maxPooling2dLayer

Max pooling layer

Description

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

Creation

Syntax

layer = maxPooling2dLayer(poolSize)

layer = maxPooling2dLayer(poolSize,Name=Value)

Description

layer = maxPooling2dLayer(poolSize) creates a max pooling layer and sets the PoolSize property.

layer = maxPooling2dLayer(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.

Before R2021a, use commas to separate each name and value, and enclose Name in quotes.

Example: maxPooling2dLayer(2,Stride=3) creates a max pooling layer with pool size [2 2] and stride [3 3].

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).

HasUnpoolingOutputs — Flag for outputs to unpooling layer

false (default) | true

Flag for outputs to unpooling layer, specified as true or false.

If the HasUnpoolingOutputs value equals false, then the max pooling layer has a single output with the name 'out'.

To use the output of a max pooling layer as the input to a max unpooling layer, set the HasUnpoolingOutputs value to true. In this case, the max pooling layer has two additional outputs that you can connect to a max unpooling layer:

• "indices" — Indices of the maximum value in each pooled region.

• "size" — Size of the input feature map.

To enable outputs to a max unpooling layer, the pooling regions of the max pooling layer must be nonoverlapping.

For more information on how to unpool the output of a max pooling layer, see maxUnpooling2dLayer.

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

Max 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.

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.

HasUnpoolingOutputs — Flag for outputs to unpooling layer

false (default) | true

Flag for outputs to unpooling layer, specified as true or false.

If the HasUnpoolingOutputs value equals false, then the max pooling layer has a single output with the name 'out'.

To use the output of a max pooling layer as the input to a max unpooling layer, set the HasUnpoolingOutputs value to true. In this case, the max pooling layer has two additional outputs that you can connect to a max unpooling layer:

• "indices" — Indices of the maximum value in each pooled region.

• "size" — Size of the input feature map.

To enable outputs to a max unpooling layer, the pooling regions of the max pooling layer must be nonoverlapping.

For more information on how to unpool the output of a max pooling layer, see maxUnpooling2dLayer.

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 MaxPooling2DLayer 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

1 (default) | 3

Number of outputs of the layer.

If the HasUnpoolingOutputs value equals false, then the max pooling layer has a single output with the name 'out'.

To use the output of a max pooling layer as the input to a max unpooling layer, set the HasUnpoolingOutputs value to true. In this case, the max pooling layer has two additional outputs that you can connect to a max unpooling layer:

• "indices" — Indices of the maximum value in each pooled region.

• "size" — Size of the input feature map.

To enable outputs to a max unpooling layer, the pooling regions of the max pooling layer must be nonoverlapping.

For more information on how to unpool the output of a max pooling layer, see maxUnpooling2dLayer.

Data Types: double

OutputNames — Output names

{'out'} (default) | {'out','indices','size'}

Output names of the layer.

If the HasUnpoolingOutputs value equals false, then the max pooling layer has a single output with the name 'out'.

To use the output of a max pooling layer as the input to a max unpooling layer, set the HasUnpoolingOutputs value to true. In this case, the max pooling layer has two additional outputs that you can connect to a max unpooling layer:

• "indices" — Indices of the maximum value in each pooled region.

• "size" — Size of the input feature map.

To enable outputs to a max unpooling layer, the pooling regions of the max pooling layer must be nonoverlapping.

For more information on how to unpool the output of a max pooling layer, see maxUnpooling2dLayer.

Data Types: cell

Examples

Create Max Pooling Layer with Nonoverlapping Pooling Regions

Create a max pooling layer with nonoverlapping pooling regions.

layer = maxPooling2dLayer(2,'Stride',2)

layer = 
  MaxPooling2DLayer with properties:

                   Name: ''
    HasUnpoolingOutputs: 0
             NumOutputs: 1
            OutputNames: {'out'}

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

The height and the 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 2].

Include a max pooling layer with nonoverlapping regions in a Layer array.

layers = [ ...
    imageInputLayer([28 28 1])
    convolution2dLayer(5,20)
    reluLayer
    maxPooling2dLayer(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 Max Pooling   2×2 max pooling with stride [2  2] and padding [0  0  0  0]
     5   ''   Fully Connected   10 fully connected layer
     6   ''   Softmax           softmax

Create Max Pooling Layer with Overlapping Pooling Regions

Create a max pooling layer with overlapping pooling regions.

layer = maxPooling2dLayer([3 2],Stride=2)

layer = 
  MaxPooling2DLayer with properties:

                   Name: ''
    HasUnpoolingOutputs: 0
             NumOutputs: 1
            OutputNames: {'out'}

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

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

Include a max pooling layer with overlapping pooling regions in a Layer array.

layers = [ ...
    imageInputLayer([28 28 1])
    convolution2dLayer(5,20)
    reluLayer
    maxPooling2dLayer([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 Max Pooling   3×2 max pooling with stride [2  2] and padding [0  0  0  0]
     5   ''   Fully Connected   10 fully connected layer
     6   ''   Softmax           softmax

Algorithms

2-D Max Pooling Layer

A 2-D max pooling layer performs downsampling by dividing the input into rectangular pooling regions, then computing the maximum 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 MaxPooling2DLayer 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)

When the HasUnpoolingOutputs property is 1 (true), the "size" output of the layer outputs unformatted dlarray objects. (since R2024b)

Before R2024b: The "size" output of the layer outputs a numeric array.

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:

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

• If equal max values exists along the off-diagonal in a kernel window, implementation differences for the maxPooling2dLayer might cause minor numerical mismatch between MATLAB^® and the generated code. This issue also causes mismatch in the indices of the maximum value in each pooled region.

  For example, consider the following input to maxPooling2dLayer. The output from MATLAB is shown.

  

  For the same input, the output from the generated code is shown.

  

GPU Code Generation

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

Refer to the usage notes and limitations in the C/C++ Code Generation section. The same limitations apply to GPU code generation.

Version History

Introduced in R2016a

R2024b: Layer outputs pooling sizes as dlarray objects

When the HasUnpoolingOutputs property is 1 (true), the "size" output of the layer outputs unformatted dlarray objects. In previous versions, the "size" output of the layer outputs a numeric array.

In most cases, there is no change in behavior and you do not need to update your code. If you have code that relies on the output being a numeric array, then to extract the numeric data from the dlarray object, use the extractdata function.