tf.keras / layers / layers.Lambda

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TensorFlow 1 version

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Layer normalization layer (Ba et al., 2016).

Inherits From: Layer, Module

tf.keras.layers.LayerNormalization(
    axis=-1, epsilon=0.001, center=True, scale=True,
    beta_initializer='zeros', gamma_initializer='ones',
    beta_regularizer=None, gamma_regularizer=None, beta_constraint=None,
    gamma_constraint=None, trainable=True, name=None, **kwargs
)

Used in the notebooks

Normalize the activations of the previous layer for each given example in a batch independently, rather than across a batch like Batch Normalization. i.e. applies a transformation that maintains the mean activation within each example close to 0 and the activation standard deviation close to 1.

Given a tensor inputs, moments are calculated and normalization is performed across the axes specified in axis.

Example:

data = tf.constant(np.arange(10).reshape(5, 2) * 10, dtype=tf.float32)
print(data)
tf.Tensor(
[[ 0. 10.]
 [20. 30.]
 [40. 50.]
 [60. 70.]
 [80. 90.]], shape=(5, 2), dtype=float32)

layer = tf.keras.layers.LayerNormalization(axis=1)
output = layer(data)
print(output)
tf.Tensor(
[[-1. 1.]
 [-1. 1.]
 [-1. 1.]
 [-1. 1.]
 [-1. 1.]], shape=(5, 2), dtype=float32)

Notice that with Layer Normalization the normalization happens across the axes within each example, rather than across different examples in the batch.

If scale or center are enabled, the layer will scale the normalized outputs by broadcasting them with a trainable variable gamma, and center the outputs by broadcasting with a trainable variable beta. gamma will default to a ones tensor and beta will default to a zeros tensor, so that centering and scaling are no-ops before training has begun.

So, with scaling and centering enabled the normalization equations are as follows: Let the intermediate activations for a mini-batch to be the inputs.

For each sample x_i in inputs with k features, we compute the mean and variance of the sample:

  mean_i = sum(x_i[j] for j in range(k)) / k
  var_i = sum((x_i[j] - mean_i) ** 2 for j in range(k)) / k

and then compute a normalized x_i_normalized, including a small factor epsilon for numerical stability.

  x_i_normalized = (x_i - mean_i) / sqrt(var_i + epsilon)

And finally x_i_normalized is linearly transformed by gamma and beta, which are learned parameters:

  output_i = x_i_normalized * gamma + beta

gamma and beta will span the axes of inputs specified in axis, and this part of the inputs' shape must be fully defined.

For example:

layer = tf.keras.layers.LayerNormalization(axis=[1, 2, 3])
layer.build([5, 20, 30, 40])
print(layer.beta.shape)
(20, 30, 40)
print(layer.gamma.shape)
(20, 30, 40)

Note that other implementations of layer normalization may choose to define gamma and beta over a separate set of axes from the axes being normalized across. For example, Group Normalization (Wu et al. 2018) with group size of 1 corresponds to a Layer Normalization that normalizes across height, width, and channel and has gamma and beta span only the channel dimension. So, this Layer Normalization implementation will not match a Group Normalization layer with group size set to 1.

Input shape: Arbitrary. Use the keyword argument input_shape (tuple of integers, does not include the samples axis) when using this layer as the first layer in a model. Output shape: Same shape as input. Reference:

• Lei Ba et al., 2016.