An Optimization on the Neuronal Networks Based on the ADEX Biological Model in Terms of LUT-State Behaviors: Digital Design and Realization on FPGA Platforms

SIMPLE SUMMARY: The brain is an incredibly complex system possessing outstanding abilities to perform difficult tasks through a vast number of densely interconnected neurons. Aimed at discovering the underlying mechanisms of the brain, a number of spiking neural networks have been proposed to mimic biological neural dynamics. Subsequently, to perceive how the neural networks in the brain work, simulation and hardware realization of large-scale systems, similar to the brain, is an essential requirement. Behavior of a single neuron can be described by the mathematical equations in different levels of computing and biological accuracy. In this approach, a new modified ADEX model is presented based on sampling frequency by the nonlinear functions of the original model. This new model is capable for reproducing all aspects of the original model in low-error and high-degree of similarity conditions. Finally, the proposed model can be implemented on digital hardware platforms to have a real digital system. Digital results show the increase in system speed (frequency) and overall saving in hardware resources (compared by the original model and other similar works). This low-cost digital hardware is applied in large-scale neuronal networks. ABSTRACT: Design and implementation of biological neural networks is a vital research field in the neuromorphic engineering. This paper presents LUT-based modeling of the Adaptive Exponential integrate-and-fire (ADEX) model using Nyquist frequency method. In this approach, a continuous term is converted to a discrete term by sampling factor. This new modeling is called N-LUT-ADEX (Nyquist-Look Up Table-ADEX) and is based on accurate sampling of the original ADEX model. Since in this modeling, the high-accuracy matching is achieved, it can exactly reproduce the spiking patterns, which have the same behaviors of the original neuron model. To confirm the N-LUT-ADEX neuron, the proposed model is realized on Virtex-II Field-Programmable Gate Array (FPGA) board for validating the final hardware. Hardware implementation results show the high degree of similarity between the proposed and original models. Furthermore, low-cost and high-speed attributes of our proposed neuron model will be validated. Indeed, the proposed model is capable of reproducing the spiking patterns in terms of low overhead costs and higher frequencies in comparison with the original one. The properties of the proposed model cause can make it a suitable choice for neuromorphic network implementations with reduced-cost attributes.