convolution2dLayer
2D convolutional layer
Description
A 2D convolutional layer applies sliding convolutional filters to 2D input. The layer convolves the input by moving the filters along the input vertically and horizontally and computing the dot product of the weights and the input, and then adding a bias term.
The dimensions that the layer convolves over depends on the layer input:
For 2D image input (data with four dimensions corresponding to pixels in two spatial dimensions, the channels, and the observations), the layer convolves over the spatial dimensions.
For 2D image sequence input (data with five dimensions corresponding to the pixels in two spatial dimensions, the channels, the observations, and the time steps), the layer convolves over the two spatial dimensions.
For 1D image sequence input (data with four dimensions corresponding to the pixels in one spatial dimension, the channels, the observations, and the time steps), the layer convolves over the spatial and time dimensions.
Creation
Syntax
Description
creates a 2D convolutional layer and sets the layer
= convolution2dLayer(filterSize
,numFilters
)FilterSize
and NumFilters
properties.
sets the optional layer
= convolution2dLayer(filterSize
,numFilters
,Name,Value
)Stride
, DilationFactor
, NumChannels
, Parameters and Initialization, Learning Rate and Regularization, and
Name
properties using namevalue pairs. To specify
input padding, use the 'Padding'
namevalue pair argument.
For example, convolution2dLayer(11,96,'Stride',4,'Padding',1)
creates a 2D convolutional layer with 96 filters of size [11
11]
, a stride of [4 4]
, and padding of size 1
along all edges of the layer input. You can specify multiple namevalue pairs.
Enclose each property name in single quotes.
Input 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: convolution2dLayer(3,16,'Padding','same')
creates a
2D convolutional layer with 16 filters of size [3 3]
and
'same'
padding. At training time, the software calculates
and sets the size of the padding so that the layer output has the same size as
the input.
Padding
— Input edge padding
[0 0 0 0]
(default)  vector of nonnegative integers  'same'
Input edge padding, specified as the commaseparated pair consisting of
'Padding'
and one of these values:
'same'
— Add padding of size calculated by the software at training or prediction time so that the output has the same size as the input when the stride equals 1. If the stride is larger than 1, then the output size isceil(inputSize/stride)
, whereinputSize
is the height or width of the input andstride
is the stride in the corresponding dimension. The software adds the same amount of padding to the top and bottom, and to the left and right, if possible. If the padding that must be added vertically has an odd value, then the software adds extra padding to the bottom. If the padding that must be added horizontally has an odd value, then the software adds extra padding to the right.Nonnegative integer
p
— Add padding of sizep
to all the edges of the input.Vector
[a b]
of nonnegative integers — Add padding of sizea
to the top and bottom of the input and padding of sizeb
to the left and right.Vector
[t b l r]
of nonnegative integers — Add padding of sizet
to the top,b
to the bottom,l
to the left, andr
to the right of the input.
Example:
'Padding',1
adds one row of padding to the top and bottom, and one
column of padding to the left and right of the input.
Example:
'Padding','same'
adds padding so that the output has the same size as
the input (if the stride equals 1).
Properties
2D Convolution
FilterSize
— Height and width of filters
vector of two positive integers
Height and width of the filters, specified as a vector [h w]
of two positive integers, 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.
When you create the layer, you can specify FilterSize
as a scalar to use
the same value for the height and width.
Example: [5 5]
specifies filters with a height of 5 and a width 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]
(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.
DilationFactor
— Factor for dilated convolution
[1 1]
(default)  vector of two positive integers
Factor for dilated convolution (also known as atrous convolution), specified as a vector [h w]
of two positive integers, where h
is the vertical dilation and w
is the horizontal dilation. When creating the layer, you can specify DilationFactor
as a scalar to use the same value for both horizontal and vertical dilations.
Use dilated convolutions to increase the receptive field (the area of the input which the layer can see) of the layer without increasing the number of parameters or computation.
The layer expands the filters by inserting zeros between each filter element. The dilation
factor determines the step size for sampling the input or equivalently the upsampling factor
of the filter. It corresponds to an effective filter size of (Filter Size
– 1) .* Dilation Factor + 1. For example, a 3by3 filter with the
dilation factor [2 2]
is equivalent to a 5by5 filter with zeros between
the elements.
