transposedConv3dLayer
Syntax
Description
A transposed 3D convolution layer upsamples threedimensional 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 3D transposed convolution layer and sets the
layer
= transposedConv3dLayer(filterSize
,numFilters
)FilterSize
and NumFilters
properties.
returns a 3D transposed convolutional layer and specifies additional options using
one or more namevalue pair arguments.layer
= transposedConv3dLayer(filterSize
,numFilters
,Name,Value
)
Examples
Create Transposed 3D Convolutional Layer
Create a transposed 3D convolutional layer with 32 filters, each with a height, width, and depth of 11. Use a stride of 4 in the horizontal and vertical directions and 2 along the depth.
layer = transposedConv3dLayer(11,32,'Stride',[4 4 2])
layer = TransposedConvolution3DLayer with properties: Name: '' Hyperparameters FilterSize: [11 11 11] NumChannels: 'auto' NumFilters: 32 Stride: [4 4 2] CroppingMode: 'manual' CroppingSize: [2x3 double] Learnable Parameters Weights: [] Bias: [] Use properties method to see a list of all properties.
Input Arguments
filterSize
— Height, width, and depth of filters
positive integer  vector of three positive integers
Height, width, and depth of the filters, specified as a positive integer
or a vector of three positive integers [h w d]
, where
h
is the height, w
is the width,
and d
is the depth. The filter size defines the size of
the local regions to which the neurons connect in the input.
If filterSize
is a scalar, then the software uses the
same value for all three dimensions.
Example:
[5 6 7]
specifies filters with a height, width, and depth
of 5
, 6
, and 7
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: transposedConv3dLayer(11,96,'Stride',4)
creates a 3D
transposed convolutional layer with 96 filters of size 11 and a stride of
4.
Stride
— Step size for traversing input
[1 1 1]
(default)  vector of three positive integers
Step size for traversing the input in three dimensions, specified as a vector
[a b c]
of three positive integers, where a
is
the vertical step size, b
is the horizontal step size, and
c
is the step size along the depth. When creating the layer, you
can specify Stride
as a scalar to use the same value for step sizes
in all three directions.
Example:
[2 3 1]
specifies a vertical step size of 2, a horizontal step size
of 3, and a step size along the depth of 1.
Data Types: single
 double
 int8
 int16
 int32
 int64
 uint8
 uint16
 uint32
 uint64
Cropping
— Output size reduction
0
(default) 
"same"
 vector of nonnegative integers  matrix of 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, width, and depth 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, the left and right, and the front and back, 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. If the depth crop amount has an odd value, then the software trims an extra plane from the back.
A positive integer – Crop the specified amount of data from all the edges.
A vector of nonnegative integers
[a b c]
– Cropa
from the top and bottom, cropb
from the left and right, and cropc
from the front and back.a matrix of nonnegative integers
[t l f; b r bk]
of nonnegative integers — Cropt
,l
,f
,b
,r
,bk
from the top, left, front, bottom, right, and back 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 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)*FilterSize(3)*NumChannels
andnumOut = FilterSize(1)*FilterSize(2)*FilterSize(3)*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)*FilterSize(3)*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 these values:
"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 have the form
bias = func(sz)
, wheresz
is the size of the biases.
The layer initializes the biases only 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)
byFilterSize(3)
bynumFilters
byNumChannels
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
and
trainNetwork
functions use 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 1by1by1bynumFilters
numeric array or
[]
.
The layer biases are learnable parameters. When you train a neural network, if Bias
is nonempty, then the trainnet
and trainNetwork
functions use the Bias
property as the initial value. If Bias
is empty, then software 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 trainnet
, trainNetwork
, assembleNetwork
, layerGraph
, and
dlnetwork
functions automatically assign
names to layers with the name ""
.
The transposedConv3dLayer
object stores this property as a character vector.
Data Types: char
 string
Output Arguments
layer
— Transposed 3D convolution layer
TransposedConvolution3DLayer
object
Transposed 3D convolution layer, returned as a TransposedConvolution3dLayer
object.
Algorithms
3D Transposed Convolutional Layer
A transposed 3D convolution layer upsamples threedimensional 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.
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
TransposedConvolution3DLayer
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, TransposedConvolution3DLayer
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 2015 IEEE International Conference on Computer Vision (ICCV), 1026–34. Santiago, Chile: IEEE, 2015. https://doi.org/10.1109/ICCV.2015.123
Version History
Introduced in R2019a
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