dlconv
Description
The convolution operation applies sliding filters to the input
data. Use the dlconv
function for deep learning convolution, grouped
convolution, and channel-wise 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.
Note
To apply convolution within a layerGraph
object
or Layer
array, use
one of the following layers:
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 2-D convolution with format
"SSCB"
(spatial, spatial, channel, batch).
specifies options using one or more name-value pair arguments using any of the previous
syntaxes. For example, Y
= dlconv(___,Name=Value
)WeightsFormat="TCU"
specifies weights for 1-D
convolution with format "TCU"
(time, channel, unspecified).
Examples
Perform 2-D 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 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),numChannels,numFilters); bias = zeros(1,numFilters);
Apply 2-D 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 100-by-100 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 Channel-Wise 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 64-by-64 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 1-D 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 1-D 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 1-D 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 | |||
1-D 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 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 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 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 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 channel-wise separable (also known as depth-wise 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).
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: DilationFactor=2
sets the dilation factor for each
convolutional filter to 2
.
DataFormat
— Dimension order of unformatted data
character vector | string scalar
Dimension order of unformatted input data, specified as a character vector or string
scalar FMT
that provides a label for each dimension of the data.
When you specify the format of a dlarray
object, each character provides a
label for each dimension of the data and must be one of these options:
"S"
— Spatial"C"
— Channel"B"
— Batch (for example, samples and observations)"T"
— Time (for example, time steps of sequences)"U"
— Unspecified
You can specify multiple dimensions labeled "S"
or
"U"
. You can use the labels "C"
,
"B"
, and "T"
at most once.
You must specify DataFormat
when the input data is not a
formatted dlarray
.
Data Types: char
| string
WeightsFormat
— Dimension order of weights
character vector | string scalar
Dimension order of the weights, specified as a character vector or string scalar that provides a label for each dimension of the weights.
The default value of WeightsFormat
depends on the
task:
Task | Default |
---|---|
1-D convolution | "SCU" (spatial, channel, unspecified) |
1-D grouped convolution | "SCUU" (spatial, channel, unspecified,
unspecified) |
2-D convolution | "SSCU" (spatial, spatial, channel,
unspecified) |
2-D grouped convolution | "SSCUU" (spatial, spatial, channel, unspecified,
unspecified) |
3-D 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.
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
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 2-D 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 | 'symmetric-include-edge'
| 'symmetric-exclude-edge'
| 'replicate'
Value to pad data, specified as one of the following:
PaddingValue | Description | Example |
---|---|---|
Scalar | Pad with the specified scalar value. |
|
'symmetric-include-edge' | Pad using mirrored values of the input, including the edge values. |
|
'symmetric-exclude-edge' | Pad using mirrored values of the input, excluding the edge values. |
|
'replicate' | Pad using repeated border elements of the input |
|
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.
Extended Capabilities
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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