dltranspconv
Deep learning transposed convolution
Syntax
Description
The transposed convolution operation upsamples feature maps.
The dltranspconv
function applies the deep learning transposed
convolution operation to dlarray
data.
Using dlarray
objects makes working with high
dimensional data easier by allowing you to label the dimensions. For example, you can label
which dimensions correspond to spatial, time, channel, and batch dimensions using the
"S"
, "T"
, "C"
, and
"B"
labels, respectively. For unspecified and other dimensions, use the
"U"
label. For dlarray
object functions that operate
over particular dimensions, you can specify the dimension labels by formatting the
dlarray
object directly, or by using the DataFormat
option.
computes the deep learning transposed convolution of the input Y
= dltranspconv(X
,weights
,bias
)X
using the filters defined by weights
, and adds the constant
bias
. The input X
must be a formatted
dlarray
. The output Y
is a formatted
dlarray
with the same dimension format as
X
.
The function, by default, convolves over up to three dimensions
of X
labeled "S"
(spatial). To convolve over dimensions
labeled "T"
(time), specify weights
with a
"T"
dimension using a formatted dlarray
object or by
using the WeightsFormat
option.
For unformatted input data, use the DataFormat
option.
specifies options using one or more name-value pair arguments in addition to the
input arguments in previous syntaxes. For example, Y
= dltranspconv(___Name=Value
)Stride=3
sets
the stride of the convolution operation.
Examples
Perform 2-D Transposed Convolution
Create a formatted dlarray
object containing a batch of 128 28-by-28 images with 3 channels. Specify the format "SSCB"
(spatial, spatial, channel, batch).
miniBatchSize = 128;
inputSize = [28 28];
numChannels = 3;
X = rand(inputSize(1),inputSize(2),numChannels,miniBatchSize);
X = dlarray(X,"SSCB");
View the size and format of the input data.
size(X)
ans = 1×4
28 28 3 128
dims(X)
ans = 'SSCB'
Initialize the weights and bias for 2-D transposed convolution. For the weights, specify 64 3-by-3 filters. For the bias, specify a vector of zeros.
filterSize = [3 3]; numFilters = 64; weights = rand(filterSize(1),filterSize(2),numFilters,numChannels); bias = zeros(1,numFilters);
Apply 2-D transposed convolution using the dltranspconv
function.
Y = dltranspconv(X,weights,bias);
View the size and format of the output.
size(Y)
ans = 1×4
30 30 64 128
dims(Y)
ans = 'SSCB'
Perform Grouped Transposed Convolution
Create a formatted dlarray
object containing a batch of 128 28-by-28 images with 16 channels. Specify the format "SSCB"
(spatial, spatial, channel, batch).
miniBatchSize = 128;
inputSize = [28 28];
numChannels = 16;
X = rand(inputSize(1),inputSize(2),numChannels,miniBatchSize);
X = dlarray(X,"SSCB");
View the size and format of the input data.
size(X)
ans = 1×4
28 28 16 128
dims(X)
ans = 'SSCB'
Initialize the weights and bias for 2-D grouped transposed convolution. For the weights, specify two groups of 64 3-by-3 filters. For the bias, specify a vector of zeros.
The number of channels per group is given by the number of channels of the input data divided by the number of groups. The size of the bias vector is the number of filters per group multiplied by the number of groups.
filterSize = [3 3]; numFiltersPerGroup = 64; numGroups = 2; numChannelsPerGroup = numChannels / numGroups; weights = rand(filterSize(1),filterSize(2),numFiltersPerGroup,numChannelsPerGroup,numGroups); bias = zeros(1,numFiltersPerGroup*numGroups);
Apply 2-D grouped transposed convolution using the dltranspconv
function.
Y = dltranspconv(X,weights,bias);
View the size and format of the output.
size(Y)
ans = 1×4
30 30 128 128
dims(Y)
ans = 'SSCB'
Input Arguments
X
— Input data
dlarray
| numeric array
Input data, specified as a formatted dlarray
, an
unformatted dlarray
, or a numeric array.
If X
is an unformatted dlarray
or a
numeric array, then you must specify the format using the DataFormat
option. If X
is a numeric
array, then either weights
or bias
must be a dlarray
object.
The function, by default, convolves over up to three dimensions
of X
labeled "S"
(spatial). To convolve over dimensions
labeled "T"
(time), specify weights
with a
"T"
dimension using a formatted dlarray
object or by
using the WeightsFormat
option.
weights
— Filters
dlarray
| numeric array
Filters, specified as a formatted dlarray
, an unformatted
dlarray
, or a numeric array.
