groupNormalizationLayer

Group normalization layer

Description

A group normalization layer divides the channels of the input data into groups and normalizes the activations across each group. To speed up training of convolutional neural networks and reduce the sensitivity to network initialization, use group normalization layers between convolutional layers and nonlinearities, such as ReLU layers. You can perform instance normalization and layer normalization by setting the appropriate number of groups.

You can use a group normalization layer in place of a batch normalization layer. This is particularly useful when training with small batch sizes as it can increase the stability of training.

The layer first normalizes the activations of each group by subtracting the group mean and dividing by the group standard deviation. Then, the layer shifts the input by a learnable offset β and scales it by a learnable scale factor γ.

Creation

Syntax

layer = groupNormalizationLayer(numGroups)

layer = groupNormalizationLayer(numGroups,Name,Value)

Description

layer = groupNormalizationLayer(numGroups) creates a group normalization layer that divides the channels in the layer input into numGroups groups and normalizes across each group.

layer = groupNormalizationLayer(numGroups,Name,Value) creates a group normalization layer and sets the optional Normalization, Parameters and Initialization, Learn Rate and Regularization, and Name properties using one or more name-value pair arguments. You can specify multiple name-value pair arguments. Enclose each property name in quotes.

Input Arguments

numGroups — Number of groups

positive integer | "all-channels" | "channel-wise"

Number of groups into which to divide the channels of the input data, specified as a positive integer, "all-channels" or "channel-wise".

If you specify numGroups as a positive integer, the layer divides the incoming channels in to the specified number of groups. The specified number of groups must divide the number of channels exactly.

If you specify numGroups as "all-channels", the layer groups all incoming channels into a single group. This is also known as layer normalization.

If you specify numGroups as a "channel-wise", the layer treats all incoming channels as separate groups. This is also known as instance normalization.

Properties

Normalization

Epsilon — Constant to add to mini-batch variances

1e-5 (default) | numeric scalar

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.

NumChannels — Number of input channels

'auto' (default) | positive integer

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 equals 'auto', then the software infers the correct value for the number of channels at training time.

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 zero mean and standard deviation 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 zero mean and standard deviation 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 training 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

Offset — Channel offsets

[] (default) | numeric array

Channel offsets β, specified as a numeric array.

The channel offsets are learnable parameters. When training 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

Learn 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.

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 equals 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.

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, 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.

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, 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

Name — Layer name

'' (default) | character vector | string scalar

Layer name, specified as a character vector or a string scalar. To include a layer in a layer graph, you must specify a nonempty unique layer name. If you train a series network with the layer and Name is set to '', then the software automatically assigns a name to the layer at training time.

Data Types: char | string

NumInputs — Number of inputs

1 (default)

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

Data Types: double

InputNames — Input names

{'in'} (default)

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

Data Types: cell

NumOutputs — Number of outputs

1 (default)

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

Data Types: double

OutputNames — Output names

{'out'} (default)

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

Data Types: cell

Examples

Create Group Normalization Layer

Create a group normalization layer that normalizes incoming data across three groups of channels. Name the layer 'groupnorm'.

layer = groupNormalizationLayer(3,'Name','groupnorm')

layer = 
  GroupNormalizationLayer with properties:

           Name: 'groupnorm'
    NumChannels: 'auto'

   Hyperparameters
      NumGroups: 3
        Epsilon: 1.0000e-05

   Learnable Parameters
         Offset: []
          Scale: []

  Show all properties

Include a group normalization layer in a Layer array. Normalize the incoming 20 channels in four groups.

layers = [
    imageInputLayer([28 28 3])
    convolution2dLayer(5,20)
    groupNormalizationLayer(4)
    reluLayer
    maxPooling2dLayer(2,'Stride',2)
    fullyConnectedLayer(10)
    softmaxLayer
    classificationLayer]

layers = 
  8x1 Layer array with layers:

     1   ''   Image Input             28x28x3 images with 'zerocenter' normalization
     2   ''   Convolution             20 5x5 convolutions with stride [1  1] and padding [0  0  0  0]
     3   ''   Group Normalization     Group normalization
     4   ''   ReLU                    ReLU
     5   ''   Max Pooling             2x2 max pooling with stride [2  2] and padding [0  0  0  0]
     6   ''   Fully Connected         10 fully connected layer
     7   ''   Softmax                 softmax
     8   ''   Classification Output   crossentropyex

More About

Group Normalization Layer

A group normalization layer divides the channels of the input data into groups and normalizes the activations across each group. To speed up training of convolutional neural networks and reduce the sensitivity to network initialization, use group normalization layers between convolutional layers and nonlinearities, such as ReLU layers.

You can also use a group normalization layer to perform layer normalization or instance normalization. Layer normalization combines and normalizes activations across all channels in a single observation. Instance normalization normalizes the activations of each channel of the observation separately.

The layer first normalizes the activations of each group by subtracting the group mean and dividing by the group standard deviation. Then, the layer shifts the input by a learnable offset β and scales it by a learnable scale factor γ.

Group normalization layers normalize the activations and gradients propagating through a neural network, making network training an easier optimization problem. To take full advantage of this fact, you can try increasing the learning rate. Since the optimization problem is easier, the parameter updates can be larger and the network can learn faster. You can also try reducing the L₂ and dropout regularization.

You can use a group normalization layer in place of a batch normalization layer. This is particularly useful when training with small batch sizes as it can increase the stability of training.

Algorithms

A group normalization normalizes its inputs x_i by first calculating the mean μ_g and variance σ_g² over the specified groups of channels. Then, it calculates the normalized activations as

$${\widehat{x}}_i=\frac{x_i-{\mu }_g}{\sqrt{{\sigma }_g^2+\epsilon }}$$

Here, ϵ (the property Epsilon) improves numerical stability when the group variance is very small. To allow for the possibility that inputs with zero mean and unit variance are not optimal for the layer that follows the group normalization layer, the group normalization layer further shifts and scales the activations as

$$y_i=\gamma {\widehat{x}}_i+\beta .$$

Here, the offset β and scale factor γ (Offset and Scale properties) are learnable parameters that are updated during network training.

References

[1] Wu, Yuxin, and Kaiming He. “Group Normalization.” ArXiv:1803.08494 [Cs], June 11, 2018. http://arxiv.org/abs/1803.08494.