TransposedConvolution2DLayer
Transposed 2-D convolution layer
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 is the transpose of convolution and does not perform deconvolution.
Creation
Create a transposed convolution 2-D layer using transposedConv2dLayer
.
Properties
Transposed Convolution
FilterSize
— Height and width of filters
vector of two positive integers
Height and width of the filters, specified as a vector of two positive
integers [h w]
, where h
is the
height and w
is the width.
FilterSize
defines the size of the local
regions to which the neurons connect in the input.
If you set FilterSize
using an input argument,
then you can specify FilterSize
as scalar to use
the same value for both dimensions.
Example:
[5 5]
specifies filters of height 5 and width
5.
Data Types: single
| double
| int8
| int16
| int32
| int64
| uint8
| uint16
| uint32
| uint64
NumFilters
— Number of filters
positive integer
This property is read-only.
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]
(default) | vector of two positive integers
Step size for traversing the input vertically and horizontally, specified as a vector
[a b]
of two positive integers, 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 step sizes.
Example:
[2 3]
specifies a vertical step size of 2 and a horizontal step size
of 3.
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 and width of the layer input.
To specify the cropping size, use the 'Cropping'
option of transposedConv2dLayer
.
CroppingSize
— Output size reduction
[0 0 0 0]
(default) | vector of four nonnegative integers
Output size reduction, specified as a vector of four nonnegative
integers [t b l r]
, where t
,
b
, l
, r
are
the amounts to crop from the top, bottom, left, and right,
respectively.
To specify the cropping size manually, use the 'Cropping'
option of transposedConv2dLayer
.
Example:
[0 1 0 1]
Cropping
— Output size reduction
[0 0]
(default) | vector of two nonnegative integers
Note
Cropping
property will be removed in a future
release. Use CroppingSize
instead. To specify the cropping size
manually, use the 'Cropping'
option of transposedConv2dLayer
.
Output size reduction, specified as a vector of two nonnegative
integers [a b]
, where a
corresponds to the cropping from the top and bottom and
b
corresponds to the cropping from the left and
right.
To specify the cropping size manually, use the 'Cropping'
option of transposedConv2dLayer
.
Example:
[0 1]
NumChannels
— Number of input channels
'auto'
(default) | positive integer
This property is read-only.
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'
| '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 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
.'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)
, 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 bias
'zeros'
(default) | 'narrow-normal'
| 'ones'
| function handle
Function to initialize the bias, specified as one of the following:
'zeros'
— Initialize the bias with zeros.'ones'
— Initialize the bias with ones.'narrow-normal'
— Initialize the bias by independently sampling from a normal distribution with a mean of zero and a standard deviation of 0.01.Function handle — Initialize the bias 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 bias.
The layer only initializes the bias when the Bias
property is
empty.
Data Types: char
| string
| function_handle
Weights
— Layer weights
[]
(default) | numeric array
Layer weights for the convolutional layer, specified as a
FilterSize(1)
-by-FilterSize(2)
-by-NumFilters
-by-NumChannels
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.
Data Types: single
| double
Bias
— Layer biases
[]
(default) | numeric array
Layer biases for the convolutional layer, specified as a numeric array.
The layer biases are learnable parameters. When you train a
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
1-by-1-by-NumFilters
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
— 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. You can
specify the global L2 regularization factor 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 name
''
.
Data Types: char
| string
NumInputs
— Number of inputs
1
(default)
This property is read-only.
Number of inputs of the layer. This layer accepts a single input only.
Data Types: double
InputNames
— Input names
{'in'}
(default)
This property is read-only.
Input names of the layer. This layer accepts a single input only.
Data Types: cell
NumOutputs
— Number of outputs
1
(default)
This property is read-only.
Number of outputs of the layer. This layer has a single output only.
Data Types: double
OutputNames
— Output names
{'out'}
(default)
This property is read-only.
Output names of the layer. This layer has a single output only.
Data Types: cell
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);
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 for the convolution matrix C and bias 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 , where C and B denote the convolution and bias matrices 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 4-by-4 filter upsampling 2-by-2 input. The lower map represents the input and the upper map represents the output. 1
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.
[2] He, Kaiming, Xiangyu Zhang, Shaoqing Ren, and Jian Sun. "Delving Deep into Rectifiers: Surpassing Human-Level Performance on ImageNet Classification." In Proceedings of the 2015 IEEE International Conference on Computer Vision, 1026–1034. Washington, DC: IEEE Computer Vision Society, 2015.
Version History
Introduced in R2017bR2019a: Default weights initialization is Glorot
Behavior changed in R2019a
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'
.
R2019a: Cropping
property of TransposedConvolution2DLayer
will be removed
Not recommended starting in R2019a
Cropping
property of
TransposedConvolution2DLayer
will be removed, use CroppingSize
instead. To update your code, replace all instances of
the Cropping
property with
CroppingSize
.
1 Image credit: Convolution arithmetic (License)
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