The size and format of the weights depends on the type of task. If
weights
is an unformatted dlarray
or a numeric array, then the size and shape of weights
depends on the WeightsFormat
option.
The following table describes the size and format of the weights for
various tasks. You can specify an array with the dimensions in any order
using formatted dlarray
objects or by using the
WeightsFormat
option. When the weights has multiple
dimensions with the same label (for example, multiple dimensions labeled
"S"
), then those dimensions must be in ordered as
described in this table.
Task | Required Dimensions | Size | Example | |
---|---|---|---|---|
Weights | Format | |||
1-D transposed convolution | "S" (spatial) or
"T" (time) | Filter size |
| "SCU" (spatial,
channel, unspecified) |
"C" (channel) | Number of channels | |||
"U" (unspecified) | Number of filters | |||
1-D grouped transposed convolution | "S" (spatial) or
"T" (time) | Filter size |
| "SCUU" (spatial,
channel, unspecified, unspecified) |
"C" (channel) | Number of channels per group | |||
First "U" (unspecified) | Number of filters per group | |||
Second "U" (unspecified) | Number of groups | |||
2-D transposed convolution | First "S" (spatial) | Filter height |
| "SSCU" (spatial,
spatial, channel, unspecified) |
Second "S" (spatial) or
"T" (time) | Filter width | |||
"C" (channel) | Number of channels | |||
"U" (unspecified) | Number of filters | |||
2-D grouped transposed convolution | First "S" (spatial) | Filter height |
| "SSCUU" (spatial,
spatial, channel, unspecified, unspecified) |
Second "S" (spatial) or
"T" (time) | Filter width | |||
"C" (channel) | Number of channels per group | |||
First "U" (unspecified) | Number of filters per group | |||
Second "U" (unspecified) | Number of groups | |||
3-D transposed convolution | First "S" (spatial) | Filter height |
| "SSSCU" (spatial,
spatial, spatial, channel, unspecified) |
Second "S" (spatial) | Filter width | |||
Third "S" (spatial) or
"T" (time) | Filter depth | |||
"C" (channel) | Number of channels | |||
"U" (unspecified) | Number of filters |
Tip
The function, by default, convolves over up to three dimensions
of X
labeled "S"
(spatial). To convolve over dimensions
labeled "T"
(time), specify weights
with a
"T"
dimension using a formatted dlarray
object or by
using the WeightsFormat
option.
bias
— Bias constant
dlarray
vector | dlarray
scalar | numeric vector | numeric scalar
Bias constant, specified as a formatted or unformatted
dlarray
vector or dlarray
scalar,
a numeric vector, or a numeric scalar.
If
bias
is a scalar or has only singleton dimensions, the same bias is applied to each entry of the output.If
bias
has a nonsingleton dimension, each element ofbias
is the bias applied to the corresponding convolutional filter specified byweights
. The number of elements ofbias
must match the number of filters specified byweights
.
If bias
is a formatted dlarray
, the
nonsingleton dimension must be a channel dimension labeled
"C"
.
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: Stride=2
sets the stride of each filter to
2.
DataFormat
— Description of data dimensions
character vector | string scalar
Description of the data dimensions, specified as a character vector or string scalar.
A data format is a string of characters, where each character describes the type of the corresponding data dimension.
The characters are:
"S"
— Spatial"C"
— Channel"B"
— Batch"T"
— Time"U"
— Unspecified
For example, consider an array containing a batch of sequences where the first, second,
and third dimensions correspond to channels, observations, and time steps, respectively. You
can specify that this array has the format "CBT"
(channel, batch,
time).
You can specify multiple dimensions labeled "S"
or "U"
.
You can use the labels "C"
, "B"
, and
"T"
once each, at most. The software ignores singleton trailing
"U"
dimensions after the second dimension.
If the input data is not a formatted dlarray
object, then you must
specify the DataFormat
option.
For more information, see Deep Learning Data Formats.
Data Types: char
| string
WeightsFormat
— Description of weights dimensions
character vector | string scalar
Description of weights dimensions, specified as a character vector or string scalar.
A data format is a string of characters, where each character describes the type of the corresponding dimension of the data.