Example: [2 3]
PaddingSize
— Size of padding
[0 0 0 0]
(default)  vector of four nonnegative integers
Size of padding to apply to input borders, specified as a vector
[t b l r]
of four nonnegative
integers, where t
is the padding applied to
the top, b
is the padding applied to the
bottom, l
is the padding applied to the left,
and r
is the padding applied to the right.
When you create a layer, use the 'Padding'
namevalue pair argument to specify the padding size.
Example:
[1 1 2 2]
adds one row of padding to the top
and bottom, and two columns of padding to the left and right of
the input.
PaddingMode
— Method to determine padding size
'manual'
(default)  'same'
Method to determine padding size, specified as 'manual'
or
'same'
.
The software automatically sets the value of PaddingMode
based on the 'Padding'
value you specify
when creating a layer.
If you set the
'Padding'
option to a scalar or a vector of nonnegative integers, then the software automatically setsPaddingMode
to'manual'
.If you set the
'Padding'
option to'same'
, then the software automatically setsPaddingMode
to'same'
and calculates the size of the padding at training time so that the output has the same size as the input when the stride equals 1. If the stride is larger than 1, then the output size isceil(inputSize/stride)
, whereinputSize
is the height or width of the input andstride
is the stride in the corresponding dimension. The software adds the same amount of padding to the top and bottom, and to the left and right, if possible. If the padding that must be added vertically has an odd value, then the software adds extra padding to the bottom. If the padding that must be added horizontally has an odd value, then the software adds extra padding to the right.
Padding
— Size of padding
[0 0]
(default)  vector of two nonnegative integers
Note
Padding
property will be removed in a future release. Use
PaddingSize
instead. When creating a layer, use the
'Padding'
namevalue pair argument to specify the padding
size.
Size of padding to apply to input borders vertically and horizontally, specified as a
vector [a b]
of two nonnegative integers, where a
is the padding applied to the top and bottom of the input data and b
is the padding applied to the left and right.
Example:
[1 1]
adds one row of padding to the top and bottom, and one column
of padding to the left and right of the input.
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
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 [4] (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 [5]. The He initializer samples from a normal distribution with zero mean and variance2/numIn
, wherenumIn = FilterSize(1)*FilterSize(2)*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 these values:
"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 have the form
bias = func(sz)
, wheresz
is the size of the biases.
The layer initializes the biases only 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 numeric array.
The layer weights are learnable parameters. You can specify the initial value of 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 the trainnet
and
trainNetwork
functions use the Weights
property as the initial value. If the Weights
property is
empty, then the software uses the initializer specified by the WeightsInitializer
property of the layer.
At training time, Weights
is a
FilterSize(1)
byFilterSize(2)
byNumChannels
byNumFilters
array.
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 neural network, if Bias
is nonempty, then the trainnet
and trainNetwork
functions use the Bias
property as the initial value. If Bias
is empty, then software uses the initializer specified by BiasInitializer
.
At training time, Bias
is a
1by1byNumFilters
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
NumInputs
— Number of inputs
1
(default)
This property is readonly.
Number of inputs to the layer, returned as 1
. This layer accepts a
single input only.
Data Types: double
InputNames
— Input names
{'in'}
(default)
This property is readonly.
Input names, returned as {'in'}
. This layer accepts a single input
only.
Data Types: cell
NumOutputs
— Number of outputs
1
(default)
This property is readonly.
Number of outputs from the layer, returned as 1
. This layer has a
single output only.
Data Types: double
OutputNames
— Output names
{'out'}
(default)
This property is readonly.
Output names, returned as {'out'}
. This layer has a single output
only.
Data Types: cell
Examples
Create Convolutional Layer
Create a convolutional layer with 96 filters, each with a height and width of 11. Use a stride (step size) of 4 in the horizontal and vertical directions.
layer = convolution2dLayer(11,96,'Stride',4)
layer = Convolution2DLayer with properties: Name: '' Hyperparameters FilterSize: [11 11] NumChannels: 'auto' NumFilters: 96 Stride: [4 4] DilationFactor: [1 1] PaddingMode: 'manual' PaddingSize: [0 0 0 0] PaddingValue: 0 Learnable Parameters Weights: [] Bias: [] Use properties method to see a list of all properties.
