Implementing spiking neuron model and spike-timing-dependent plasticity with generalized Laguerre-Volterra models

To perform large-scale simulations of the brain or build biologically-inspired cognitive architectures, it is essential to have a succinct and flexible model of spiking neurons. The model should be able to capture the nonlinear dynamical properties of various types of neurons and the nonstationary properties such as the spike-timing-dependent plasticity (STDP). In this paper, we propose a generalized Laguerre-Volterra modeling approach for such a task. Due to its built-in nonlinear dynamical terms, the generalized Laguerre-Volterra model (GLVM) can capture various biological processes/mechanisms. Using Laguerre expansion of Volterra kernel technique, the model is fully represented with a small set of coefficients. The calculation of the model variables can be expressed recursively based on only the current and the one-step-before values and thus can be performed efficiently. In addition, we show that, using the same methodology, STDP can be implemented as a specific form of second-order Volterra kernel describing the causal relationship between pairs of input-output spikes and the changes of the feedforward kernels in the GLVMs.