三层神经网络实现

数据都是随意给出，并没有实际意义。

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

#第零层到第一层

X = np.array([1.0,0.5])
W1 = np.array([[0.1,0.3,0.5],[0.2,0.4,0.6]])
B1 = np.array([0.1,0.2,0.3])

print(W1.shape)#(2,3)
print(X.shape)#(2,)
print(B1.shape)#(3,)

A1 = np.dot(X,W1) + B1
Z1 = sigmoid(A1)

print(A1)#(3,)
print(Z1)#(3,)

#第一层到第二层
W2 = np.array([[0.1,0.4],[0.2,0.5],[0.3,0.6]])
B2 = np.array([0.1,0.2])

print(Z1.shape)#(3,)
print(W2.shape)#(3,2)
print(B2.shape)#(2,)

A2 = np.dot(Z1,W2) + B2
Z2 = sigmoid(A2)
print(A2)#(2,)
print(Z2)#(2,)


#从第二层到输出层，信号传递

def identify_function(x):
    return x

W3 = np.array([[0.1,0.3],[0.2,0.4]])
B3 = np.array([0.1,0.2])

A3 = np.dot(Z2,W3) + B3
Y = identify_function(A3)
print(A3)
print(Y)
#这里定义了identify_function()函数（也称为恒等函数）并将其作为输出层的激活函数。

将上述代码整合：

import numpy as np
def sigmoid(x):
    return 1 / (1 + np.exp(-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 identify_function(x):
    return x


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 = identify_function(a3)
    return y

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

 init_network()进行权重和偏执的初始化，并将它们保存在字典network中。