批量归一化batch_normalization

为了解决在深度神经网络训练初期降低梯度消失/爆炸问题，Sergey loffe和Christian Szegedy提出了使用批量归一化的技术的方案，该技术包括在每一层激活函数之前在模型里加一个操作，简单零中心化和归一化输入，之后再通过每层的两个新参数(一个缩放，另一个移动)缩放和移动结果，话句话说，这个操作让模型学会最佳模型和每层输入的平均值

批量归一化原理

(1)\(\mu_B = \frac{1}{m_B}\sum_{i=1}^{m_B}x^{(i)}\) #经验平均值，评估整个小批量B

(2)\(\theta_B = \frac{1}{m_B}\sum_{i=1}^{m_b}(x^{(i)} - \mu_B)^2\) #评估整个小批量B的方差

(3)\(x_{(i)}^* = \frac{x^{(i)} - \mu_B}{\sqrt{\theta_B^2+\xi}}\)#零中心化和归一化

(4)\(z^{(i)} = \lambda x_{(i)}^* + \beta\)#将输入进行缩放和移动

在测试期间，没有小批量的数据来计算经验平均值和标准方差，所有可以简单地用整个训练集的平均值和标准方差来代替，在训练过程中可以用变动平均值有效计算出来

但是，批量归一化的确也给模型增加了一些复杂度和运行代价，使得神经网络的预测速度变慢，所以如果逆需要快速预测，可能需要在进行批量归一化之前先检查以下ELU+He初始化的表现如何

tf.layers.batch_normalization使用

函数原型

def batch_normalization(inputs,
                    axis=-1,
                    momentum=0.99,
                    epsilon=1e-3,
                    center=True,
                    scale=True,
                    beta_initializer=init_ops.zeros_initializer(),
                    gamma_initializer=init_ops.ones_initializer(),
                    moving_mean_initializer=init_ops.zeros_initializer(),
                    moving_variance_initializer=init_ops.ones_initializer(),
                    beta_regularizer=None,
                    gamma_regularizer=None,
                    beta_constraint=None,
                    gamma_constraint=None,
                    training=False,
                    trainable=True,
                    name=None,
                    reuse=None,
                    renorm=False,
                    renorm_clipping=None,
                    renorm_momentum=0.99,
                    fused=None,
                    virtual_batch_size=None,
                    adjustment=None):

使用注意事项

(1)使用batch_normalization需要三步：

a.在卷积层将激活函数设置为None
b.使用batch_normalization
c.使用激活函数激活

例子：
inputs = tf.layers.dense(inputs,self.n_neurons,
                                   kernel_initializer=self.initializer,
                                   name = 'hidden%d'%(layer+1))
if self.batch_normal_momentum:
    inputs = tf.layers.batch_normalization(inputs,momentum=self.batch_normal_momentum,train=self._training)

inputs = self.activation(inputs,name = 'hidden%d_out'%(layer+1))

(2)在训练时，将参数training设置为True，在测试时，将training设置为False,同时要特别注意update_ops的使用

update_ops = tf.get_collection(tf.GraphKeys.UPDATE_OPS)
需要在每次训练时更新，可以使用sess.run(update_ops)
也可以：
with tf.control_dependencies(update_ops):
    train_op = tf.train.AdamOptimizer(learning_rate).minimize(loss)

使用mnist数据集进行简单测试

from tensorflow.examples.tutorials.mnist import input_data
import tensorflow as tf
import numpy as np

mnist = input_data.read_data_sets('MNIST_data',one_hot=True)
x_train,y_train = mnist.train.images,mnist.train.labels
x_test,y_test = mnist.test.images,mnist.test.labels

Extracting MNIST_data\train-images-idx3-ubyte.gz
Extracting MNIST_data\train-labels-idx1-ubyte.gz
Extracting MNIST_data\t10k-images-idx3-ubyte.gz
Extracting MNIST_data\t10k-labels-idx1-ubyte.gz

he_init = tf.contrib.layers.variance_scaling_initializer()
def dnn(inputs,n_hiddens=1,n_neurons=100,initializer=he_init,activation=tf.nn.elu,batch_normalization=None,training=None):
    for layer in range(n_hiddens):
        inputs = tf.layers.dense(inputs,n_neurons,kernel_initializer=initializer,name = 'hidden%d'%(layer+1))
        if batch_normalization is not None:
            inputs = tf.layers.batch_normalization(inputs,momentum=batch_normalization,training=training)
        inputs = activation(inputs,name = 'hidden%d'%(layer+1))
    return inputs

tf.reset_default_graph()
n_inputs = 28*28
n_hidden = 100
n_outputs = 10

X = tf.placeholder(tf.float32,shape=(None,n_inputs),name='X')
Y = tf.placeholder(tf.int32,shape=(None,n_outputs),name='Y')

training = tf.placeholder_with_default(False,shape=(),name='tarining')
dnn_outputs = dnn(X)

logits = tf.layers.dense(dnn_outputs,n_outputs,kernel_initializer = he_init,name='logits')
y_proba = tf.nn.softmax(logits,name='y_proba')
xentropy = tf.nn.softmax_cross_entropy_with_logits(labels=Y,logits=y_proba)
loss = tf.reduce_mean(xentropy,name='loss')
train_op = tf.train.AdamOptimizer(learning_rate=0.01).minimize(loss)

correct = tf.equal(tf.argmax(Y,1),tf.argmax(y_proba,1))
accuracy = tf.reduce_mean(tf.cast(correct,tf.float32))

epoches = 20
batch_size = 100
np.random.seed(42)

init = tf.global_variables_initializer()
rnd_index = np.random.permutation(len(x_train))
n_batches = len(x_train) // batch_size
with tf.Session() as sess:
    sess.run(init)
    for epoch in range(epoches):
        for batch_index in np.array_split(rnd_index,n_batches):
            x_batch,y_batch = x_train[batch_index],y_train[batch_index]
            feed_dict = {X:x_batch,Y:y_batch,training:True}
            sess.run(train_op,feed_dict=feed_dict)
        loss_val,accuracy_val = sess.run([loss,accuracy],feed_dict={X:x_test,Y:y_test,training:False})
        print('epoch:{},loss:{},accuracy:{}'.format(epoch,loss_val,accuracy_val))