TensorFlow训练神经网络cost一直为0

问题描述

这几天在用TensorFlow搭建一个神经网络来做一个binary classifier，搭建一个典型的神经网络的基本思路是：

• 定义神经网络的layers(层)以及初始化每一层的参数
• 然后迭代：
  • 前向传播（Forward propagation）
  • 计算cost（Compute cost）
  • 反向传播（Backward propagation）
  • 更新参数（Update parameters）
• 使用训练好的参数去做预测

在训练的时候发现了一个很奇怪的现象：每一次迭代所有的cost都为0。一开始以为是参数初始化出了问题，花了好多时间在上面。后来仔细研究了一下发现是最后一层的输出函数用错了，我用的是tf.nn.softmax_cross_entropy_with_logits来计算cost。 我们知道softmax一般是用来做multiclass classifier的，也就是输出的类别要大于两个。对于一个binary classifier而言，很明显我们要用sigmoid函数也就是tf.nn.sigmoid_cross_entropy_with_logits来计算cost，于是问题解决。

为什么？

那么为什么在binary classifier中使用了softmax之后cost就一直是0呢？我们先来看一下softmax的公式：

$$\mathrm{s(z)j=ezj\sum Kk=1ezks(z)j=ezj\sum k=1Kezk}$$

• binary classifier的output是一维的（one-dimension 0/1），那么如果只有一个元素，那么s(z)就永远等于1，不管z的值是多少。
• 恒定输出1之后，我们结合交叉熵的计算公式可知：
  • 如果true label是0，那么 -0*log(1) = 0
  • 如果true label是1，那么 -1*log(1) = 0

Tensorflow函数：tf.nn.softmax_cross_entropy_with_logits 讲解

 

首先把Tensorflow英文API搬过来：

tf.nn.softmax_cross_entropy_with_logits(_sentinel=None, labels=None, logits=None, dim=-1, name=None)

Computes softmax cross entropy between logits and labels.

Measures the probability error in discrete classification tasks in which the classes are mutually exclusive (each entry is in exactly one class). For example, each CIFAR-10 image is labeled with one and only one label: an image can be a dog or a truck, but not both.

NOTE: While the classes are mutually exclusive, their probabilities need not be. All that is required is that each row oflabels is a valid probability distribution. If they are not, the computation of the gradient will be incorrect.

If using exclusive labels (wherein one and only one class is true at a time), seesparse_softmax_cross_entropy_with_logits.

WARNING: This op expects unscaled logits, since it performs a softmax on logits internally for efficiency. Do not call this op with the output of softmax, as it will produce incorrect results.

logits and labels must have the same shape [batch_size, num_classes] and the same dtype (either float16,float32, or float64).

Note that to avoid confusion, it is required to pass only named arguments to this function.

Args:

• _sentinel: Used to prevent positional parameters. Internal, do not use.
• labels: Each row labels[i] must be a valid probability distribution.
• logits: Unscaled log probabilities.
• dim: The class dimension. Defaulted to -1 which is the last dimension.
• name: A name for the operation (optional).

这个函数至少需要两个参数:labels, logits.

labels：为神经网络期望的输出

logits：为神经网络最后一层的输出

警告：这个函数内部自动计算softmax，然后再计算交叉熵代价函数，也就是说logits必须是没有经过tf.nn.softmax函数处理的数据，否则导致训练结果有问题。建议编程序时使用这个函数，而不必自己编写交叉熵代价函数。

下面是两层CNN识别mnist的softmax回归实验:

#coding=utf-8
import tensorflow as tf
from tensorflow.examples.tutorials.mnist import input_data
mnist = input_data.read_data_sets("MNIST_data/", one_hot=True)

def compute_accuracy(v_xs,v_ys):
    global prediction
    y_pre=sess.run(prediction,feed_dict={xs:v_xs,keep_prob:1}) #这里的keep_prob是保留概率，即我们要保留的RELU的结果所占比例
    correct_prediction=tf.equal(tf.argmax(y_pre,1),tf.argmax(v_ys,1))
    accuracy=tf.reduce_mean(tf.cast(correct_prediction,tf.float32))
    result=sess.run(accuracy,feed_dict={xs:v_xs,ys:v_ys,keep_prob:1})
    return result

def weight_variable(shape):
    inital=tf.truncated_normal(shape,stddev=0.1)     #stddev爲標準差
    return tf.Variable(inital)

def bias_variable(shape):
    inital=tf.constant(0.1,shape=shape)
    return tf.Variable(inital)

def conv2d(x,W):    #x爲像素值，W爲權值
    #strides[1,x_movement,y_movement,1]
    #must have strides[0]=strides[3]=1
    #padding=????
    return tf.nn.conv2d(x,W,strides=[1,1,1,1],padding='SAME')#

def max_pool_2x2(x):
    # strides[1,x_movement,y_movement,1]
    return tf.nn.max_pool(x,ksize=[1,2,2,1],strides=[1,2,2,1],padding='SAME')#ksize二三维为池化窗口

