激励函数的目的是为了调节权重和误差。
relu
max(0，x)
relu6
min(max(0，x)，6)
sigmoid
1/(1+exp(-x))
tanh
((exp(x)-exp(-x))/(exp(x)+exp(-x))
双曲正切函数的值域是(-1,1)
softsign
x/(abs(x)+1)
softplus
log(exp(x)+1)
elu
(exp(x)+1)if x<0 else x
import math
import numpy as np
import pandas as pd
import matplotlib.pyplot as plt
x = np.linspace(-10, 10, 500)
relu = list(map(lambda m: max(0, m), x))
relu6 = list(map(lambda m: min(max(0, m), 6), x))
sigmoid = 1 / (np.exp(-x) + 1)
tanh = (np.exp(x) - np.exp(-x)) / (np.exp(x) + np.exp(-x))
softsign = x / (np.abs(x) + 1)
softplus = np.log(np.exp(x) + 1)
elu = list(map(lambda m: math.exp(m) + 1 if m < 0 else m, x))
data = {
‘relu‘: relu,
‘relu6‘: relu6,
‘sigmoid‘: sigmoid,
‘tanh‘: tanh,
‘softsign‘: softsign,
‘softplus‘: softplus,
‘elu‘: elu
}
df = pd.DataFrame(data, index=x)
# print(df)
df[["relu", "relu6"]].plot(
kind="line", grid=True,
style={"relu": "y-", "relu6": "r:"},
yticks=np.linspace(-1, 8, 10),
xlim=[-10, 10], ylim=[-1, 8])
df[["softplus", "elu"]].plot(
kind="line", grid=True,
style={"softplus": "y-", "elu": "m:"},
yticks=np.linspace(-1, 8, 10),
xlim=[-10, 10], ylim=[-1, 8])
df[["sigmoid", "tanh", "softsign"]].plot(
kind="line", grid=True,
yticks=np.linspace(-1.5, 1.5, 7),
xlim=[-10, 10], ylim=[-1.5, 1.5])
plt.show()
