TensorFlow MLP不訓練XOR

Question

我已經用Google的TensorFlow庫構建了MLP。網絡正在工作，但不知何故它拒絕正確學習。無論輸入的是什麼，它總是收斂到接近1.0的輸出。

完整代碼可以看到here。

任何想法？

---

的輸入和輸出（批次大小4）如下：

input_data = [[0., 0.], [0., 1.], [1., 0.], [1., 1.]] # XOR input 
output_data = [[0.], [1.], [1.], [0.]] # XOR output 

n_input = tf.placeholder(tf.float32, shape=[None, 2], name="n_input") 
n_output = tf.placeholder(tf.float32, shape=[None, 1], name="n_output") 

---

隱藏層配置：

# hidden layer's bias neuron 
b_hidden = tf.Variable(0.1, name="hidden_bias") 

# hidden layer's weight matrix initialized with a uniform distribution 
W_hidden = tf.Variable(tf.random_uniform([2, hidden_nodes], -1.0, 1.0), name="hidden_weights") 

# calc hidden layer's activation 
hidden = tf.sigmoid(tf.matmul(n_input, W_hidden) + b_hidden) 

---

輸出層配置：

W_output = tf.Variable(tf.random_uniform([hidden_nodes, 1], -1.0, 1.0), name="output_weights") # output layer's weight matrix 
output = tf.sigmoid(tf.matmul(hidden, W_output)) # calc output layer's activation 

---

我學習方法是這樣的：

loss = tf.reduce_mean(cross_entropy) # mean the cross_entropy 
optimizer = tf.train.GradientDescentOptimizer(0.01) # take a gradient descent for optimizing 
train = optimizer.minimize(loss) # let the optimizer train 

我都嘗試設置爲交叉熵：

cross_entropy = -tf.reduce_sum(n_output * tf.log(output)) 

和

cross_entropy = tf.nn.sigmoid_cross_entropy_with_logits(n_output, output) 

其中n_output是如在我的網絡output_data和output預測/計算值描述的原始輸出。

---

的培訓內部的for循環（n個時期）是這樣的：

cvalues = sess.run([train, loss, W_hidden, b_hidden, W_output], 
        feed_dict={n_input: input_data, n_output: output_data}) 

我節省了成果cvalues爲loss，W_hidden調試printig，...

---

無論我嘗試過什麼，當我測試我的網絡時，試圖驗證輸出，它總是產生一些東西E本：

(...) 
step: 2000 
loss: 0.0137040186673 
b_hidden: 1.3272010088 
W_hidden: [[ 0.23195425 0.53248233 -0.21644847 -0.54775208 0.52298909] 
[ 0.73933059 0.51440752 -0.08397482 -0.62724304 -0.53347367]] 
W_output: [[ 1.65939867] 
[ 0.78912479] 
[ 1.4831928 ] 
[ 1.28612828] 
[ 1.12486529]] 

(--- finished with 2000 epochs ---) 

(Test input for validation:) 

input: [0.0, 0.0] | output: [[ 0.99339396]] 
input: [0.0, 1.0] | output: [[ 0.99289012]] 
input: [1.0, 0.0] | output: [[ 0.99346077]] 
input: [1.0, 1.0] | output: [[ 0.99261558]] 

所以不是學習方法不當，但總是收斂到接近1.0無論哪個輸入饋。

Answer 1

與此同時，在一位同事的幫助下，我能夠解決我的解決方案，並希望將其完整發布。我的解決方案工作與交叉熵和而不改變訓練數據。此外，它具有所需的輸入形狀（1,2）和輸出是標量。

它利用一個AdamOptimizer從而降低了錯誤比GradientDescentOptimizer多快。有關優化器的更多信息，請參閱this post（&問題^^）。

事實上，我的網絡在400-800個學習步驟中產生了相當好的結果。

2000學習步驟後的輸出幾乎是 「完美」：

step: 2000 
loss: 0.00103311243281 

input: [0.0, 0.0] | output: [[ 0.00019799]] 
input: [0.0, 1.0] | output: [[ 0.99979786]] 
input: [1.0, 0.0] | output: [[ 0.99996307]] 
input: [1.0, 1.0] | output: [[ 0.00033751]] 

---

import tensorflow as tf  

##################### 
# preparation stuff # 
##################### 

# define input and output data 
input_data = [[0., 0.], [0., 1.], [1., 0.], [1., 1.]] # XOR input 
output_data = [[0.], [1.], [1.], [0.]] # XOR output 

# create a placeholder for the input 
# None indicates a variable batch size for the input 
# one input's dimension is [1, 2] and output's [1, 1] 
n_input = tf.placeholder(tf.float32, shape=[None, 2], name="n_input") 
n_output = tf.placeholder(tf.float32, shape=[None, 1], name="n_output") 