The characters are:
"S"
— Spatial"C"
— Channel"B"
— Batch"T"
— Time"U"
— Unspecified
The default value of WeightsFormat
depends on the
task:
Task | Default |
---|---|
1-D transposed convolution | "SCU" (spatial, channel,
unspecified) |
1-D grouped transposed convolution | "SCUU" (spatial, channel,
unspecified, unspecified) |
2-D transposed convolution | "SSCU" (spatial, spatial,
channel, unspecified) |
2-D grouped transposed convolution | "SSCUU" (spatial, spatial,
channel, unspecified, unspecified) |
3-D transposed convolution | "SSSCU" (spatial, spatial,
spatial, channel, unspecified) |
The supported combinations of dimension labels depends on the type of
convolution, for more information, see the weights
argument.
For more information, see Deep Learning Data Formats.
Tip
The function, by default, convolves over up to three dimensions
of X
labeled "S"
(spatial). To convolve over dimensions
labeled "T"
(time), specify weights
with a
"T"
dimension using a formatted dlarray
object or by
using the WeightsFormat
option.
Data Types: char
| string
Stride
— Step size for traversing input data
1
(default) | numeric scalar | numeric vector
Step size for traversing the input data, specified as a numeric scalar or numeric vector.
To use the same step size for all convolution dimensions, specify the stride as a scalar. To specify a different value for each convolution dimension, specify the stride as a vector with elements ordered corresponding to the dimensions labels in the data format.
Data Types: single
| double
| int8
| int16
| int32
| int64
| uint8
| uint16
| uint32
| uint64
DilationFactor
— Filter dilation factor
1
(default) | numeric scalar | numeric vector
Filter dilation factor, specified as specified as a numeric scalar or numeric vector.
To use the dilation factor all convolution dimensions, specify the dilation factor as a scalar. To specify a different value for each convolution dimension, specify the dilation factor as a vector with elements ordered corresponding to the dimensions labels in the data format.
Use the dilation factor to increase the receptive field of the filter (the area of the input that the filter can see) on the input data. Using a dilation factor corresponds to an effective filter size of filterSize + (filterSize-1)*(dilationFactor-1)
.
Data Types: single
| double
| int8
| int16
| int32
| int64
| uint8
| uint16
| uint32
| uint64
Cropping
— Cropping applied to edges of data
0 (default) | "same"
| numeric scalar | numeric vector | numeric matrix
Cropping applied to edges of data, specified as one of the following.
"same"
— Cropping is set so that the output size is the same as the input size when the stride is1
. More generally, the output size of each spatial dimension isinputSize*stride
, whereinputSize
is the size of the input along the convolution dimension.Numeric scalar — The same cropping value is applied to both ends of the convolution dimensions.
Numeric vector — A different cropping value is applied along each convolution dimension. Use a vector of size
d
, whered
is the number of convolution dimensions of the input data. Thei
th element of the vector specifies the cropping applied to the start and the end along thei
th convolution dimension.Numeric matrix — A different cropping value is applied to the start and end of each convolution dimension. Use a matrix of size 2-by-
d
, whered
is the number of convolution dimensions of the input data. The element(1,d)
specifies the cropping applied to the start of convolution dimensiond
. The element(2,d)
specifies the cropping applied to the end of convolution dimensiond
. For example, in 2-D the format is[top, left; bottom, right]
.
Data Types: single
| double
| int8
| int16
| int32
| int64
| uint8
| uint16
| uint32
| uint64
Output Arguments
Y
— Feature map
dlarray
Feature map, returned as a dlarray
. The output
Y
has the same underlying data type as the input
X
.
If the input data X
is a formatted
dlarray
, then Y
has the same
format as X
. If the input data is not a formatted
dlarray
, then Y
is an unformatted
dlarray
or numeric array with the same dimension
order as the input data.
The size of the "C"
(channel) dimension of
Y
depends on the size of the
weights
input. The size of the "C"
(channel) dimension of output Y
is the product of the
size of the dimensions numFiltersPerGroup
and
numGroups
in the weights
argument.
If weights
is a formatted dlarray
,
this product is the same as the product of the size of the
"C"
(channel) dimension and the second
"U"
(unspecified) dimension.
Algorithms
Transposed Convolution
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 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 , 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.
Extended Capabilities
GPU Arrays
Accelerate code by running on a graphics processing unit (GPU) using Parallel Computing Toolbox™.
The dltranspconv
function
supports GPU array input with these usage notes and limitations:
When at least one of the following input arguments is a
gpuArray
or adlarray
with underlying data of typegpuArray
, this function runs on the GPU.X
weights
bias
For more information, see Run MATLAB Functions on a GPU (Parallel Computing Toolbox).
Version History
Introduced in R2019b
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