averagePooling2dLayer

Average pooling layer

Description

A 2-D average pooling layer performs downsampling by dividing the input into rectangular pooling regions, then computing the average of each region.

Creation

Syntax

layer = averagePooling2dLayer(poolSize)

layer = averagePooling2dLayer(poolSize,Name=Value)

Description

layer = averagePooling2dLayer(poolSize) creates an average pooling layer and sets the PoolSize property.

layer = averagePooling2dLayer(poolSize,Name=Value) sets optional properties using one or more name-value arguments.

Input Arguments

poolSize — Dimensions of pooling regions

vector of two positive integers | positive integer

Dimensions of the pooling regions, specified as a vector of two positive integers [h w], where h is the height and w is the width. When creating the layer, you can specify poolSize as a scalar to use the same value for both dimensions.

If the stride dimensions Stride are less than the respective pooling dimensions, then the pooling regions overlap.

The padding dimensions PaddingSize must be less than the pooling region dimensions poolSize.

Example: [2 1] specifies pooling regions of height 2 and width 1.

Name-Value Arguments

Specify optional pairs of arguments as Name1=Value1,...,NameN=ValueN, where Name is the argument name and Value is the corresponding value. Name-value arguments must appear after other arguments, but the order of the pairs does not matter.

Example: averagePooling2dLayer(2,Stride=2) creates an average pooling layer with pool size [2 2] and stride [2 2].

Stride — Step size for traversing input

[1 1] (default) | vector of two positive integers | positive integer

Step size for traversing the input vertically and horizontally, specified as a vector of two positive integers [a b], where a is the vertical step size and b is the horizontal step size. When creating the layer, you can specify Stride as a scalar to use the same value for both dimensions.

If the stride dimensions Stride are less than the respective pooling dimensions, then the pooling regions overlap.

The padding dimensions PaddingSize must be less than the pooling region dimensions PoolSize.

Example: [2 3] specifies a vertical step size of 2 and a horizontal step size of 3.

Padding — Input edge padding

[0 0 0 0] (default) | vector of nonnegative integers | "same"

Input edge padding, specified as one of these values:

• "same" — Add padding of size calculated by the software at training or prediction time so that the output has the same size as the input when the stride equals 1. If the stride is larger than 1, then the output size is ceil(inputSize/stride), where inputSize is the height or width of the input and stride is the stride in the corresponding dimension. The software adds the same amount of padding to the top and bottom, and to the left and right, if possible. If the padding that must be added vertically has an odd value, then the software adds extra padding to the bottom. If the padding that must be added horizontally has an odd value, then the software adds extra padding to the right.

• Nonnegative integer p — Add padding of size p to all the edges of the input.

• Vector [a b] of nonnegative integers — Add padding of size a to the top and bottom of the input and padding of size b to the left and right.

• Vector [t b l r] of nonnegative integers — Add padding of size t to the top, b to the bottom, l to the left, and r to the right of the input.

Example: Padding=1 adds one row of padding to the top and bottom, and one column of padding to the left and right of the input.

Example: Padding="same" adds padding so that the output has the same size as the input (if the stride equals 1).

PaddingValue — Value used to pad input

0 (default) | "mean"

Value used to pad input, specified as 0 or "mean".

When you use the Padding option to add padding to the input, the value of the padding applied can be one of the following:

• 0 — Input is padded with zeros at the positions specified by the Padding property. The padded areas are included in the calculation of the average value of the pooling regions along the edges.

• "mean" — Input is padded with the mean of the pooling region at the positions specified by the Padding option. The padded areas are effectively excluded from the calculation of the average value of each pooling region.

Name — Layer name

"" (default) | character vector | string scalar

Layer name, specified as a character vector or a string scalar. For Layer array input, the trainnet and dlnetwork functions automatically assign names to layers with the name "".

This argument sets the Name property.

Data Types: char | string

Properties

Average Pooling

PoolSize — Dimensions of pooling regions

vector of two positive integers

Dimensions of the pooling regions, specified as a vector of two positive integers [h w], where h is the height and w is the width. When creating the layer, you can specify PoolSize as a scalar to use the same value for both dimensions.

If the stride dimensions Stride are less than the respective pooling dimensions, then the pooling regions overlap.

The padding dimensions PaddingSize must be less than the pooling region dimensions PoolSize.

Example: [2 1] specifies pooling regions of height 2 and width 1.

Stride — Step size for traversing input

[1 1] (default) | vector of two positive integers

Step size for traversing the input vertically and horizontally, specified as a vector of two positive integers [a b], where a is the vertical step size and b is the horizontal step size. When creating the layer, you can specify Stride as a scalar to use the same value for both dimensions.

If the stride dimensions Stride are less than the respective pooling dimensions, then the pooling regions overlap.

The padding dimensions PaddingSize must be less than the pooling region dimensions PoolSize.

Example: [2 3] specifies a vertical step size of 2 and a horizontal step size of 3.

PaddingSize — Size of padding

[0 0 0 0] (default) | vector of four nonnegative integers

Size of padding to apply to input borders, specified as a vector [t b l r] of four nonnegative integers, where t is the padding applied to the top, b is the padding applied to the bottom, l is the padding applied to the left, and r is the padding applied to the right.

