Integer Quadratic Integrate-and-Fire (IQIF): A Neuron Model for Digital Neuromorphic Systems

Simulation of a spiking neural network involves solving a large number of differential equations. This is a challenge even for modern computer systems, especially when simulating large-scale neural networks. To address this challenge, we design a neuron model: the Integer Quadratic Integrate-and-Fire (IQIF) neuron. Instead of computing on floating point numbers, as is typical with other spiking neuron models, the IQIF model is computed purely on integers. The IQIF model is a quantized and linearized version of the classic quadratic integrate-and-fire (QIF) model. The IQIF model retains all dynamic characteristics of the QIF model with much lower computation complexity, at the cost of a limited dynamic range of the membrane potential and the synaptic current. We compare IQIF to other spiking neuron models based on their simulation speeds and the number of neuronal behaviors they can perform. We further compare the performance of IQIF with the leaky integrate-and-fire model in a classical decision-making network that exhibits nonlinear attractor dynamics. Our results show that the IQIF neurons are capable of performing computation that other spiking neuron models can do while having the advantages of speed. Moreover, the IQIF model is digital hardware friendly due to its pure integer operation and is therefore easily to be implemented in custom-built neuromorphic systems.