同或门(XNOR)电路的网络学习

主要内容，参考http://www.analyticsvidhya.com/blog/2016/04/neural-networks-python-theano/

本文使用Theano实现XNOR功能。对tensor的变量定义、自动求导，以及theano.function做一个简单学习。具体如下：

XNOR函数的网络表达：



真值表：



编程实现：

import theano
import theano.tensor as T
import numpy as np
import matplotlib.pyplot as plt

if __name__ == '__main__':
#Define variables:
x = T.matrix('x')
w1 = theano.shared(np.random.rand(2,2)) # weight for layer1
w2 = theano.shared(np.random.rand(2))
b = theano.shared(np.ones(2)) # bias
learning_rate = 1.;

#Step2:Define mathematical expression
a1 = 1/(1+T.exp(-T.dot(x,w1)-b[0]))
a = 1/(1+T.exp(-T.dot(a1,w2)-b[1])) # predict output

#Step3:Define gradient and update rule
y = T.vector('y') #Actual output
cost = -(y*T.log(a) + (1-y)*T.log(1-a)).sum()
dw1,dw2,db = T.grad(cost,[w1,w2,b])

train = theano.function(
inputs = [x,y],
outputs = [a,cost],
updates = [
[w1, w1-learning_rate*dw1],
[w2, w2-learning_rate*dw2],
[b, b-learning_rate*db]
]
)

inputs = [
[0, 0],
[0, 1],
[1, 0],
[1, 1]
]
outputs = [1,0,0,1]

#Iterate through all inputs and find outputs:
cost = []
for iteration in range(1000):
pred, cost_iter = train(inputs, outputs)
cost.append(cost_iter)

#Print the outputs:
print 'The outputs of the NN are:'
for i in range(len(inputs)):
print 'The output for x1=%d | x2=%d is %.2f' % (inputs[i][0],inputs[i][1],pred[i])

#Plot the flow of cost:
print '\nThe flow of cost during model run is as following:'
plt.plot(cost)

实验结果：

The outputs of the NN are:

The output for x1=0 | x2=0 is 1.00

The output for x1=0 | x2=1 is 0.00

The output for x1=1 | x2=0 is 0.00

The output for x1=1 | x2=1 is 1.00

The flow of cost during model run is as following: