Passive nonlinear dendritic interactions as a general computational resource in functional spiking neural networks

Nonlinear interactions in the dendritic tree play a key role in neural computation. Nevertheless, modeling frameworks aimed at the construction of large-scale, functional spiking neural networks, such as the Neural Engineering Framework, tend to assume a linear superposition of post-synaptic currents. In this paper, we present a series of extensions to the Neural Engineering Framework that facilitate the construction of networks incorporating Dale's principle and nonlinear conductance-based synapses. We apply these extensions to a two-compartment LIF neuron that can be seen as a simple model of passive dendritic computation. We show that it is possible to incorporate neuron models with input-dependent nonlinearities into the Neural Engineering Framework without compromising high-level function and that nonlinear post-synaptic currents can be systematically exploited to compute a wide variety of multivariate, bandlimited functions, including the Euclidean norm, controlled shunting, and non-negative multiplication. By avoiding an additional source of spike noise, the function-approximation accuracy of a single layer of two-compartment LIF neurons is on a par with or even surpasses that of two-layer spiking neural networks up to a certain target function bandwidth.