Include a convolutional layer in a Layer
array.
layers = [
imageInputLayer([28 28 1])
convolution2dLayer(5,20)
reluLayer
maxPooling2dLayer(2,'Stride',2)
fullyConnectedLayer(10)
softmaxLayer]
layers = 6x1 Layer array with layers: 1 '' Image Input 28x28x1 images with 'zerocenter' normalization 2 '' 2D Convolution 20 5x5 convolutions with stride [1 1] and padding [0 0 0 0] 3 '' ReLU ReLU 4 '' 2D Max Pooling 2x2 max pooling with stride [2 2] and padding [0 0 0 0] 5 '' Fully Connected 10 fully connected layer 6 '' Softmax softmax
Specify Initial Weights and Biases in Convolutional Layer
To specify the weights and bias initializer functions, use the WeightsInitializer
and BiasInitializer
properties respectively. To specify the weights and biases directly, use the Weights
and Bias
properties respectively.
Specify Initialization Functions
Create a convolutional layer with 32 filters, each with a height and width of 5 and specify the weights initializer to be the He initializer.
filterSize = 5; numFilters = 32; layer = convolution2dLayer(filterSize,numFilters, ... 'WeightsInitializer','he')
layer = Convolution2DLayer with properties: Name: '' Hyperparameters FilterSize: [5 5] NumChannels: 'auto' NumFilters: 32 Stride: [1 1] DilationFactor: [1 1] PaddingMode: 'manual' PaddingSize: [0 0 0 0] PaddingValue: 0 Learnable Parameters Weights: [] Bias: [] Use properties method to see a list of all properties.
Note that the Weights
and Bias
properties are empty. At training time, the software initializes these properties using the specified initialization functions.
Specify Custom Initialization Functions
To specify your own initialization function for the weights and biases, set the WeightsInitializer
and BiasInitializer
properties to a function handle. For these properties, specify function handles that take the size of the weights and biases as input and output the initialized value.
Create a convolutional layer with 32 filters, each with a height and width of 5 and specify initializers that sample the weights and biases from a Gaussian distribution with a standard deviation of 0.0001.
filterSize = 5; numFilters = 32; layer = convolution2dLayer(filterSize,numFilters, ... 'WeightsInitializer', @(sz) rand(sz) * 0.0001, ... 'BiasInitializer', @(sz) rand(sz) * 0.0001)
layer = Convolution2DLayer with properties: Name: '' Hyperparameters FilterSize: [5 5] NumChannels: 'auto' NumFilters: 32 Stride: [1 1] DilationFactor: [1 1] PaddingMode: 'manual' PaddingSize: [0 0 0 0] PaddingValue: 0 Learnable Parameters Weights: [] Bias: [] Use properties method to see a list of all properties.
Again, the Weights
and Bias
properties are empty. At training time, the software initializes these properties using the specified initialization functions.
Specify Weights and Bias Directly
Create a fully connected layer with an output size of 10 and set the weights and bias to W
and b
in the MAT file Conv2dWeights.mat
respectively.
filterSize = 5; numFilters = 32; load Conv2dWeights layer = convolution2dLayer(filterSize,numFilters, ... 'Weights',W, ... 'Bias',b)
layer = Convolution2DLayer with properties: Name: '' Hyperparameters FilterSize: [5 5] NumChannels: 3 NumFilters: 32 Stride: [1 1] DilationFactor: [1 1] PaddingMode: 'manual' PaddingSize: [0 0 0 0] PaddingValue: 0 Learnable Parameters Weights: [5x5x3x32 double] Bias: [1x1x32 double] Use properties method to see a list of all properties.
Here, the Weights
and Bias
properties contain the specified values. At training time, if these properties are nonempty, then the software uses the specified values as the initial weights and biases. In this case, the software does not use the initializer functions.
Create Convolutional Layer That Fully Covers Input
Suppose the size of the input is 28by28by1. Create a convolutional layer with 16 filters, each with a height of 6 and a width of 4. Set the horizontal and vertical stride to 4.