When you create a layer, use the 'Padding' name-value pair argument to specify the padding size.

Example: [1 1 2 2] adds one row of padding to the top and bottom, and two columns of padding to the left and right of the input.

PaddingMode — Method to determine padding size

"manual" (default) | "same"

Method to determine padding size, specified as "manual" or "same".

The software automatically sets the value of PaddingMode based on the Padding value you specify when creating a layer.

• If you set the Padding option to a scalar or a vector of nonnegative integers, then the software automatically sets PaddingMode to "manual".

• If you set the Padding option to "same", then the software automatically sets PaddingMode to 'same' and calculates the size of the padding at training time so that the output has the same size as the input when the stride equals 1. If the stride is larger than 1, then the output size is ceil(inputSize/stride), where inputSize is the height or width of the input and stride is the stride in the corresponding dimension. The software adds the same amount of padding to the top and bottom, and to the left and right, if possible. If the padding that must be added vertically has an odd value, then the software adds extra padding to the bottom. If the padding that must be added horizontally has an odd value, then the software adds extra padding to the right.

PaddingValue — Value used to pad input

0 (default) | "mean"

Value used to pad input, specified as 0 or "mean".

When you use the Padding option to add padding to the input, the value of the padding applied can be one of the following:

• 0 — Input is padded with zeros at the positions specified by the Padding property. The padded areas are included in the calculation of the average value of the pooling regions along the edges.

• "mean" — Input is padded with the mean of the pooling region at the positions specified by the Padding option. The padded areas are effectively excluded from the calculation of the average value of each pooling region.

Padding — Size of padding

[0 0] (default) | vector of two nonnegative integers

Note

Padding property will be removed in a future release. Use PaddingSize instead. When creating a layer, use the Padding name-value argument to specify the padding size.

Size of padding to apply to input borders vertically and horizontally, specified as a vector [a b] of two nonnegative integers, where a is the padding applied to the top and bottom of the input data and b is the padding applied to the left and right.

Example: [1 1] adds one row of padding to the top and bottom, and one column of padding to the left and right of the input.

Layer

Name — Layer name

'' (default) | character vector | string scalar

Layer name, specified as a character vector or a string scalar. For Layer array input, the trainnet and dlnetwork functions automatically assign names to unnamed layers.

The AveragePooling2DLayer object stores this property as a character vector.

Data Types: char | string

NumInputs — Number of inputs

Read-only: 1 (default)

This property is read-only.

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

Data Types: double

InputNames — Input names

Read-only: {'in'} (default)

This property is read-only.

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

Data Types: cell

NumOutputs — Number of outputs

Read-only: 1 (default)

This property is read-only.

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

Data Types: double

OutputNames — Output names

Read-only: {'out'} (default)

This property is read-only.

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

Data Types: cell

Examples

Create Average Pooling Layer

Create an average pooling layer with the name avg1.

layer = averagePooling2dLayer(2,Name="avg1")

layer = 
  AveragePooling2DLayer with properties:

            Name: 'avg1'

   Hyperparameters
        PoolSize: [2 2]
          Stride: [1 1]
     PaddingMode: 'manual'
     PaddingSize: [0 0 0 0]
    PaddingValue: 0

Include an average pooling layer in a Layer array.

layers = [ ...
    imageInputLayer([28 28 1])
    convolution2dLayer(5,20)
    reluLayer
    averagePooling2dLayer(2)
    fullyConnectedLayer(10)
    softmaxLayer]

layers = 
  6×1 Layer array with layers:

     1   ''   Image Input           28×28×1 images with 'zerocenter' normalization
     2   ''   2-D Convolution       20 5×5 convolutions with stride [1  1] and padding [0  0  0  0]
     3   ''   ReLU                  ReLU
     4   ''   2-D Average Pooling   2×2 average pooling with stride [1  1] and padding [0  0  0  0]
     5   ''   Fully Connected       10 fully connected layer
     6   ''   Softmax               softmax

Create Average Pooling Layer with Nonoverlapping Pooling Regions

Create an average pooling layer with nonoverlapping pooling regions.

layer = averagePooling2dLayer(2,'Stride',2)

layer = 
  AveragePooling2DLayer with properties:

            Name: ''

   Hyperparameters
        PoolSize: [2 2]
          Stride: [2 2]
     PaddingMode: 'manual'
     PaddingSize: [0 0 0 0]
    PaddingValue: 0

The height and width of the rectangular regions (pool size) are both 2. The pooling regions do not overlap because the step size for traversing the images vertically and horizontally (stride) is also 2.

