Update July 2016 The easiest way to use batch normalization in TensorFlow is through the higher-level interfaces provided in either contrib/layers, tflearn, or slim.
Previous answer if you want to DIY:
The documentation string for this has improved since the release – see the docs comment in the master branch instead of the one you found. It clarifies, in particular, that it’s the output from tf.nn.moments.
You can see a very simple example of its use in the batch_norm test code. For a more real-world use example, I’ve included below the helper class and use notes that I scribbled up for my own use (no warranty provided!):
"""A helper class for managing batch normalization state.
This class is designed to simplify adding batch normalization
(http://arxiv.org/pdf/1502.03167v3.pdf) to your model by
managing the state variables associated with it.
Important use note: The function get_assigner() returns
an op that must be executed to save the updated state.
A suggested way to do this is to make execution of the
model optimizer force it, e.g., by:
update_assignments = tf.group(bn1.get_assigner(),
bn2.get_assigner())
with tf.control_dependencies([optimizer]):
optimizer = tf.group(update_assignments)
"""
import tensorflow as tf
class ConvolutionalBatchNormalizer(object):
"""Helper class that groups the normalization logic and variables.
Use:
ewma = tf.train.ExponentialMovingAverage(decay=0.99)
bn = ConvolutionalBatchNormalizer(depth, 0.001, ewma, True)
update_assignments = bn.get_assigner()
x = bn.normalize(y, train=training?)
(the output x will be batch-normalized).
"""
def __init__(self, depth, epsilon, ewma_trainer, scale_after_norm):
self.mean = tf.Variable(tf.constant(0.0, shape=[depth]),
trainable=False)
self.variance = tf.Variable(tf.constant(1.0, shape=[depth]),
trainable=False)
self.beta = tf.Variable(tf.constant(0.0, shape=[depth]))
self.gamma = tf.Variable(tf.constant(1.0, shape=[depth]))
self.ewma_trainer = ewma_trainer
self.epsilon = epsilon
self.scale_after_norm = scale_after_norm
def get_assigner(self):
"""Returns an EWMA apply op that must be invoked after optimization."""
return self.ewma_trainer.apply([self.mean, self.variance])
def normalize(self, x, train=True):
"""Returns a batch-normalized version of x."""
if train:
mean, variance = tf.nn.moments(x, [0, 1, 2])
assign_mean = self.mean.assign(mean)
assign_variance = self.variance.assign(variance)
with tf.control_dependencies([assign_mean, assign_variance]):
return tf.nn.batch_norm_with_global_normalization(
x, mean, variance, self.beta, self.gamma,
self.epsilon, self.scale_after_norm)
else:
mean = self.ewma_trainer.average(self.mean)
variance = self.ewma_trainer.average(self.variance)
local_beta = tf.identity(self.beta)
local_gamma = tf.identity(self.gamma)
return tf.nn.batch_norm_with_global_normalization(
x, mean, variance, local_beta, local_gamma,
self.epsilon, self.scale_after_norm)
Note that I called it a ConvolutionalBatchNormalizer because it pins the use of tf.nn.moments to sum across axes 0, 1, and 2, whereas for non-convolutional use you might only want axis 0.
Feedback appreciated if you use it.