dlconv
Description
The convolution operation applies sliding filters to the input
data. Use the dlconv
function for deep learning convolution, grouped
convolution, and channelwise separable convolution.
The dlconv
function applies the deep learning 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.
applies the deep learning convolution operation to the formatted
Y
= dlconv(X
,weights
,bias
)dlarray
object X
. The function uses sliding
convolutional filters defined by weights
and adds the constant
bias
. The output Y
is a formatted
dlarray
object with the same 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.
applies the deep learning convolution operation to the unformatted
Y
= dlconv(X
,weights
,bias
,DataFormat=FMT)dlarray
object X
with format specified by
FMT
. The output Y
is an unformatted
dlarray
object with dimensions in the same order as
X
. For example, DataFormat="SSCB"
specifies data for 2D convolution with format "SSCB"
(spatial,
spatial, channel, batch).
specifies options using one or more namevalue pair arguments using any of the
previous syntaxes. For example, Y
= dlconv(___,Name=Value
)WeightsFormat="TCU"
specifies
weights for 1D convolution with format "TCU"
(time, channel,
unspecified).
Examples
Perform 2D Convolution
Create a formatted dlarray
object containing a batch of 128 28by28 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 2D convolution. For the weights, specify 64 3by3 filters. For the bias, specify a vector of zeros.
filterSize = [3 3]; numFilters = 64; weights = rand(filterSize(1),filterSize(2),numChannels,numFilters); bias = zeros(1,numFilters);
Apply 2D convolution using the dlconv
function.
Y = dlconv(X,weights,bias);
View the size and format of the output.
size(Y)
ans = 1×4
26 26 64 128
dims(Y)
ans = 'SSCB'
Perform Grouped Convolution
Convolve the input data in three groups of two channels each. Apply four filters per group.
Create the input data as 10 observations of size 100by100 with six channels.
height = 100;
width = 100;
channels = 6;
numObservations = 10;
X = rand(height,width,channels,numObservations);
X = dlarray(X,"SSCB");
Initialize the convolutional filters. Specify three groups of convolutions that each apply four convolution filters to two channels of the input data.
filterHeight = 8; filterWidth = 8; numChannelsPerGroup = 2; numFiltersPerGroup = 4; numGroups = 3; weights = rand(filterHeight,filterWidth,numChannelsPerGroup,numFiltersPerGroup,numGroups);
Initialize the bias term.
bias = rand(numFiltersPerGroup*numGroups,1);
Perform the convolution.
Y = dlconv(X,weights,bias); size(Y)
ans = 1×4
93 93 12 10
dims(Y)
ans = 'SSCB'
The 12 channels of the convolution output represent the three groups of convolutions with four filters per group.
Perform ChannelWise Separable Convolution
Separate the input data into channels and perform convolution on each channel separately.
Create the input data as a single observation with a size of 64by64 and 10 channels. Create the data as an unformatted dlarray
.
height = 64; width = 64; numChannels = 10; X = rand(height,width,numChannels); X = dlarray(X);
Initialize the convolutional filters. Specify an ungrouped convolution that applies a single convolution to all three channels of the input data.
filterHeight = 8; filterWidth = 8; numChannelsPerGroup = 1; numFiltersPerGroup = 1; numGroups = numChannels; weights = rand(filterHeight,filterWidth,numChannelsPerGroup,numFiltersPerGroup,numGroups);
Initialize the bias term.
bias = rand(numFiltersPerGroup*numGroups,1);
Perform the convolution. Specify the dimension labels of the input data using the DataFormat
option.
Y = dlconv(X,weights,bias,DataFormat="SSC");
size(Y)
ans = 1×3
57 57 10
Each channel is convolved separately, so there are 10 channels in the output.
Perform 1D Convolution
Create a formatted dlarray
object containing 128 sequences of length 512 containing 5 features. Specify the format "CBT"
(channel, batch, time).
numChannels = 5;
miniBatchSize = 128;
sequenceLength = 512;
X = rand(numChannels,miniBatchSize,sequenceLength);
X = dlarray(X,"CBT");
Initialize the weights and bias for 1D convolution. For the weights, specify 64 filters with a filter size of 3. For the bias, specify a vector of zeros.
filterSize = 3; numFilters = 64; weights = rand(filterSize,numChannels,numFilters); bias = zeros(1,numFilters);
Apply 1D convolution using the dlconv
function. To convolve over the "T"
(time) dimension of the input data, specify the weights format "TCU"
(time, channel, unspecified) using the WeightsFormat
option.
