# layerNormalizationLayer

Layer normalization layer

## 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

### 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 numeric scalar equal to or larger than 1e-5.

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

Number of input channels, specified as 'auto' or a positive integer.

This property is always equal to the number of channels of the input to the layer. If NumChannels is 'auto', then the software automatically determines the correct value for the number of channels at training time.

### 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, if Scale is nonempty, then trainNetwork uses the Scale property as the initial value. If Scale is empty, then trainNetwork uses the initializer specified by ScaleInitializer.

At training time, Scale is one of the following:

• For 2-D image input, a numeric array of size 1-by-1-by-NumChannels

• For 3-D image input, a numeric array of size 1-by-1-by-1-by-NumChannels

• For feature or sequence input, a numeric array of size NumChannels-by-1

Channel offsets β, specified as a numeric array.

The channel offsets are learnable parameters. When you train a network, if Offset is nonempty, then trainNetwork uses the Offset property as the initial value. If Offset is empty, then trainNetwork uses the initializer specified by OffsetInitializer.

At training time, Offset is one of the following:

• For 2-D image input, a numeric array of size 1-by-1-by-NumChannels

• For 3-D image input, a numeric array of size 1-by-1-by-1-by-NumChannels

• For feature or sequence input, a numeric array of size NumChannels-by-1

### 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.

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.

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.

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.

### 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 Name set to ''.

Data Types: char | string

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

Data Types: double

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

Data Types: cell

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

Data Types: double

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

Learnable Parameters
Offset: []
Scale: []

Show all properties

Include a layer normalization layer in a Layer array.

layers = [
imageInputLayer([32 32 3])
layerNormalizationLayer
reluLayer
maxPooling2dLayer(2,'Stride',2)
layerNormalizationLayer
reluLayer
fullyConnectedLayer(10)
softmaxLayer
classificationLayer]
layers =
11x1 Layer array with layers:

1   ''   Image Input             32x32x3 images with 'zerocenter' normalization
2   ''   Convolution             16 3x3 convolutions with stride [1  1] and padding [1  1  1  1]
3   ''   Layer Normalization     Layer normalization
4   ''   ReLU                    ReLU
5   ''   Max Pooling             2x2 max pooling with stride [2  2] and padding [0  0  0  0]
6   ''   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

## Algorithms

The layer normalization operation normalizes the elements xi of the input by first calculating the mean μL and variance σL2 over the spatial, time, and channel dimensions for each observation independently. Then, it calculates the normalized activations as

$\stackrel{^}{{x}_{i}}=\frac{{x}_{i}-{\mu }_{L}}{\sqrt{{\sigma }_{L}^{2}+ϵ}},$

where ϵ is a constant that improves numerical stability when the variance is very small.

To allow for the possibility that inputs with zero mean and unit variance are not optimal for the operations that follow layer normalization, the layer normalization operation further shifts and scales the activations using the transformation

${y}_{i}=\gamma {\stackrel{^}{x}}_{i}+\beta ,$

where the offset β and scale factor γ are learnable parameters that are updated during network training.

## 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.

Introduced in R2021a