transposedConv2dLayer

Transposed 2-D convolution layer

Syntax

layer = transposedConv2dLayer(filterSize,numFilters)

layer = transposedConv2dLayer(filterSize,numFilters,Name,Value)

Description

A transposed 2-D convolution layer upsamples two-dimensional feature maps.

This layer is sometimes incorrectly known as a "deconvolution" or "deconv" layer. This layer performs the transpose of convolution and does not perform deconvolution.

layer = transposedConv2dLayer(filterSize,numFilters) returns a 2-D transposed convolution layer and sets the FilterSize and NumFilters properties.

layer = transposedConv2dLayer(filterSize,numFilters,Name,Value) returns a 2-D transposed convolutional layer and specifies additional options using one or more name-value pair arguments.

Examples

Create Transposed Convolutional Layer

Create a transposed convolutional layer with 96 filters, each with a height and width of 11. Use a stride of 4 in the horizontal and vertical directions.

layer = transposedConv2dLayer(11,96,'Stride',4);

Input Arguments

filterSize — Height and width of filters

positive integer | vector of two positive integers

Height and width of the filters, specified as a positive integer or a vector of two positive integers [h w], where h is the height and w is the width. The filter size defines the size of the local regions to which the neurons connect in the input.

If filterSize is a positive integer, then the software uses the same value for both dimensions.

Example: [5 6] specifies filters of height and width of 5 and 6, respectively.

Data Types: single | double | int8 | int16 | int32 | int64 | uint8 | uint16 | uint32 | uint64

numFilters — Number of filters

positive integer

Number of filters, specified as a positive integer. This number corresponds to the number of neurons in the layer that connect to the same region in the input. This parameter determines the number of channels (feature maps) in the output of the layer.

Data Types: single | double | int8 | int16 | int32 | int64 | uint8 | uint16 | uint32 | uint64

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: transposedConv2dLayer(11,96,'Stride',4) creates a 2-D transposed convolutional layer with 96 filters of size 11 and a stride of 4.

Transposed Convolution

Stride — Up-sampling factor

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

Up-sampling factor of the input, specified as one of the following:

• A vector of two positive integers [a b], where a is the vertical stride and b is the horizontal stride.

• A positive integer the corresponds to both the vertical and horizontal stride.

Example: 'Stride',[2 1]

Data Types: single | double | int8 | int16 | int32 | int64 | uint8 | uint16 | uint32 | uint64

Cropping — Output size reduction

0 (default) | "same" | nonnegative integer | vector of two nonnegative integers

Output size reduction, specified as one of the following:

• "same" – Set the cropping so that the output size equals inputSize.*Stride, where inputSize is the height and width of the layer input. If you set the Cropping option to "same", then the software automatically sets the CroppingMode property of the layer to 'same'.

  The software trims an equal amount from the top and bottom, and the left and right, if possible. If the vertical crop amount has an odd value, then the software trims an extra row from the bottom. If the horizontal crop amount has an odd value, then the software trims an extra column from the right.

• A positive integer – Crop the specified amount of data from all the edges.

• A vector of nonnegative integers [a b] - Crop a from the top and bottom and crop b from the left and right.

• A vector [t b l r] - Crop t, b, l, r from the top, bottom, left, and right of the input, respectively.

If you set the Cropping option to a numeric value, then the software automatically sets the CroppingMode property of the layer to 'manual'.

Example: [1 2]

Data Types: single | double | int8 | int16 | int32 | int64 | uint8 | uint16 | uint32 | uint64 | char | string

NumChannels — Number of input channels

"auto" (default) | positive integer

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

Parameters and Initialization

WeightsInitializer — Function to initialize weights

"glorot" (default) | "he" | "narrow-normal" | "zeros" | "ones" | function handle

Function to initialize the weights, specified as one of the following:

• "glorot" – Initialize the weights with the Glorot initializer [1] (also known as Xavier initializer). The Glorot initializer independently samples from a uniform distribution with zero mean and variance 2/(numIn + numOut), where numIn = FilterSize(1)*FilterSize(2)*NumChannels and numOut = FilterSize(1)*FilterSize(2)*NumFilters.