Y = dlconv(X,weights,bias,WeightsFormat="TCU");
View the size and format of the output.
size(Y)
ans = 1×3
64 128 510
dims(Y)
ans = 'CBT'
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
— Convolutional filters
dlarray
 numeric array
Convolutional 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  
1D convolution  "S" (spatial) or
"T" (time)  Filter size 
 "SCU" (spatial,
channel, unspecified) 
"C" (channel)  Number of channels  
"U" (unspecified)  Number of filters  
1D grouped 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  
2D 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  
2D grouped 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  
3D 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 
For channelwise separable (also known as depthwise separable) convolution, use grouped convolution with number of groups equal to the number of channels.
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
 numeric vector  numeric scalar
Bias constant, specified as a formatted dlarray
, an
unformatted dlarray
, a numeric vector, or a numeric
scalar.
If
bias
is a scalar, then the same bias is applied to each output.If
bias
has a nonsingleton dimension, then 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
is0
, then the bias term is disabled and no bias is added during the convolution operation.
If bias
is a formatted dlarray
, then
the nonsingleton dimension must be a channel dimension with label
'C'
(channel).
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: DilationFactor=2
sets the dilation factor for each
convolutional 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"
at most once. 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 

1D convolution  "SCU" (spatial, channel,
unspecified) 
1D grouped convolution  "SCUU" (spatial, channel,
unspecified, unspecified) 
2D convolution  "SSCU" (spatial, spatial,
channel, unspecified) 
2D grouped convolution  "SSCUU" (spatial, spatial,
channel, unspecified, unspecified) 
3D 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 + (filterSize1)*(dilationFactor1)
.
Data Types: single
 double
 int8
 int16
 int32
 int64
 uint8
 uint16
 uint32
 uint64
Padding
— Size of padding
0
(default) 
"same"

"causal"
 numeric scalar  numeric vector  numeric matrix
Size of padding applied to the "S"
and
"T"
dimensions given by the format of the
weights, specified as one of the following:
"same"
— Apply padding such that the output dimension sizes areceil(inputSize/stride)
, whereinputSize
is the size of the corresponding input dimension. WhenStride
is1
, the output is the same size as the input."causal"
– Apply left padding with size(FilterSize  1)
.*DilationFactor
. This option supports convolving over a single time or spatial dimension only. WhenStride
is1
, the output is the same size as the input.Nonnegative integer
sz
— Add padding of sizesz
to both ends of the"S"
or"T"
dimensions given by the format of the weights.Vector of integers
sz
— Add padding of sizesz(i)
to both ends of thei
th"S"
or"T"
dimensions given by the format of the weights. The number of elements ofsz
must match the number of"S"
or"T"
dimensions of the weights.Matrix of integers
sz
— Add padding of sizesz(1,i)
andsz(2,i)
to the start and end of thei
th"S"
or"T"
dimensions given by the format of the weights. For example, for 2D input,[t l; b r]
applies padding of sizet
,b
,l
, andr
to the top, bottom, left, and right of the input, respectively.
Data Types: single
 double
 int8
 int16
 int32
 int64
 uint8
 uint16
 uint32
 uint64
 char
 string
PaddingValue
— Value to pad data
0 (default)  scalar  'symmetricincludeedge'
 'symmetricexcludeedge'
 'replicate'
Value to pad data, specified as one of the following:
PaddingValue  Description  Example 

Scalar  Pad with the specified scalar value. 
$$\left[\begin{array}{ccc}3& 1& 4\\ 1& 5& 9\\ 2& 6& 5\end{array}\right]\to \left[\begin{array}{ccccccc}0& 0& 0& 0& 0& 0& 0\\ 0& 0& 0& 0& 0& 0& 0\\ 0& 0& 3& 1& 4& 0& 0\\ 0& 0& 1& 5& 9& 0& 0\\ 0& 0& 2& 6& 5& 0& 0\\ 0& 0& 0& 0& 0& 0& 0\\ 0& 0& 0& 0& 0& 0& 0\end{array}\right]$$ 
'symmetricincludeedge'  Pad using mirrored values of the input, including the edge values. 
$$\left[\begin{array}{ccc}3& 1& 4\\ 1& 5& 9\\ 2& 6& 5\end{array}\right]\to \left[\begin{array}{ccccccc}5& 1& 1& 5& 9& 9& 5\\ 1& 3& 3& 1& 4& 4& 1\\ 1& 3& 3& 1& 4& 4& 1\\ 5& 1& 1& 5& 9& 9& 5\\ 6& 2& 2& 6& 5& 5& 6\\ 6& 2& 2& 6& 5& 5& 6\\ 5& 1& 1& 5& 9& 9& 5\end{array}\right]$$ 
'symmetricexcludeedge'  Pad using mirrored values of the input, excluding the edge values. 
