# layerNormalizationLayer

Layer normalization layer

Since R2021a

## Description

A layer normalization layer normalizes a mini-batch of data across all channels for each observation independently. To speed up training of recurrent and multilayer perceptron neural networks and reduce the sensitivity to network initialization, use layer normalization layers after the learnable layers, such as LSTM and fully connected layers.

After normalization, the layer scales the input with a learnable scale factor γ and shifts it by a learnable offset β.

## Creation

### Syntax

``layer = layerNormalizationLayer``
``layer = layerNormalizationLayer(Name,Value)``

### Description

````layer = layerNormalizationLayer` creates a layer normalization layer.```

example

````layer = layerNormalizationLayer(Name,Value)` sets the optional `Epsilon`, Parameters and Initialization, Learning Rate and Regularization, and `Name` properties using one or more name-value arguments. For example, `layerNormalizationLayer('Name','layernorm')` creates a layer normalization layer with name `'layernorm'`.```

## Properties

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### Layer Normalization

Constant to add to the mini-batch variances, specified as a positive scalar.

The software adds this constant to the mini-batch variances before normalization to ensure numerical stability and avoid division by zero.

Before R2023a: `Epsilon` must be greater than or equal to `1e-5`.

Data Types: `single` | `double` | `int8` | `int16` | `int32` | `int64` | `uint8` | `uint16` | `uint32` | `uint64`

This property is read-only.

Number of input channels, specified as one of the following:

• `'auto'` — Automatically determine the number of input channels at training time.

• Positive integer — Configure the layer for the specified number of input channels. `NumChannels` and the number of channels in the layer input data must match. For example, if the input is an RGB image, then `NumChannels` must be 3. If the input is the output of a convolutional layer with 16 filters, then `NumChannels` must be 16.

Data Types: `single` | `double` | `int8` | `int16` | `int32` | `int64` | `uint8` | `uint16` | `uint32` | `uint64` | `char` | `string`

Since R2023a

Dimension to normalize over, specified as one of these values:

• `"auto"` — For feature, sequence, 1-D image, or spatial-temporal input, normalize over the channel dimension. Otherwise, normalize over the spatial and channel dimensions.

• `"channel-only"` — Normalize over the channel dimension.

• `"spatial-channel"` — Normalize over the spatial and channel dimensions.

• `"batch-excluded"` — Normalize over all dimensions except for the batch dimension.

### Parameters and Initialization

Function to initialize the channel scale factors, specified as one of the following:

• `'ones'` – Initialize the channel scale factors with ones.

• `'zeros'` – Initialize the channel scale factors with zeros.

• `'narrow-normal'` – Initialize the channel scale factors by independently sampling from a normal distribution with a mean of zero and standard deviation of 0.01.

• Function handle – Initialize the channel scale factors with a custom function. If you specify a function handle, then the function must be of the form `scale = func(sz)`, where `sz` is the size of the scale. For an example, see Specify Custom Weight Initialization Function.

The layer only initializes the channel scale factors when the `Scale` property is empty.

Data Types: `char` | `string` | `function_handle`

Function to initialize the channel offsets, specified as one of the following:

• `'zeros'` – Initialize the channel offsets with zeros.

• `'ones'` – Initialize the channel offsets with ones.

• `'narrow-normal'` – Initialize the channel offsets by independently sampling from a normal distribution with a mean of zero and standard deviation of 0.01.

• Function handle – Initialize the channel offsets with a custom function. If you specify a function handle, then the function must be of the form `offset = func(sz)`, where `sz` is the size of the scale. For an example, see Specify Custom Weight Initialization Function.

The layer only initializes the channel offsets when the `Offset` property is empty.

Data Types: `char` | `string` | `function_handle`

Channel scale factors γ, specified as a numeric array.

The channel scale factors are learnable parameters. When you train a network using the `trainNetwork` function or initialize a `dlnetwork` object, if `Scale` is nonempty, then the software uses the `Scale` property as the initial value. If `Scale` is empty, then the software uses the initializer specified by `ScaleInitializer`.

Depending on the type of layer input, the `trainNetwork`, `assembleNetwork`, `layerGraph`, and `dlnetwork` functions automatically reshape this property to have of the following sizes:

Layer InputProperty Size
feature input`NumChannels`-by-1
vector sequence input

1-D image input (since R2023a)

1-by-`NumChannels`

1-D image sequence input (since R2023a)

2-D image input1-by-1-by-`NumChannels`
2-D image sequence input
3-D image input1-by-1-by-1-by-`NumChannels`
3-D image sequence input

Data Types: `single` | `double`

Channel offsets β, specified as a numeric vector.

The channel offsets are learnable parameters. When you train a network using the `trainNetwork` function or initialize a `dlnetwork` object, if `Offset` is nonempty, then the software uses the `Offset` property as the initial value. If `Offset` is empty, then the software uses the initializer specified by `OffsetInitializer`.

