TensorFlow MLP没有训练异或

Question

我用谷歌的TensorFlow库建立了一个MLP .网络正在运行但不知何故它拒绝正确学习.无论输入实际是什么,它总是收敛到接近1.0的输出.

将完整的代码可以看出这里.

有任何想法吗？

---

的输入和输出(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")

---

隐藏层配置:

# 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)

---

输出层配置:

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

---

我的学习方法如下:

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

我尝试了两种交叉熵设置:

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描述的原始输出output_data和output我的网络的预测/计算值.

---

for循环中的训练(对于n个时期)如下:

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

我节省了成果cvalues用于调试printig loss,W_hidden...

---

无论我尝试过什么,当我测试我的网络,尝试验证输出时,它总是产生这样的东西:

(...)
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]]

所以它无法正常学习,但无论输入哪个输入,总是收敛到接近1.0.

Answer 1

与此同时,在同事的帮助下,我能够修复我的解决方案,并希望将其发布为完整性.我的解决方案适用于交叉熵,无需更改训练数据.此外,它具有所需的输入形状(1,2),输出是标量.

它利用了AdamOptimizer其减小误差远小于更快GradientDescentOptimizer.有关优化程序的更多信息(和问题^^),请参阅此文章.

事实上,我的网络仅在400-800个学习步骤中产生了相当不错的结果.

在2000个学习步骤之后,输出几乎是"完美的":

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]]})))