深度学习卷积神经网络中常见的激活函数图像绘制python

论文专用：各个种类的激活函数的图像绘制

import numpy as np
import matplotlib.pyplot as plt


def Sigmoid(x):
    y = 1 / (1 + np.exp(-x))
    y = np.sum(y)
    print(y)

    # 画图
    xx = np.arange(-10, 10, 0.1)
    yy = 1 / (1 + np.exp(-xx))
    dy = 1 / (1 + np.exp(-xx)) * (1 - 1 / (1 + np.exp(-xx)))

    plt.plot(xx, yy, label='Sigmoid')
    plt.plot(xx, dy, label="Sigmoid'")
    plt.xlabel("x")
    plt.ylabel("f(x)")
    plt.legend()
    plt.show()


def Tanh(x):
    y = (np.exp(x) - np.exp(-x)) / (np.exp(x) + np.exp(-x))
    y = np.sum(y)
    print(y)

    # 画图
    xx = np.arange(-10, 10, 0.1)
    yy = (np.exp(xx) - np.exp(-xx)) / (np.exp(xx) + np.exp(-xx))
    dy = 1 - ((np.exp(xx) - np.exp(-xx)) / (np.exp(xx) + np.exp(-xx))) ** 2

    plt.plot(xx, yy, label="Tanh")
    plt.plot(xx, dy, label="Tanh'")
    plt.xlabel("x")
    plt.ylabel("y")
    plt.legend()
    plt.show()


def ReLU(x):
    y = np.sum(x[x > 0])
    print(y)

    # 画图
    xx = np.arange(-10, 10, 0.1)
    yy = np.where(xx > 0, xx, 0)
    dy = np.where(xx > 0, 1, 0)

    plt.plot(xx, yy ,label="ReLU")
    plt.plot(xx, dy ,label="ReLU'")
    plt.xlabel("x")
    plt.ylabel("f(x)")
    plt.legend()
    plt.show()


def Leaky_ReLU(x):
    y = np.where(x > 0, x, 0.01 * x)
    y = np.sum(y)
    print(y)

    # 画图
    xx = np.arange(-10, 10, 0.1)
    yy = np.where(xx > 0, xx, 0.01 * xx)
    dy = np.where(xx > 0, 1, 0.01)

    plt.plot(xx, yy, label="Leaky_ReLU")
    plt.plot(xx, dy, label="Leaky_ReLU'")
    plt.xlabel("x")
    plt.ylabel("y")
    plt.legend()
    plt.show()


def SiLU(x):
    y = x * (1 / (1 + np.exp(-x)))
    y = np.sum(y)

    # 画图
    xx = np.arange(-10, 10, 0.1)
    yy = xx * (1 / (1 + np.exp(-xx)))
    dy = 1 / (1 + np.exp(-xx)) * (1 + xx * (1 - 1 / (1 + np.exp(-xx))))

    plt.plot(xx, yy, label="SiLU")
    plt.plot(xx, dy, label="SiLU'")
    plt.xlabel("x")
    plt.ylabel("f(x)")
    plt.legend()
    plt.show()

    # ReLU 对比
    # ReLU_y = np.where(xx > 0, xx, 0)
    # plt.plot(xx, yy, label="SiLU")
    # plt.plot(xx, ReLU_y, label="ReLU")
    # plt.xlabel("x")
    # plt.ylabel("y")
    # plt.legend()
    # plt.show()
    #
    # # Sigmoid 对比  SiLU导数和Sigmoid激活函数
    # Sigmoid_dy = 1 / (1 + np.exp(-xx))
    # plt.plot(xx, dy, label="SiLU'")
    # plt.plot(xx, Sigmoid_dy, label="Sigmoid'")
    # plt.xlabel("x")
    # plt.ylabel("y")
    # plt.legend()
    # plt.show()


def tanh(x):
    return (np.exp(x) - np.exp(-x)) / (np.exp(x) + np.exp(-x))


def softplus(x):
    return np.log(1 + np.exp(x))


def Mish(x):
    y = x * tanh(softplus(x))
    y = np.sum(y)
    print(y)

    # 画图
    xx = np.arange(-10, 10, 0.1)
    yy = xx * tanh(softplus(xx))

    Omega = 4 * (xx + 1) + 4 * np.exp(2 * xx) + np.exp(3 * xx) + (4 * xx + 6) * np.exp(xx)
    Delta = 2 * np.exp(xx) + np.exp(2 * xx) + 2
    dy = (np.exp(xx) * Omega) / Delta ** 2

    plt.plot(xx, yy, label="Mish")
    plt.plot(xx, dy, label="Mish'")
    plt.xlabel("x")
    plt.ylabel("y")
    plt.legend()
    plt.show()



if __name__ == "__main__":
    x = np.random.randn(10)
    print(x)
    Sigmoid(x)
    Tanh(x)
    ReLU(x)
    Leaky_ReLU(x)
    SiLU(x)
    Mish(x)