#define placeholder for inputs to network
xs=tf.placeholder(tf.float32,[None,784])/255
ys=tf.placeholder(tf.float32,[None,10])
keep_prob=tf.placeholder(tf.float32)
x_image=tf.reshape(xs, [-1,28,28,1]) #-1为这个维度不确定,变成一个4维的矩阵，最后为最里面的维数
#print x_image.shape                 #最后这个1理解为输入的channel，因为为黑白色所以为1

##conv1 layer##
W_conv1=weight_variable([5,5,1,32]) #patch 5x5,in size 1 是image的厚度,outsize 32 是提取的特征的维数
b_conv1=bias_variable([32])
h_conv1=tf.nn.relu(conv2d(x_image,W_conv1)+b_conv1)# output size 28x28x32 因为padding='SAME'
h_pool1=max_pool_2x2(h_conv1)      #output size 14x14x32

##conv2 layer##
W_conv2=weight_variable([5,5,32,64]) #patch 5x5,in size 32 是conv1的厚度,outsize 64 是提取的特征的维数
b_conv2=bias_variable([64])
h_conv2=tf.nn.relu(conv2d(h_pool1,W_conv2)+b_conv2)# output size 14x14x64 因为padding='SAME'
h_pool2=max_pool_2x2(h_conv2)      #output size 7x7x64

##func1 layer##
W_fc1=weight_variable([7*7*64,1024])
b_fc1=bias_variable([1024])
#[n_samples,7,7,64]->>[n_samples,7*7*64]
h_pool2_flat=tf.reshape(h_pool2,[-1,7*7*64])
h_fc1=tf.nn.relu(tf.matmul(h_pool2_flat,W_fc1)+b_fc1)
h_fc1_drop=tf.nn.dropout(h_fc1,keep_prob)  #防止过拟合

##func2 layer##
W_fc2=weight_variable([1024,10])
b_fc2=bias_variable([10])
#prediction=tf.nn.softmax(tf.matmul(h_fc1_drop,W_fc2)+b_fc2)
prediction=tf.matmul(h_fc1_drop,W_fc2)+b_fc2

#h_fc1_drop=tf.nn.dropout(h_fc1,keep_prob)  #防止过拟合

#the errro between prediction and real data

#cross_entropy = tf.reduce_mean(-tf.reduce_sum(ys*tf.log(prediction),reduction_indices=[1]))

cross_entropy = tf.reduce_mean(tf.nn.softmax_cross_entropy_with_logits(labels=ys, logits=prediction)
train_step = tf.train.AdamOptimizer(1e-4).minimize(cross_entropy)
sess=tf.Session()
sess.run(tf.global_variables_initializer())

for i in range(1000):
    batch_xs,batch_ys=mnist.train.next_batch(100)
    sess.run(train_step,feed_dict={xs:batch_xs,ys:batch_ys,keep_prob:0.5})
    if i%50 ==0:
        accuracy = 0
        for j in range(10):
            test_batch = mnist.test.next_batch(1000)
            acc_forone=compute_accuracy(test_batch[0], test_batch[1])
            #print 'once=%f' %(acc_forone)
            accuracy=acc_forone+accuracy
        print '测试结果:batch:%g,准确率:%f' %(i,accuracy/10)

实验结果为：

测试结果:batch:0,准确率:0.090000
测试结果:batch:50,准确率:0.788600
测试结果:batch:100,准确率:0.880200
测试结果:batch:150,准确率:0.904600
测试结果:batch:200,准确率:0.927500
测试结果:batch:250,准确率:0.929800
测试结果:batch:300,准确率:0.939600
测试结果:batch:350,准确率:0.942100
测试结果:batch:400,准确率:0.950600
测试结果:batch:450,准确率:0.950700
测试结果:batch:500,准确率:0.956700
测试结果:batch:550,准确率:0.956000
测试结果:batch:600,准确率:0.957100
测试结果:batch:650,准确率:0.958400
测试结果:batch:700,准确率:0.961500
测试结果:batch:750,准确率:0.963800
测试结果:batch:800,准确率:0.965000
测试结果:batch:850,准确率:0.966300
测试结果:batch:900,准确率:0.967800
测试结果:batch:950,准确率:0.967700

迭代次数没有太多，否则准确率还会提高。