transposedConv2dLayer
Transposed 2D convolution layer
Syntax
Description
A transposed 2D convolution layer upsamples twodimensional 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.
returns a 2D transposed convolution layer and sets the
layer
= transposedConv2dLayer(filterSize
,numFilters
)FilterSize
and NumFilters
properties.
returns a 2D transposed convolutional layer and specifies additional options using
one or more namevalue pair arguments.layer
= transposedConv2dLayer(filterSize
,numFilters
,Name,Value
)
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
NameValue Arguments
Specify optional pairs of arguments as
Name1=Value1,...,NameN=ValueN
, where Name
is
the argument name and Value
is the corresponding value.
Namevalue 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 2D
transposed convolutional layer with 96 filters of size 11 and a stride of
4.
Stride
— Upsampling factor
1
(default)  vector of two positive integers  positive integer
Upsampling factor of the input, specified as one of the following:
A vector of two positive integers
[a b]
, wherea
is the vertical stride andb
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 equalsinputSize.*Stride
, whereinputSize
is the height and width of the layer input. If you set theCropping
option to"same"
, then the software automatically sets theCroppingMode
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]
 Cropa
from the top and bottom and cropb
from the left and right.A vector
[t b l r]
 Cropt
,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, thenNumChannels
must be 3. If the input is the output of a convolutional layer with 16 filters, thenNumChannels
must be 16.
Data Types: single
 double
 int8
 int16
 int32
 int64
 uint8
 uint16
 uint32
 uint64
 char
 string
WeightsInitializer
— Function to initialize weights
'glorot'
(default)  'he'
 'narrownormal'
 '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 variance2/(numIn + numOut)
, wherenumIn = FilterSize(1)*FilterSize(2)*NumChannels
andnumOut = 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 variance2/numIn
, wherenumIn = FilterSize(1)*FilterSize(2)*NumChannels
.'narrownormal'
– 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)
, wheresz
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)  'narrownormal'
 'ones'
 function handle
Function to initialize the biases, specified as one of the following:
'zeros'
— Initialize the biases with zeros.'ones'
— Initialize the biases with ones.'narrownormal'
— 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 be of the form
bias = func(sz)
, wheresz
is the size of the biases.
The layer only initializes the biases when the Bias
property is
empty.
Data Types: char
 string
 function_handle
Weights
— Layer weights
[]
(default)  numeric array
Layer weights for the transposed convolution operation, specified as a
filterSize(1)
byfilterSize(2)
bynumFilters
byNumChannels
numeric array or []
.
The layer weights are learnable parameters. You can specify the
initial value for 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 trainNetwork
uses the Weights
property as the
initial value. If the Weights
property is empty, then
trainNetwork
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 1by1bynumFilters
numeric array or
[]
.
The layer biases are learnable parameters. When you train a
neural network, if Bias
is nonempty, then trainNetwork
uses the Bias
property as the
initial value. If Bias
is empty, then
trainNetwork
uses the initializer specified by BiasInitializer
.
Data Types: single
 double
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
— L_{2} regularization factor for weights
1 (default)  nonnegative scalar
L_{2} regularization factor for the weights, specified as a nonnegative scalar.
The software multiplies this factor by the global L_{2} regularization factor to determine the L_{2} regularization for the weights in this layer. For example, if WeightL2Factor
is 2
, then the L_{2} regularization for the weights in this layer is twice the global L_{2} regularization factor. You can specify the global L_{2} regularization factor using the trainingOptions
function.
Data Types: single
 double
 int8
 int16
 int32
 int64
 uint8
 uint16
 uint32
 uint64
BiasL2Factor
— L_{2} regularization factor for biases
0
(default)  nonnegative scalar
L_{2} regularization factor for the biases, specified as a nonnegative scalar.
The software multiplies this factor by the global
L_{2} regularization factor to
determine the L_{2} regularization for the biases in
this layer. For example, if BiasL2Factor
is 2
, then
the L_{2} regularization for the biases in this layer
is twice the global L_{2} regularization factor. The
software determines the global L_{2} regularization
factor based on the settings you specify using the trainingOptions
function.
Data Types: single
 double
 int8
 int16
 int32
 int64
 uint8
 uint16
 uint32
 uint64
Name
— Layer name
''
(default)  character vector  string scalar
Layer name, specified as a character vector or a string scalar.
For Layer
array input, the trainNetwork
, assembleNetwork
, layerGraph
, and
dlnetwork
functions automatically assign
names to layers with the name ''
.
Data Types: char
 string
Output Arguments
layer
— Transposed 2D convolution layer
TransposedConvolution2DLayer
object
Transposed 2D convolution layer, returned as a TransposedConvolution2DLayer
object.
Algorithms
2D Transposed Convolutional Layer
A transposed 2D convolution layer upsamples twodimensional 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 zeropads 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 3by3 filter upsampling 2by2 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 consists of one or
more of these characters:
"S"
— Spatial"C"
— Channel"B"
— Batch"T"
— Time"U"
— Unspecified
For example, 2D image data represented as a 4D 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, can be
described 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 





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





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 HumanLevel Performance on ImageNet Classification." In Proceedings of the 2015 IEEE International Conference on Computer Vision, 1026–1034. Washington, DC: IEEE Computer Vision Society, 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 R2017bR2019a: 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
'narrownormal'
.
^{1} Image credit: Convolution arithmetic (License)
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