Depending on the type of layer input, the `trainNetwork`, `assembleNetwork`, `layerGraph`, and `dlnetwork` functions automatically reshape this property to have of the following sizes:

Layer InputProperty Size
feature input`NumChannels`-by-1
vector sequence input

1-D image input (since R2023a)

1-by-`NumChannels`

1-D image sequence input (since R2023a)

2-D image input1-by-1-by-`NumChannels`
2-D image sequence input
3-D image input1-by-1-by-1-by-`NumChannels`
3-D image sequence input

Data Types: `single` | `double`

### Learning Rate and Regularization

Learning rate factor for the scale factors, specified as a nonnegative scalar.

The software multiplies this factor by the global learning rate to determine the learning rate for the scale factors in a layer. For example, if `ScaleLearnRateFactor` is `2`, then the learning rate for the scale factors in the layer is twice the current global learning rate. The software determines the global learning rate based on the settings specified with the `trainingOptions` function.

Data Types: `single` | `double` | `int8` | `int16` | `int32` | `int64` | `uint8` | `uint16` | `uint32` | `uint64`

Learning rate factor for the offsets, specified as a nonnegative scalar.

The software multiplies this factor by the global learning rate to determine the learning rate for the offsets in a layer. For example, if `OffsetLearnRateFactor` is `2`, then the learning rate for the offsets in the layer is twice the current global learning rate. The software determines the global learning rate based on the settings specified with the `trainingOptions` function.

Data Types: `single` | `double` | `int8` | `int16` | `int32` | `int64` | `uint8` | `uint16` | `uint32` | `uint64`

L2 regularization factor for the scale factors, specified as a nonnegative scalar.

The software multiplies this factor by the global L2 regularization factor to determine the learning rate for the scale factors in a layer. For example, if `ScaleL2Factor` is `2`, then the L2 regularization for the offsets in the layer is twice the global L2 regularization factor. You can specify the global L2 regularization factor using the `trainingOptions` function.

Data Types: `single` | `double` | `int8` | `int16` | `int32` | `int64` | `uint8` | `uint16` | `uint32` | `uint64`

L2 regularization factor for the offsets, specified as a nonnegative scalar.

The software multiplies this factor by the global L2 regularization factor to determine the learning rate for the offsets in a layer. For example, if `OffsetL2Factor` is `2`, then the L2 regularization for the offsets in the layer is twice the global L2 regularization factor. You can specify the global L2 regularization factor using the `trainingOptions` function.

Data Types: `single` | `double` | `int8` | `int16` | `int32` | `int64` | `uint8` | `uint16` | `uint32` | `uint64`

### Layer

Layer name, specified as a character vector or a string scalar. For `Layer` array input, the `trainNetwork`, `assembleNetwork`, `layerGraph`, and `dlnetwork` functions automatically assign names to layers with the name `''`.

Data Types: `char` | `string`

This property is read-only.

Number of inputs of the layer. This layer accepts a single input only.

Data Types: `double`

This property is read-only.

Input names of the layer. This layer accepts a single input only.

Data Types: `cell`

This property is read-only.

Number of outputs of the layer. This layer has a single output only.

Data Types: `double`

This property is read-only.

Output names of the layer. This layer has a single output only.

Data Types: `cell`

## Examples

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Create a layer normalization layer with the name `'layernorm'`.

`layer = layerNormalizationLayer('Name','layernorm')`
```layer = LayerNormalizationLayer with properties: Name: 'layernorm' NumChannels: 'auto' Hyperparameters Epsilon: 1.0000e-05 OperationDimension: 'auto' Learnable Parameters Offset: [] Scale: [] Show all properties ```

Include a layer normalization layer in a `Layer` array.

```layers = [ imageInputLayer([32 32 3]) convolution2dLayer(3,16,'Padding',1) layerNormalizationLayer reluLayer maxPooling2dLayer(2,'Stride',2) convolution2dLayer(3,32,'Padding',1) layerNormalizationLayer reluLayer fullyConnectedLayer(10) softmaxLayer classificationLayer]```
```layers = 11x1 Layer array with layers: 1 '' Image Input 32x32x3 images with 'zerocenter' normalization 2 '' 2-D Convolution 16 3x3 convolutions with stride [1 1] and padding [1 1 1 1] 3 '' Layer Normalization Layer normalization 4 '' ReLU ReLU 5 '' 2-D Max Pooling 2x2 max pooling with stride [2 2] and padding [0 0 0 0] 6 '' 2-D Convolution 32 3x3 convolutions with stride [1 1] and padding [1 1 1 1] 7 '' Layer Normalization Layer normalization 8 '' ReLU ReLU 9 '' Fully Connected 10 fully connected layer 10 '' Softmax softmax 11 '' Classification Output crossentropyex ```

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## References

[1] Ba, Jimmy Lei, Jamie Ryan Kiros, and Geoffrey E. Hinton. “Layer Normalization.” Preprint, submitted July 21, 2016. https://arxiv.org/abs/1607.06450.

## Version History

Introduced in R2021a

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