Controlled accuracy approximation of sigmoid function for efficient FPGA-based implementation of artificial neurons

A controlled accuracy approximation scheme of the sigmoid function for artificial neuron implementation based on Taylor´s theorem and the Lagrange form of the error is proposed. The main advantages of the proposed solution are two: it provides a systematic way to guarantee the required accuracy and it reuses the circuitry of the linear part of the neuron to compute the sigmoid function. The sigmoid derivative is also available for artificial neural networks with online learning capabilities.