• "he" – Initialize the weights with the He initializer [2]. The He initializer samples from a normal distribution with zero mean and variance 2/numIn, where numIn = FilterSize(1)*FilterSize(2)*NumChannels.

• "narrow-normal" – Initialize the weights by independently sampling from a normal distribution with zero mean and standard deviation 0.01.

• "zeros" – Initialize the weights with zeros.

• "ones" – Initialize the weights with ones.

• Function handle – Initialize the weights with a custom function. If you specify a function handle, then the function must be of the form weights = func(sz), where sz is the size of the weights. For an example, see Specify Custom Weight Initialization Function.

The layer only initializes the weights when the Weights property is empty.

Data Types: char | string | function_handle

BiasInitializer — Function to initialize biases

"zeros" (default) | "narrow-normal" | "ones" | function handle

Function to initialize the biases, specified as one of these values:

• "zeros" — Initialize the biases with zeros.

• "ones" — Initialize the biases with ones.

• "narrow-normal" — Initialize the biases by independently sampling from a normal distribution with a mean of zero and a standard deviation of 0.01.

• Function handle — Initialize the biases with a custom function. If you specify a function handle, then the function must have the form bias = func(sz), where sz is the size of the biases.

The layer initializes the biases only when the Bias property is empty.

The transposedConv2dLayer object stores this property as a character vector or a function handle.

Data Types: char | string | function_handle

Weights — Layer weights

[] (default) | numeric array

Layer weights for the transposed convolution operation, specified as a filterSize(1)-by-filterSize(2)-by-numFilters-by-NumChannels numeric array or [].

The layer weights are learnable parameters. You can specify the initial value of the weights directly using the Weights property of the layer. When you train a network, if the Weights property of the layer is nonempty, then the trainnet function uses the Weights property as the initial value. If the Weights property is empty, then the software uses the initializer specified by the WeightsInitializer property of the layer.

Data Types: single | double

Bias — Layer biases

[] (default) | numeric array

Layer biases for the transposed convolutional operation, specified as a 1-by-1-by-numFilters numeric array or [].

The layer biases are learnable parameters. When you train a neural network, if Bias is nonempty, then the trainnet function uses the Bias property as the initial value. If Bias is empty, then software uses the initializer specified by BiasInitializer.

Data Types: single | double

Learning Rate and Regularization

WeightLearnRateFactor — Learning rate factor for weights

1 (default) | nonnegative scalar

Learning rate factor for the weights, specified as a nonnegative scalar.

The software multiplies this factor by the global learning rate to determine the learning rate for the weights in this layer. For example, if WeightLearnRateFactor is 2, then the learning rate for the weights in this layer is twice the current global learning rate. The software determines the global learning rate based on the settings you specify using the trainingOptions function.

Data Types: single | double | int8 | int16 | int32 | int64 | uint8 | uint16 | uint32 | uint64

BiasLearnRateFactor — Learning rate factor for biases

1 (default) | nonnegative scalar

Learning rate factor for the biases, specified as a nonnegative scalar.

The software multiplies this factor by the global learning rate to determine the learning rate for the biases in this layer. For example, if BiasLearnRateFactor is 2, then the learning rate for the biases in the layer is twice the current global learning rate. The software determines the global learning rate based on the settings you specify using the trainingOptions function.

Data Types: single | double | int8 | int16 | int32 | int64 | uint8 | uint16 | uint32 | uint64

WeightL2Factor — L₂ regularization factor for weights

1 (default) | nonnegative scalar

L₂ regularization factor for the weights, specified as a nonnegative scalar.

The software multiplies this factor by the global L₂ regularization factor to determine the L₂ regularization for the weights in this layer. For example, if WeightL2Factor is 2, then the L₂ regularization for the weights in this 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

BiasL2Factor — L₂ regularization factor for biases

0 (default) | nonnegative scalar

L₂ regularization factor for the biases, specified as a nonnegative scalar.

