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

Inherits From: Layer

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.


data = tf.constant(np.arange(10).reshape(5, 2) * 10, dtype=tf.float32)
[[ 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)
[[-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])[5, 20, 30, 40])
(20, 30, 40)
(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.

axis Integer or List/Tuple. The axis or axes to normalize across. Typically this is the features axis/axes. The left-out axes are typically the batch axis/axes. This argument defaults to -1, the last dimension in the input.
epsilon Small float added to variance to avoid dividing by zero. Defaults to 1e-3
center If True, add offset of beta to normalized tensor. If False, beta is ignored. Defaults to True.
scale If True, multiply by gamma. If False, gamma is not used. Defaults to True. When the next layer is linear (also e.g. nn.relu), this can be disabled since the scaling will be done by the next layer.
beta_initializer Initializer for the beta weight. Defaults to zeros.
gamma_initializer Initializer for the gamma weight. Defaults to ones.
beta_regularizer Optional regularizer for the beta weight. None by default.
gamma_regularizer Optional regularizer for the gamma weight. None by default.
beta_constraint Optional constraint for the beta weight. None by default.
gamma_constraint Optional constraint for the gamma weight. None by default.
trainable Boolean, if True the variables will be marked as trainable. Defaults to True.

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: