instanceNormalizationLayer

Instance normalization layer

Description

An instance normalization layer normalizes a mini-batch of data across each channel for each observation independently. To improve the convergence of training the convolutional neural network and reduce the sensitivity to network hyperparameters, use instance normalization layers between convolutional layers and nonlinearities, such as ReLU layers.

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

Creation

Syntax

layer = instanceNormalizationLayer

layer = instanceNormalizationLayer(Name,Value)

Description

layer = instanceNormalizationLayer creates an instance normalization layer.

layer = instanceNormalizationLayer(Name,Value) creates an instance normalization layer and sets the optional Epsilon, Parameters and Initialization, Learn Rate and Regularization, and Name properties using one or more name-value arguments. You can specify multiple name-value arguments. Enclose each property name in quotes.

Example: instanceNormalizationLayer('Name','instancenorm') creates an instance normalization layer with the name 'instancenorm'

Properties

Instance 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 automatically determines 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 Instance Normalization Layer

Create an instance normalization layer with the name 'instancenorm'.

layer = instanceNormalizationLayer('Name','instancenorm')

layer = 
  InstanceNormalizationLayer with properties:

           Name: 'instancenorm'
    NumChannels: 'auto'

   Hyperparameters
        Epsilon: 1.0000e-05

   Learnable Parameters
         Offset: []
          Scale: []

  Show all properties

Include an instance normalization layer in a Layer array.

layers = [
    imageInputLayer([28 28 3])
    convolution2dLayer(5,20)
    instanceNormalizationLayer
    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   ''   Instance Normalization   Instance 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

Algorithms

The instance normalization operation normalizes the elements x_i of the input by first calculating the mean μ_I and variance σ_I² over the spatial and time dimensions for each channel in each observation independently. Then, it calculates the normalized activations as

$$\widehat{x_i}=\frac{x_i-{\mu }_I}{\sqrt{{\sigma }_I^2+ϵ}},$$

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 instance normalization, the instance normalization operation further shifts and scales the activations using the transformation

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

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