Centre for Theoretical Neuroscience, University of Waterloo, Waterloo, Ontario, N2L 3G1, Canada
Neural Comput. 2021 Jan;33(1):96-128. doi: 10.1162/neco_a_01338. Epub 2020 Oct 20.
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 postsynaptic currents. In this letter, 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 postsynaptic currents can be systematically exploited to compute a wide variety of multivariate, band-limited functions, including the Euclidean norm, controlled shunting, and nonnegative 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.
树突中的非线性相互作用在神经计算中起着关键作用。然而，旨在构建大规模、功能齐全的尖峰神经网络的建模框架，如神经工程框架，往往假设突触后电流的线性叠加。在这封信中，我们提出了一系列对神经工程框架的扩展，以方便构建包含戴尔原则和基于非线性电导的突触的网络。我们将这些扩展应用于一个两室 LIF 神经元，它可以被视为被动树突计算的简单模型。我们表明，可以将具有输入相关非线性的神经元模型纳入神经工程框架中，而不会影响高级功能，并且可以系统地利用非线性突触后电流来计算各种多元、带限函数，包括欧几里得范数、控制分流和非负乘法。通过避免额外的尖峰噪声源，两层 LIF 神经元的单层函数逼近精度与一定目标函数带宽内的两层尖峰神经网络的精度相当，甚至超过。