# number of neurons in the hidden layer 
hidden_nodes = 5 


################ 
# hidden layer # 
################ 

# hidden layer's bias neuron 
b_hidden = tf.Variable(tf.random_normal([hidden_nodes]), name="hidden_bias") 

# hidden layer's weight matrix initialized with a uniform distribution 
W_hidden = tf.Variable(tf.random_normal([2, hidden_nodes]), name="hidden_weights") 

# calc hidden layer's activation 
hidden = tf.sigmoid(tf.matmul(n_input, W_hidden) + b_hidden) 


################ 
# output layer # 
################ 

W_output = tf.Variable(tf.random_normal([hidden_nodes, 1]), name="output_weights") # output layer's weight matrix 
output = tf.sigmoid(tf.matmul(hidden, W_output)) # calc output layer's activation 


############ 
# learning # 
############ 
cross_entropy = -(n_output * tf.log(output) + (1 - n_output) * tf.log(1 - output)) 
# cross_entropy = tf.square(n_output - output) # simpler, but also works 

loss = tf.reduce_mean(cross_entropy) # mean the cross_entropy 
optimizer = tf.train.AdamOptimizer(0.01) # take a gradient descent for optimizing with a "stepsize" of 0.1 
train = optimizer.minimize(loss) # let the optimizer train 


#################### 
# initialize graph # 
#################### 
init = tf.initialize_all_variables() 

sess = tf.Session() # create the session and therefore the graph 
sess.run(init) # initialize all variables 

##################### 
# train the network # 
##################### 
for epoch in xrange(0, 2001): 
    # run the training operation 
    cvalues = sess.run([train, loss, W_hidden, b_hidden, W_output], 
         feed_dict={n_input: input_data, n_output: output_data}) 

    # print some debug stuff 
    if epoch % 200 == 0: 
     print("") 
     print("step: {:>3}".format(epoch)) 
     print("loss: {}".format(cvalues[1])) 
     # print("b_hidden: {}".format(cvalues[3])) 
     # print("W_hidden: {}".format(cvalues[2])) 
     # print("W_output: {}".format(cvalues[4])) 


print("") 
print("input: {} | output: {}".format(input_data[0], sess.run(output, feed_dict={n_input: [input_data[0]]}))) 
print("input: {} | output: {}".format(input_data[1], sess.run(output, feed_dict={n_input: [input_data[1]]}))) 
print("input: {} | output: {}".format(input_data[2], sess.run(output, feed_dict={n_input: [input_data[2]]}))) 
print("input: {} | output: {}".format(input_data[3], sess.run(output, feed_dict={n_input: [input_data[3]]}))) 

Answer 2

我不能評論，因爲我沒有足夠的聲譽，但我有一些關於答案mrry的問題。 $ L_2 $損失函數是有道理的，因爲它基本上是MSE函數，但爲什麼不會交叉熵工作？當然可以用於其他NN庫。其次，爲什麼在世界上將您的輸入空間從$ [0,1] - > [-1,1] $轉換爲，尤其是，因爲您添加了偏向量。

EDIT這是使用交叉熵和一個熱從多個源編譯 EDIT^2改變了代碼中使用交叉熵沒有任何額外的編碼或任何奇怪的目標值的溶液移

import math 
import tensorflow as tf 
import numpy as np 

HIDDEN_NODES = 10 

x = tf.placeholder(tf.float32, [None, 2]) 
W_hidden = tf.Variable(tf.truncated_normal([2, HIDDEN_NODES])) 
b_hidden = tf.Variable(tf.zeros([HIDDEN_NODES])) 
hidden = tf.nn.relu(tf.matmul(x, W_hidden) + b_hidden) 

W_logits = tf.Variable(tf.truncated_normal([HIDDEN_NODES, 1])) 
b_logits = tf.Variable(tf.zeros([1])) 
logits = tf.add(tf.matmul(hidden, W_logits),b_logits) 


y = tf.nn.sigmoid(logits) 


y_input = tf.placeholder(tf.float32, [None, 1]) 



loss = -(y_input * tf.log(y) + (1 - y_input) * tf.log(1 - y)) 

train_op = tf.train.GradientDescentOptimizer(0.01).minimize(loss) 

init_op = tf.initialize_all_variables() 

sess = tf.Session() 
sess.run(init_op) 

xTrain = np.array([[0, 0], [0, 1], [1, 0], [1, 1]]) 


yTrain = np.array([[0], [1], [1], [0]]) 


for i in xrange(2000): 
    _, loss_val,logitsval = sess.run([train_op, loss,logits], feed_dict={x: xTrain, y_input: yTrain}) 

    if i % 10 == 0: 
    print "Step:", i, "Current loss:", loss_val,"logits",logitsval 

print "---------" 
print sess.run(y,feed_dict={x: xTrain})