def sigmoid_cross_entropy_with_logits(_sentinel=None, # pylint: disable=invalid-name,labels=None, logits=None,name=None):
import numpy as np
import tensorflow as tf
input_data = tf.Variable(np.random.rand(1, 3), dtype=tf.float32)
# np.random.rand()传入一个shape,返回一个在[0,1)区间符合均匀分布的array
output = tf.nn.sigmoid_cross_entropy_with_logits(logits=input_data, labels=[[1.0, 0.0, 0.0]])
with tf.Session() as sess:
init = tf.global_variables_initializer()
sess.run(init)
print(sess.run(output))
# [[ 0.5583781 1.06925142 1.08170223]]
输入
设x = logits
, z = labels
.
z * -log(sigmoid(x)) + (1 - z) * -log(1 - sigmoid(x))
= z * -log(1 / (1 + exp(-x))) + (1 - z) * -log(exp(-x) / (1 + exp(-x)))
= z * log(1 + exp(-x)) + (1 - z) * (-log(exp(-x)) + log(1 + exp(-x)))
= z * log(1 + exp(-x)) + (1 - z) * (x + log(1 + exp(-x))
= (1 - z) * x + log(1 + exp(-x))
= x - x * z + log(1 + exp(-x))
对于x<0时,为了避免计算exp(-x)时溢出,我们使用以下这种形式表示
x - x * z + log(1 + exp(-x))
= log(exp(x)) - x * z + log(1 + exp(-x))
= - x * z + log(1 + exp(x))
综合x>0和x<0的情况,我们使用以下函数式
注意logits和labels必须具有相同的type和shape