Include an average pooling layer with nonoverlapping regions in a Layer array.

layers = [ ...
    imageInputLayer([28 28 1])
    convolution2dLayer(5,20)
    reluLayer
    averagePooling2dLayer(2,'Stride',2)
    fullyConnectedLayer(10)
    softmaxLayer]

layers = 
  6×1 Layer array with layers:

     1   ''   Image Input           28×28×1 images with 'zerocenter' normalization
     2   ''   2-D Convolution       20 5×5 convolutions with stride [1  1] and padding [0  0  0  0]
     3   ''   ReLU                  ReLU
     4   ''   2-D Average Pooling   2×2 average pooling with stride [2  2] and padding [0  0  0  0]
     5   ''   Fully Connected       10 fully connected layer
     6   ''   Softmax               softmax

Create Average Pooling Layer with Overlapping Pooling Regions

Create an average pooling layer with overlapping pooling regions.

layer = averagePooling2dLayer([3 2],'Stride',2)

layer = 
  AveragePooling2DLayer with properties:

            Name: ''

   Hyperparameters
        PoolSize: [3 2]
          Stride: [2 2]
     PaddingMode: 'manual'
     PaddingSize: [0 0 0 0]
    PaddingValue: 0

This layer creates pooling regions of size [3 2] and takes the average of the six elements in each region. The pooling regions overlap because Stride includes dimensions that are less than the respective pooling dimensions PoolSize.

Include an average pooling layer with overlapping pooling regions in a Layer array.

layers = [ ...
    imageInputLayer([28 28 1])
    convolution2dLayer(5,20)
    reluLayer
    averagePooling2dLayer([3 2],'Stride',2)
    fullyConnectedLayer(10)
    softmaxLayer]

layers = 
  6×1 Layer array with layers:

     1   ''   Image Input           28×28×1 images with 'zerocenter' normalization
     2   ''   2-D Convolution       20 5×5 convolutions with stride [1  1] and padding [0  0  0  0]
     3   ''   ReLU                  ReLU
     4   ''   2-D Average Pooling   3×2 average pooling with stride [2  2] and padding [0  0  0  0]
     5   ''   Fully Connected       10 fully connected layer
     6   ''   Softmax               softmax

Algorithms

2-D Average Pooling Layer

A 2-D average pooling layer performs downsampling by dividing the input into rectangular pooling regions, then computing the average of each region.

The dimensions that the layer pools over depends on the layer input:

• For 2-D image input (data with four dimensions corresponding to pixels in two spatial dimensions, the channels, and the observations), the layer pools over the spatial dimensions.

• For 2-D image sequence input (data with five dimensions corresponding to the pixels in two spatial dimensions, the channels, the observations, and the time steps), the layer pools over the spatial dimensions.

• For 1-D image sequence input (data with four dimensions corresponding to the pixels in one spatial dimension, the channels, the observations, and the time steps), the layer pools over the spatial and time dimensions.

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 format consists 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 with dlnetwork objects.

This table shows the supported input formats of AveragePooling2DLayer 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 a FunctionLayer 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.

Input Format	Output Format
"SSCB" (spatial, spatial, channel, batch)	"SSCB" (spatial, spatial, channel, batch)
"SCBT" (spatial, channel, batch, time)	"SCBT" (spatial, channel, batch, time)
"SSCBT" (spatial, spatial, channel, batch, time)	"SSCBT" (spatial, spatial, channel, batch, time)
"SSB" (spatial, spatial, batch)	"SSB" (spatial, spatial, batch)
"SSC" (spatial, spatial, channel)	"SSC" (spatial, spatial, channel)
"SCT" (spatial, channel, time)	"SCT" (spatial, channel, time)
"SSCT" (spatial, spatial, channel, time)	"SSCT" (spatial, spatial, channel, time)
"SBT" (spatial, batch, time)	"SBT" (spatial, batch, time)
"SSBT" (spatial, spatial, batch, time)	"SSBT" (spatial, spatial, batch, time)

References

[1] Nagi, J., F. Ducatelle, G. A. Di Caro, D. Ciresan, U. Meier, A. Giusti, F. Nagi, J. Schmidhuber, L. M. Gambardella. ''Max-Pooling Convolutional Neural Networks for Vision-based Hand Gesture Recognition''. IEEE International Conference on Signal and Image Processing Applications (ICSIPA2011), 2011.

Extended Capabilities

C/C++ Code Generation

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

Usage notes and limitations:

• You can generate C/C++ code using "mean" setting for PaddingValue property.

• For Simulink^® models that implement deep learning functionality using MATLAB Function block, simulation errors out if the network contains an average pooling layer with non-zero padding value. In such cases, use the blocks from the Deep Neural Networks library instead of a MATLAB Function to implement the deep learning functionality.

• Code generation does not support passing dlarray objects with unspecified (U) dimensions to this layer.

GPU Code Generation

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

Usage notes and limitations:

• You can generate code using the NVIDIA^® cuDNN and TensorRT libraries by using the "mean" setting for the PaddingValue property if the padding size is symmetric. For example, specify PaddingSize property as the vector [2 2 3 3] to add two rows of padding to the top and bottom, and three columns of padding to the left and right of the input.

• For Simulink models that implement deep learning functionality using MATLAB Function block, simulation errors out if the network contains an average pooling layer with non-zero padding value. In such cases, use the blocks from the Deep Neural Networks library instead of a MATLAB Function to implement the deep learning functionality.

• Code generation does not support passing dlarray objects with unspecified (U) dimensions to this layer.

Version History

Introduced in R2016a