A probability-based sigmoid function approximation (P-SFA), which is based on piecewise linear function and neuron's values statistical probability distribution in each layer, is proposed to lower the complexity of neural network hardware implementation with only addition circuit. The sigmoid function is divided into three fixed regions, and the number of sub-regions with different sizes in each fixed region is adapted to neuron's values distribution in each layer to reduce the error between the sigmoid function and P-SFA function. The experimental results on FPGA show that the P-SFA function is efficient in terms of power and speed, and the recognition accuracies in DNN and CNN for MNIST with P-SFA are the highest among the state-of-the-art methods, up to 97.46% and 99.02% respectively.

提出了一种基于分段线性函数和神经元值统计概率分布的基于概率的S形函数逼近（P-SFA），以降低仅需加法电路的神经网络硬件实现的复杂性。乙状结肠功能分为三个固定区域，每个固定区域中大小不同的子区域的数量与每一层神经元的值分布相适应，以减少乙状结肠功能与P-SFA函数之间的误差。在FPGA上的实验结果表明，P-SFA功能在功率和速度方面都是有效的，并且在最新技术中，DIST和CNN对带有P-SFA的MNIST的识别精度最高。分别为97.46％和99.02％。