A Novel Nonlinear Function Evaluation Approach for Efficient FPGA Mapping of Neuron and Synaptic Plasticity Models

Efficient hardware realization of spiking neural networks is of great significance in a wide variety of applications, such as high-speed modeling and simulation of large-scale neural systems. Exploiting the key features of FPGAs, this paper presents a novel nonlinear function evaluation approach, based on an effective uniform piecewise linear segmentation method, to efficiently approximate the nonlinear terms of neuron and synaptic plasticity models targeting low-cost digital implementation. The proposed approach takes advantage of a high-speed and extremely simple segment address encoder unit regardless of the number of segments, and therefore is capable of accurately approximating a given nonlinear function with a large number of straight lines. In addition, this approach can be efficiently mapped into FPGAs with minimal hardware cost. To investigate the application of the proposed nonlinear function evaluation approach in low-cost neuromorphic circuit design, it is applied to four case studies: the Izhikevich and FitzHugh-Nagumo neuron models as 2-dimensional case studies, the Hindmarsh-Rose neuron model as a relatively complex 3-dimensional model containing two nonlinear terms, and a calcium-based synaptic plasticity model capable of producing various STDP curves. Simulation and FPGA synthesis results demonstrate that the hardware proposed for each case study is capable of producing various responses remarkably similar to the original model and significantly outperforms the previously published counterparts in terms of resource utilization and maximum clock frequency.