LayerNormalizationLayer - Layer normalization layer - MATLAB (original) (raw)

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

Description

`layer` = layerNormalizationLayer creates a layer normalization layer.

Properties

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Layer Normalization

Epsilon — Constant to add to mini-batch variances

1e-5 (default) | positive scalar

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

NumChannels — Number of input channels

"auto" (default) | positive integer

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

OperationDimension — Dimension to normalize over

"auto" (default) | "channel-only" | "spatial-channel" | "batch-excluded"

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

ScaleInitializer — Function to initialize channel scale factors

'ones' (default) | 'narrow-normal' | function handle

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

OffsetInitializer — Function to initialize channel offsets

'zeros' (default) | 'ones' | 'narrow-normal' | 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

Scale — Channel scale factors

[] (default) | numeric array

Channel scale factors γ, specified as a numeric array.

The channel scale factors are learnable parameters. When you train a network using thetrainnet 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 byScaleInitializer.

Depending on the type of layer input, the trainnet anddlnetwork functions automatically reshape this property to have of the following sizes:

Data Types: single | double

Offset — Channel offsets

[] (default) | numeric array

Channel offsets β, specified as a numeric vector.

The channel offsets are learnable parameters. When you train a network using the trainnet 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 byOffsetInitializer.

Depending on the type of layer input, the trainnet anddlnetwork functions automatically reshape this property to have of the following sizes:

Data Types: single | double

Learning Rate and Regularization

ScaleLearnRateFactor — Learning rate factor for scale factors

1 (default) | nonnegative scalar

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

OffsetLearnRateFactor — Learning rate factor for offsets

1 (default) | nonnegative scalar

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

ScaleL2Factor — L2 regularization factor for scale factors

1 (default) | nonnegative scalar

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, ifScaleL2Factor 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

OffsetL2Factor — L2 regularization factor for offsets

1 (default) | nonnegative scalar

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, ifOffsetL2Factor 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 string scalar. For Layer array input, the trainnet anddlnetwork functions automatically assign names to layers with the name "".

The LayerNormalizationLayer object stores this property as a character vector.

Data Types: char | string

NumInputs — Number of inputs

1 (default)

This property is read-only.

Number of inputs to the layer, returned as 1. This layer accepts a single input only.

Data Types: double

InputNames — Input names

{'in'} (default)

This property is read-only.

Input names, returned as {'in'}. This layer accepts a single input only.

Data Types: cell

NumOutputs — Number of outputs

1 (default)

This property is read-only.

Number of outputs from the layer, returned as 1. This layer has a single output only.

Data Types: double

OutputNames — Output names

{'out'} (default)

This property is read-only.

Output names, returned as {'out'}. This layer has a single output only.

Data Types: cell

Examples

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Create Layer Normalization Layer

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: []

Use properties method to see a list of 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]

layers = 10x1 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

Algorithms

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Layer Normalization Layer

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

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

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

Layer Input and Output Formats

Layers in a layer array or layer graph pass data to subsequent layers as formatted dlarray objects. The format of a dlarray object is a string of characters in which each character describes the corresponding dimension of the data. The formats consist of one or more of these characters:

• "S" — Spatial
• "C" — Channel
• "B" — Batch
• "T" — Time
• "U" — Unspecified

For example, you can describe 2-D image data that is represented as a 4-D array, where the first two dimensions correspond to the spatial dimensions of the images, the third dimension corresponds to the channels of the images, and the fourth dimension corresponds to the batch dimension, as having the format "SSCB" (spatial, spatial, channel, batch).

You can interact with these dlarray objects in automatic differentiation workflows, such as those for developing a custom layer, using a functionLayer object, or using the forward and predict functions withdlnetwork objects.

This table shows the supported input formats of LayerNormalizationLayer objects and the corresponding output format. If the software passes the output of the layer to a custom layer that does not inherit from the nnet.layer.Formattable class, or aFunctionLayer object with the Formattable property set to 0 (false), then the layer receives an unformatted dlarray object with dimensions ordered according to the formats in this table. The formats listed here are only a subset. The layer may support additional formats such as formats with additional "S" (spatial) or"U" (unspecified) dimensions.

In dlnetwork objects, LayerNormalizationLayer objects also support these input and output format combinations.

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.

Extended Capabilities

C/C++ Code Generation

Generate C and C++ code using MATLAB® Coder™.

GPU Code Generation

Generate CUDA® code for NVIDIA® GPUs using GPU Coder™.

Version History

Introduced in R2021a

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R2023b: Code generation support

Generate C or C++ code using MATLAB® Coder™ or generate CUDA® code for NVIDIA® GPUs using GPU Coder™.

R2023a: Specify operation dimension

Specify which dimensions to normalize over using the OperationDimension option.

R2023a: Epsilon supports values less than 1e-5

The Epsilon option also supports positive values less than 1e-5.

R2023a: Layer supports 1-D image sequence data

LayerNormalizationLayer objects support normalizing 1-D image sequence data (data with one spatial and one time dimension).

R2023a: Layer normalizes over channel and spatial dimensions of sequence data

Starting in R2023a, by default, the layer normalizes sequence data over the channel and spatial dimensions. In previous versions, the software normalizes over all dimensions except for the batch dimension (the spatial, time, and channel dimensions). Normalization over the channel and spatial dimensions is usually better suited for this type of data. To reproduce the previous behavior, set OperationDimension to"batch-excluded".