TransposedConvolution3dLayer
Description
A transposed 3D convolution layer upsamples threedimensional feature maps.
This layer is sometimes incorrectly known as a "deconvolution" or "deconv" layer. This layer is the transpose of convolution and does not perform deconvolution.
Creation
Create a transposed convolution 3D layer using transposedConv3dLayer
.
Properties
Transposed Convolution
FilterSize
— Height, width, and depth of filters
vector of three positive integers
Height, width, and depth of the filters, specified as a vector [h w
d]
of three positive integers, where h
is the height,
w
is the width, and d
is the depth.
FilterSize
defines the size of the local regions to which the
neurons connect in the input.
When creating the layer, you can specify FilterSize
as a
scalar to use the same value for the height, width, and depth.
Example:
[5 5 5]
specifies filters with a height, width, and depth of
5.
NumFilters
— Number of filters
positive integer
This property is readonly.
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 layer output.
Data Types: single
 double
 int8
 int16
 int32
 int64
 uint8
 uint16
 uint32
 uint64
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
CroppingMode
— Method to determine cropping size
'manual'
(default)  'same'
Method to determine cropping size, specified as 'manual'
or
'same'
.
The software automatically sets the value of CroppingMode
based on the 'Cropping'
value you
specify when creating the layer.
If you set the
Cropping
option to a numeric value, then the software automatically sets theCroppingMode
property of the layer to'manual'
.If you set the
'Cropping'
option to'same'
, then the software automatically sets theCroppingMode
property of the layer to'same'
and set the cropping so that the output size equalsinputSize .* Stride
, whereinputSize
is the height, width, and depth of the layer input.
To specify the cropping size, use the 'Cropping'
option of transposedConv3dLayer
.
CroppingSize
— Output size reduction
[0 0 0;0 0 0]
(default)  matrix of nonnegative integers
Output size reduction, specified as a matrix of nonnegative integers [t l
f; b r bk]
, t
, l
,
f
, b
, r
,
bk
are the amounts to crop from the top, left, front, bottom,
right, and back of the input, respectively.
To specify the cropping size manually, use the 'Cropping'
option of transposedConv2dLayer
.
Example:
[0 1 0 1 0 1]
NumChannels
— Number of input channels
'auto'
(default)  positive integer
This property is readonly.
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
Parameters and Initialization
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 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 convolutional layer, specified as a numeric array.
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.
At training time, Weights
is a
FilterSize(1)
byFilterSize(2)
byFilterSize(3)
byNumFilters
byNumChannels
array.
Data Types: single
 double
Bias
— Layer biases
[]
(default)  numeric array
Layer biases for the transposed convolutional layer, specified as a numeric array.
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
.
At training time, Bias
is a
1by1by1byNumFilters
array.
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
— 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
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 trainNetwork
, assembleNetwork
, layerGraph
, and
dlnetwork
functions automatically assign
names to layers with the name ''
.
Data Types: char
 string
NumInputs
— Number of inputs
1
(default)
This property is readonly.
Number of inputs of the layer. This layer accepts a single input only.
Data Types: double
InputNames
— Input names
{"in"}
(default)
This property is readonly.
Input names of the layer. This layer accepts a single input only.
Data Types: cell
NumOutputs
— Number of outputs
1
(default)
This property is readonly.
Number of outputs of the layer. This layer has a single output only.
Data Types: double
OutputNames
— Output names
{'out'}
(default)
This property is readonly.
Output names of the layer. This layer has a single output only.
Data Types: cell
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: [] Show all properties
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 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
Version History
Introduced in R2019a
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