$$\left[\begin{array}{ccc}3& 1& 4\\ 1& 5& 9\\ 2& 6& 5\end{array}\right]\to \left[\begin{array}{ccccccc}5& 6& 2& 6& 5& 6& 2\\ 9& 5& 1& 5& 9& 5& 1\\ 4& 1& 3& 1& 4& 1& 3\\ 9& 5& 1& 5& 9& 5& 1\\ 5& 6& 2& 6& 5& 6& 2\\ 9& 5& 1& 5& 9& 5& 1\\ 4& 1& 3& 1& 4& 1& 3\end{array}\right]$$ 
'replicate'  Pad using repeated border elements of the input 
$$\left[\begin{array}{ccc}3& 1& 4\\ 1& 5& 9\\ 2& 6& 5\end{array}\right]\to \left[\begin{array}{ccccccc}3& 3& 3& 1& 4& 4& 4\\ 3& 3& 3& 1& 4& 4& 4\\ 3& 3& 3& 1& 4& 4& 4\\ 1& 1& 1& 5& 9& 9& 9\\ 2& 2& 2& 6& 5& 5& 5\\ 2& 2& 2& 6& 5& 5& 5\\ 2& 2& 2& 6& 5& 5& 5\end{array}\right]$$ 
Data Types: single
 double
 int8
 int16
 int32
 int64
 uint8
 uint16
 uint32
 uint64
 char
 string
Output Arguments
Y
— Convolved feature map
dlarray
Convolved feature map, returned as a dlarray
with the
same underlying data type as 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
with the same dimension order as the input
data.
The size of the "C"
(channel) dimension of
Y
depends on the task.
Task  Size of "C" Dimension 

Convolution  Number of filters 
Grouped convolution  Number of filters per group multiplied by the number of groups 
More About
Deep Learning Convolution
The dlconv
function applies sliding
convolution filters to the input data. The dlconv
function
supports convolution in one, two, or three spatial dimensions or one time dimension.
To learn more about deep learning convolution, see the definition of convolutional
layer on the convolution2dLayer
reference page.
Deep Learning Array Formats
Most deep learning networks and functions operate on different dimensions of the input data in different ways.
For example, an LSTM operation iterates over the time dimension of the input data and a batch normalization operation normalizes over the batch dimension of the input data.
To provide input data with labeled dimensions or input data with additional layout information, you can use data formats.
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).
To create formatted input data, create a dlarray
object and specify the format using the second argument.
To provide additional layout information with unformatted data, specify the formats using the DataFormat
and WeightsFormat
arguments.
For more information, see Deep Learning Data Formats.
Extended Capabilities
C/C++ Code Generation
Generate C and C++ code using MATLAB® Coder™.
Usage notes and limitations:
Code generation supports only 1D and 2D spatial and spatiotemporal data. Convolving over 3D spatial and spatiotemporal data format such as "SSS" or "SST" is not supported.
Code generation supports only channelwise (depthwise) separable convolution and regular convolution. Both
NumChannelsPerGroup
andNumFiltersPerGroup
must be equal to 1.The input must be single underlying data type.
The convolution dimensions must be fixed size.
The dimension that corresponds to the channel in the input must be fixed size.
The
Stride
,DilationFactor
,Padding
andPaddingValue
namevalue pairs must be compiletime constants.PaddingValue
must be 0.
GPU Code Generation
Generate CUDA® code for NVIDIA® GPUs using GPU Coder™.
Usage notes and limitations:
Code generation supports only 1D and 2D spatial and spatiotemporal data. Convolving over 3D spatial and spatiotemporal data format such as "SSS" or "SST" is not supported.
Code generation supports only channelwise (depthwise) separable convolution and regular convolution. Both
NumChannelsPerGroup
andNumFiltersPerGroup
must be equal to 1.The input must be single underlying data type.
The convolution dimensions must be fixed size.
The dimension that corresponds to the channel in the input must be fixed size.
The
Stride
,DilationFactor
,Padding
andPaddingValue
namevalue pairs must be compiletime constants.PaddingValue
must be 0.
GPU Arrays
Accelerate code by running on a graphics processing unit (GPU) using Parallel Computing Toolbox™.
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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