深度学习入门 3 神经网络

深度学习入门 3 神经网络

• 3.2.3 阶跃函数的图形

import numpy as np
import matplotlib.pylab as plt


def step_function(x):
    return np.array(x > 0, dtype=np.int64)


x = np.arange(-5.0, 5.0, 0.1)
y = step_function(x)
plt.plot(x, y)
plt.ylim(-0.1, 1.1)  # 指定y轴的范围
plt.show()

• 3.2.4 sigmoid函数的实现

import numpy as np
import matplotlib.pylab as plt


def step_function(x):
    return np.array(x > 0, dtype=np.int64)


def sigmoid(x):
    return 1 / (1 + np.exp(-x))


x = np.arange(-5.0, 5.0, 0.1)
# y = step_function(x)
y = sigmoid(x)
plt.plot(x, y)
plt.ylim(-0.1, 1.1)  # 指定y轴的范围
plt.show()

• relu函数的简单实现

import matplotlib.pylab as plt


def step_function(x):
    return np.array(x > 0, dtype=np.int64)


def sigmoid(x):
    return 1 / (1 + np.exp(-x))


def relu(x):
    return np.maximum(0, x)


x = np.arange(-5.0, 5.0, 0.1)
# y = step_function(x)
# y = sigmoid(x)
y = relu(x)
# 绘图
plt.plot(x, y)
plt.ylim(-0.1, 1.1)  # 指定y轴的范围
plt.show()

• 简单神经网络实现小结

import numpy as np


def sigmoid(x):
    return 1 / (1 + np.exp(-x))


def identity_function(x):
    return x


def init_network():
    network = {}
    network['W1'] = np.array([[0.1, 0.3, 0.5], [0.2, 0.4, 0.6]])
    network['b1'] = np.array([0.1, 0.2, 0.3])
    network['W2'] = np.array([[0.1, 0.4], [0.2, 0.5], [0.3, 0.6]])
    network['b2'] = np.array([0.1, 0.2])
    network['W3'] = np.array([[0.1, 0.3], [0.2, 0.4]])
    network['b3'] = np.array([0.1, 0.2])
    return network


def forward(network, x):
    W1, W2, W3 = network['W1'], network['W2'], network['W3']
    b1, b2, b3 = network['b1'], network['b2'], network['b3']

    a1 = np.dot(x, W1) + b1
    z1 = sigmoid(a1)
    a2 = np.dot(z1, W2) + b2
    z2 = sigmoid(a2)
    a3 = np.dot(z2, W3) + b3
    y = identity_function(a3)

    return y


network = init_network()
x = np.array([1.0, 0.5])
y = forward(network, x)
print(y)    # [0.31682708 0.69627909]