多层神经网络实现（异或）问题

import numpy as np
import tensorflow as tf
import matplotlib.pyplot as plt
import warnings
warnings.filterwarnings(‘ignore’)
tf.set_random_seed(777)
xdata = [[0, 0], [0, 1], [1, 0], [1, 1]]
ydata = [[0], [1], [1], [0]]

占位符

x = tf.placeholder(tf.float32, [None, 2])
y = tf.placeholder(tf.float32, [None, 1])

前向传播

w1 = tf.Variable(tf.random_normal([2, 5]), name=‘w1’)
b1 = tf.Variable(tf.random_normal([5]), name=‘b1’)
w2 = tf.Variable(tf.random_normal([5, 1]), name=‘w2’)
b2 = tf.Variable(tf.random_normal([1]), name=‘b2’)

z1 = tf.matmul(x, w1)+b1
a1 = tf.tanh(z1)
z2 = tf.matmul(a1, w2)+b2
a2 = tf.sigmoid(z2)

代价函数

cost = -tf.reduce_mean(y*tf.log(a2)+(1-y)*tf.log(1-a2))

反向传播

dz2 = a2-y
dw2 = tf.matmul(tf.transpose(a1), dz2)/tf.cast(tf.shape(x)[0], tf.float32)
db2 = tf.reduce_mean(dz2, axis=0)
da1 = tf.matmul(dz2, tf.transpose(w2))
dz1 = da1*(1-a1*a1)
dw1 = tf.matmul(tf.transpose(x), dz1)/tf.cast(tf.shape(x)[0], tf.float32)
db1 = tf.reduce_mean(dz1, axis=0)

alpha = 0.1
update = [
tf.assign(w1, w1-alphadw1),
tf.assign(b1, b1-alphadb1),
tf.assign(w2, w2-alphadw2),
tf.assign(b2, b2-alphadb2)
]

执行会话

sess = tf.Session()
sess.run(tf.global_variables_initializer())
his = []
for i in range(10001):
cost_var, _ = sess.run([cost, update], feed_dict={x:xdata, y:ydata})
if i%200==0:
print(i, cost_var)
his.append(cost_var)
import matplotlib.pyplot as plt
plt.plot(his[1:])
plt.show()

预测值

a = sess.run(a2, feed_dict={x:xdata})
print(a)