torch.erf()/gelu()/误差函数科普

• erf() in Pytorch
  torch.erf(tensor, out=None)
  Computes the error function of each element. The error function is defined as follows:$$erf(x)=\frac{2}{\pi }{\int }_0^x{e}^{-t^2}dt$$
• What is error function?
  Error function (also called the Gauss error function) is a special function (non-elementary) of sigmoid shape that occurs in probility, statistics, and partial differential equations describing diffusion.
• Look at the picture:

import numpy as np 
from scipy import integrate
import matplotlib.pyplot as plt 
x = np.linspace(-5,5,100)
erf = []
sigmoid = []
for x_ in x:
    erf.append( integrate.quad(lambda t:np.exp(-t**2),-x_,x_) / np.sqrt(np.pi))
plt.plot(erf)
plt.grid(True)
plt.show()

阅读：https://www.cnblogs.com/htj10/p/8621771.html