`LayerNormalization`

class```
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,
**kwargs
)
```

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

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.

**Arguments**

**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.

**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**