosts the generalization efficiency of the unit, which may also be the answer for the puzzling ubiquity of synaptic clustering in the real neurons. Our theoretical analysis is backed up by simulations. The study could pave the way to new artificial neural networks.