Make sure the convolution covers the input completely. For the convolution to fully cover the input, both the horizontal and vertical output dimensions must be integer numbers. For the horizontal output dimension to be an integer, one row of padding is required on the top and bottom of the image: (28 – 6+ 2 * 1)/4 + 1 = 7. For the vertical output dimension to be an integer, no zero padding is required: (28 – 4+ 2 * 0)/4 + 1 = 7.
Construct the convolutional layer.
layer = convolution2dLayer([6 4],16,'Stride',4,'Padding',[1 0])
layer = Convolution2DLayer with properties: Name: '' Hyperparameters FilterSize: [6 4] NumChannels: 'auto' NumFilters: 16 Stride: [4 4] DilationFactor: [1 1] PaddingMode: 'manual' PaddingSize: [1 1 0 0] PaddingValue: 0 Learnable Parameters Weights: [] Bias: [] Use properties method to see a list of all properties.
Algorithms
2D Convolutional Layer
A 2D convolutional layer applies sliding convolutional filters to 2D input. The layer convolves the input by moving the filters along the input vertically and horizontally, computing the dot product of the weights and the input, and then adding a bias term.
The dimensions that the layer convolves over depends on the layer input:
For 2D image input (data with four dimensions corresponding to pixels in two spatial dimensions, the channels, and the observations), the layer convolves over the spatial dimensions.
For 2D image sequence input (data with five dimensions corresponding to the pixels in two spatial dimensions, the channels, the observations, and the time steps), the layer convolves over the two spatial dimensions.
For 1D image sequence input (data with four dimensions corresponding to the pixels in one spatial dimension, the channels, the observations, and the time steps), the layer convolves over the spatial and time dimensions.
The convolutional layer consists of various components.^{1}
A convolutional layer consists of neurons that connect to subregions of the input images or
the outputs of the previous layer. The layer learns the features localized by these regions
while scanning through an image. When creating a layer using the convolution2dLayer
function, you can specify the size of these regions using
the filterSize
input argument.
For each region, the layer computes a dot product of the weights and the input, and then adds a bias term. A set of weights that is applied to a region in the image is called a filter. The filter moves along the input image vertically and horizontally, repeating the same computation for each region. In other words, the filter convolves the input.
This image shows a 3by3 filter scanning through the input. The lower map represents the input and the upper map represents the output.
The step size with which the filter moves is called a stride. You can
specify the step size with the Stride
namevalue pair argument. The
local regions that the neurons connect to can overlap depending on the
filterSize
and 'Stride'
values.
This image shows a 3by3 filter scanning through the input with a stride of 2. The lower map represents the input and the upper map represents the output.
The number of weights in a filter is h * w *
c, where h is the height, and w
is the width of the filter, respectively, and c is the number of channels
in the input. For example, if the input is a color image, the number of color channels is 3.
The number of filters determines the number of channels in the output of a convolutional
layer. Specify the number of filters using the numFilters
argument with
the convolution2dLayer
function.
A dilated convolution is a convolution in which the filters are expanded by spaces inserted
between the elements of the filter. Specify the dilation factor using the
'DilationFactor'
property.
Use dilated convolutions to increase the receptive field (the area of the input which the layer can see) of the layer without increasing the number of parameters or computation.
The layer expands the filters by inserting zeros between each filter element. The dilation
factor determines the step size for sampling the input or equivalently the upsampling factor
of the filter. It corresponds to an effective filter size of (Filter Size
– 1) .* Dilation Factor + 1. For example, a 3by3 filter with the
dilation factor [2 2]
is equivalent to a 5by5 filter with zeros between
the elements.
This image shows a 3by3 filter dilated by a factor of two scanning through the input. The lower map represents the input and the upper map represents the output.
As a filter moves along the input, it uses the same set of weights and the same bias for the convolution, forming a feature map. Each feature map is the result of a convolution using a different set of weights and a different bias. Hence, the number of feature maps is equal to the number of filters. The total number of parameters in a convolutional layer is ((h*w*c + 1)*Number of Filters), where 1 is the bias.
You can also apply padding to input image borders vertically and horizontally
using the 'Padding'
namevalue pair argument. Padding is values
appended to the borders of a the input to increase its size. By adjusting the padding, you
can control the output size of the layer.
