Adaptation of a comprehensive simplification method to the Adaptive Exponential Integrate and Fire Neuron and Its FPGA-based verification

The preference of a comprehensive method usage is as important as less hardware usage on digital device-based implementations. The mathematical series expansions have a widespread usage in the transformation of expressions into simpler forms. The exponential, trigonometric, logarithmic, etc. functions are usually converted to simpler expressions for digital implementation easiness. In these implementations, it is an expected output that as the operands of the series increases, the revised model converges to the original one. However, the most appropriate number determination of these operands is important for hardware efficiency. In here, the exponential expression of the Adaptive Exponential Integrate and Fire (ADEX) neuron model is expanded up to the tenth operand of the Taylor series. Then, an optimum operand number is identified for getting both hardware utilization efficiency and neuronal meaningfulness. The differences between the original and revised models are compared with the error calculations and the neuronal observations. Lastly, the revised ADEX neuron model is realized by FPGA device to prove the efficiency of the proposed adaptation.