The software multiplies this factor by the global L₂ regularization factor to determine the L₂ regularization for the biases in this layer. For example, if BiasL2Factor is 2, then the L₂ regularization for the biases in this layer is twice the global L₂ regularization factor. The software determines the global L₂ regularization factor based on the settings you specify using the trainingOptions function.

Data Types: single | double | int8 | int16 | int32 | int64 | uint8 | uint16 | uint32 | uint64

Layer

Name — Layer name

"" (default) | character vector | string scalar

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

The transposedConv2dLayer object stores this property as a character vector.

Data Types: char | string

Output Arguments

layer — Transposed 2-D convolution layer

TransposedConvolution2DLayer object

Transposed 2-D convolution layer, returned as a TransposedConvolution2DLayer object.

Algorithms

2-D Transposed Convolutional Layer

A transposed 2-D convolution layer upsamples two-dimensional feature maps.

The standard convolution operation downsamples the input by applying sliding convolutional filters to the input. By flattening the input and output, you can express the convolution operation as $$Y=CX+B$$ for the convolution matrix C and bias vector B that can be derived from the layer weights and biases.

Similarly, the transposed convolution operation upsamples the input by applying sliding convolutional filters to the input. To upsample the input instead of downsampling using sliding filters, the layer zero-pads each edge of the input with padding that has the size of the corresponding filter edge size minus 1.

By flattening the input and output, the transposed convolution operation is equivalent to $$Y=C^{\top }X+B$$, where C and B denote the convolution matrix and bias vector for standard convolution derived from the layer weights and biases, respectively. This operation is equivalent to the backward function of a standard convolution layer.

This image shows a 3-by-3 filter upsampling 2-by-2 input. The lower map represents the input and the upper map represents the output. ¹

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 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 TransposedConvolution2DLayer objects and the corresponding output format. If the output of the layer is passed 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 corresponding to the formats in this table.

Input Format	Output Format
"SSCB" (spatial, spatial, channel, batch)	"SSCB" (spatial, spatial, channel, batch)
"SSC" (spatial, spatial, channel)	"SSC" (spatial, spatial, channel)

In dlnetwork objects, TransposedConvolution2DLayer objects also support these input and output format combinations.

Input Format	Output Format
"SSCBT" (spatial, spatial, channel, batch, time)	"SSCBT" (spatial, spatial, channel, batch, time)
"SSCT" (spatial, spatial, channel, time)	"SSCT" (spatial, spatial, channel, time)

References

[1] Glorot, Xavier, and Yoshua Bengio. "Understanding the Difficulty of Training Deep Feedforward Neural Networks." In Proceedings of the Thirteenth International Conference on Artificial Intelligence and Statistics, 249–356. Sardinia, Italy: AISTATS, 2010. https://proceedings.mlr.press/v9/glorot10a/glorot10a.pdf

[2] He, Kaiming, Xiangyu Zhang, Shaoqing Ren, and Jian Sun. "Delving Deep into Rectifiers: Surpassing Human-Level Performance on ImageNet Classification." In 2015 IEEE International Conference on Computer Vision (ICCV), 1026–34. Santiago, Chile: IEEE, 2015. https://doi.org/10.1109/ICCV.2015.123

Extended Capabilities

C/C++ Code Generation

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

Usage notes and limitations:

• Code generation does not support asymmetric cropping of the input. For example, specifying a vector [t b l r] for the 'Cropping' parameter to crop the top, bottom, left, and right of the input is not supported.

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

Version History

Introduced in R2017b

R2019a: Default weights initialization is Glorot

Starting in R2019a, the software, by default, initializes the layer weights of this layer using the Glorot initializer. This behavior helps stabilize training and usually reduces the training time of deep networks.

In previous releases, the software, by default, initializes the layer weights by sampling from a normal distribution with zero mean and variance 0.01. To reproduce this behavior, set the 'WeightsInitializer' option of the layer to 'narrow-normal'.