【python实现卷积神经网络】激活函数的实现（sigmoid、softmax、tanh、relu、leakyrelu、elu、selu、softplus）

代码来源：https://github.com/eriklindernoren/ML-From-Scratch

卷积神经网络中卷积层Conv2D（带stride、padding）的具体实现：https://www.cnblogs.com/xiximayou/p/12706576.html

激活函数并没有多少要说的，根据公式定义好就行了，需要注意的是梯度公式的计算。

import numpy as np

# Collection of activation functions
# Reference: https://en.wikipedia.org/wiki/Activation_function

class Sigmoid():
    def __call__(self, x):
        return 1 / (1 + np.exp(-x))

    def gradient(self, x):
        return self.__call__(x) * (1 - self.__call__(x))

class Softmax():
    def __call__(self, x):
        e_x = np.exp(x - np.max(x, axis=-1, keepdims=True))
        return e_x / np.sum(e_x, axis=-1, keepdims=True)

    def gradient(self, x):
        p = self.__call__(x)
        return p * (1 - p)

class TanH():
    def __call__(self, x):
        return 2 / (1 + np.exp(-2*x)) - 1

    def gradient(self, x):
        return 1 - np.power(self.__call__(x), 2)

class ReLU():
    def __call__(self, x):
        return np.where(x >= 0, x, 0)

    def gradient(self, x):
        return np.where(x >= 0, 1, 0)

class LeakyReLU():
    def __init__(self, alpha=0.2):
        self.alpha = alpha

    def __call__(self, x):
        return np.where(x >= 0, x, self.alpha * x)

    def gradient(self, x):
        return np.where(x >= 0, 1, self.alpha)

class ELU():
    def __init__(self, alpha=0.1):
        self.alpha = alpha 

    def __call__(self, x):
        return np.where(x >= 0.0, x, self.alpha * (np.exp(x) - 1))

    def gradient(self, x):
        return np.where(x >= 0.0, 1, self.__call__(x) + self.alpha)

class SELU():
    # Reference : https://arxiv.org/abs/1706.02515,
    # https://github.com/bioinf-jku/SNNs/blob/master/SelfNormalizingNetworks_MLP_MNIST.ipynb
    def __init__(self):
        self.alpha = 1.6732632423543772848170429916717
        self.scale = 1.0507009873554804934193349852946 

    def __call__(self, x):
        return self.scale * np.where(x >= 0.0, x, self.alpha*(np.exp(x)-1))

    def gradient(self, x):
        return self.scale * np.where(x >= 0.0, 1, self.alpha * np.exp(x))

class SoftPlus():
    def __call__(self, x):
        return np.log(1 + np.exp(x))

    def gradient(self, x):
        return 1 / (1 + np.exp(-x))