This image shows a 3by3 filter scanning through the input with padding of size 1. The lower map represents the input and the upper map represents the output.
The output height and width of a convolutional layer is (Input Size – ((Filter Size – 1)*Dilation Factor + 1) + 2*Padding)/Stride + 1. This value must be an integer for the whole image to be fully covered. If the combination of these options does not lead the image to be fully covered, the software by default ignores the remaining part of the image along the right and bottom edges in the convolution.
The product of the output height and width gives the total number of neurons in a feature map, say Map Size. The total number of neurons (output size) in a convolutional layer is Map Size*Number of Filters.
For example, suppose that the input image is a 32by32by3 color image. For a convolutional layer with eight filters and a filter size of 5by5, the number of weights per filter is 5 * 5 * 3 = 75, and the total number of parameters in the layer is (75 + 1) * 8 = 608. If the stride is 2 in each direction and padding of size 2 is specified, then each feature map is 16by16. This is because (32 – 5 + 2 * 2)/2 + 1 = 16.5, and some of the outermost padding to the right and bottom of the image is discarded. Finally, the total number of neurons in the layer is 16 * 16 * 8 = 2048.
Usually, the results from these neurons pass through some form of nonlinearity, such as rectified linear units (ReLU).
You can adjust the learning rates and regularization options
for the layer using namevalue pair arguments while defining the convolutional layer. If you
choose not to specify these options, then the trainnet
function uses the
global training options defined with the trainingOptions
function.
A convolutional neural network can consist of one or multiple convolutional layers. The number of convolutional layers depends on the amount and complexity of the data.
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 consist of one or
more of these characters:
"S"
— Spatial"C"
— Channel"B"
— Batch"T"
— Time"U"
— Unspecified
For example, 2D image data that is 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 those for 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 Convolution2DLayer
objects and the
corresponding output format. If the software passes the output of the layer 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 according to the formats
in this table. The formats listed here are only a subset. The layer may support additional
formats such as formats with additional "S"
(spatial) or
"U"
(unspecified) dimensions.
Input Format  Output Format 







In dlnetwork
objects, Convolution2DLayer
objects also
support these input and output format combinations.
Input Format  Output Format 







References
[1] LeCun, Y., B. Boser, J. S. Denker, D. Henderson, R. E. Howard, W. Hubbard, and L. D. Jackel. "Handwritten Digit Recognition with a BackPropagation Network." In Advances in Neural Information Processing Systems 2 (D. Touretzky, ed.). San Francisco: Morgan Kaufmann, 1990.
[2] LeCun, Y., L. Bottou, Y. Bengio, and P. Haffner. ''GradientBased Learning Applied to Document Recognition.'' Proceedings of the IEEE. Vol. 86, Number 11, 1998, pp. 2278–2324.
[3] Murphy, K. P. Machine Learning: A Probabilistic Perspective. Cambridge, MA: MIT Press, 2012.
[4] 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
[5] He, Kaiming, Xiangyu Zhang, Shaoqing Ren, and Jian Sun. "Delving Deep into Rectifiers: Surpassing HumanLevel Performance on ImageNet Classification." In 2015 IEEE International Conference on Computer Vision (ICCV), 1026–34. Santiago, Chile: IEEE, 2015. https://doi.org/10.1109/ICCV.2015.123
Extended Capabilities
C/C++ Code Generation
Generate C and C++ code using MATLAB® Coder™.
Usage notes and limitations:
For code generation, the
PaddingValue
parameter must be equal to0
, which is the default value.
GPU Code Generation
Generate CUDA® code for NVIDIA® GPUs using GPU Coder™.
Usage notes and limitations:
For code generation, the
PaddingValue
parameter must be equal to0
, which is the default value.
Version History
Introduced in R2016aR2019a: Default weights initialization is Glorot
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
'narrownormal'
.
See Also
trainnet
 trainingOptions
 dlnetwork
 reluLayer
 batchNormalizationLayer
 maxPooling2dLayer
 fullyConnectedLayer
 groupedConvolution2dLayer
 Deep Network
Designer
^{1} Image credit: Convolution arithmetic (License)
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