convolution1dLayer
1D convolutional layer
Description
A 1D convolutional layer applies sliding convolutional filters to 1D input. The layer convolves the input by moving the filters along the input and computing the dot product of the weights and the input, then adding a bias term.
The dimension that the layer convolves over depends on the layer input:
For time series and vector sequence input (data with three dimensions corresponding to the channels, observations, and time steps), the layer convolves over the time dimension.
For 1D image input (data with three dimensions corresponding to the spatial pixels, channels, and observations), the layer convolves over the spatial dimension.
For 1D image sequence input (data with four dimensions corresponding to the spatial pixels, channels, observations, and time steps), the layer convolves over the spatial dimension.
Creation
Syntax
Description
creates a 1D convolutional layer and sets the layer
= convolution1dLayer(filterSize
,numFilters
)FilterSize
and NumFilters
properties.
also sets the optional layer
= convolution1dLayer(filterSize
,numFilters
,Name=Value
)Stride
, DilationFactor
, NumChannels
, Parameters and Initialization, Learning Rate and Regularization, and Name
properties using one or more namevalue arguments. To
specify input padding, use the Padding
namevalue argument. For example, convolution1dLayer(11,96,Padding=1)
creates a 1D convolutional layer with 96 filters of size 11, and specifies padding of
size 1 on the left and right of the layer input.
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.
Example: convolution1dLayer(11,96,Padding=1)
creates a 1D
convolutional layer with 96 filters of size 11, and specifies padding of size 1 on the
left and right of the layer input.
Padding
— Padding to apply to input
[0 0]
(default)  "same"
 "causal"
 nonnegative integer  vector of nonnegative integers
Padding to apply to the input, specified as one of the following:
"same"
— Apply padding such that the output size isceil(inputSize/stride)
, whereinputSize
is the length of the input. WhenStride
is1
, the output is the same size as the input."causal"
— Apply left padding to the input, equal to(FilterSize  1) .* DilationFactor
. WhenStride
is1
, the output is the same size as the input.Nonnegative integer
sz
— Add padding of sizesz
to both ends of the input.Vector
[l r]
of nonnegative integers — Add padding of sizel
to the left andr
to the right of the input.
Example: Padding=[2 1]
adds padding of size 2 to the left and
size 1 to the right of the input.
Data Types: single
 double
 int8
 int16
 int32
 int64
 uint8
 uint16
 uint32
 uint64
 char
 string
Properties
Convolution
FilterSize
— Width of filters
positive integer
This property is readonly.
Width of the filters, specified as a positive integer.
Data Types: single
 double
 int8
 int16
 int32
 int64
 uint8
 uint16
 uint32
 uint64
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
(default)  positive integer
Step size for traversing the input, specified as a positive integer.
Data Types: single
 double
 int8
 int16
 int32
 int64
 uint8
 uint16
 uint32
 uint64
DilationFactor
— Factor for dilated convolution
1
(default)  positive integer
Factor for dilated convolution (also known as atrous convolution), specified as a positive integer.
Use dilated convolutions to increase the receptive field (the area of the input that 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
(FilterSize – 1) .* DilationFactor + 1
. For example, a 1by3
filter with a dilation factor of 2
is equivalent to a 1by5 filter
with zeros between the elements.
Data Types: single
 double
 int8
 int16
 int32
 int64
 uint8
 uint16
 uint32
 uint64
PaddingSize
— Size of padding
[0 0]
(default)  vector of two nonnegative integers
Size of padding to apply to each side of the input, specified as a vector [l
r]
of two nonnegative integers, where 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 argument to specify the padding size.
Data Types: double
PaddingMode
— Method to determine padding size
'manual'
(default)  'same'
 'causal'
This property is readonly.
Method to determine padding size, specified as one of the following:
'manual'
– Pad using the integer or vector specified byPadding
.'same'
– Apply padding such that the output size isceil(inputSize/Stride)
, whereinputSize
is the length of the input. WhenStride
is1
, the output is the same as the input.'causal'
– Apply causal padding. Pad the left of the input with padding size(FilterSize  1) .* DilationFactor
.
To specify the layer padding, use the Padding
namevalue argument.
Data Types: char
PaddingValue
— Value to pad data
0
(default)  scalar  'symmetricincludeedge'
 'symmetricexcludeedge'
 'replicate'
This property is readonly.
Value to pad data, specified as one of the following:
PaddingValue  Description  Example 

Scalar  Pad with the specified scalar value. 
$$\left[\begin{array}{ccc}3& 1& 4\end{array}\right]\to \left[\begin{array}{ccccccc}0& 0& 3& 1& 4& 0& 0\end{array}\right]$$ 
'symmetricincludeedge'  Pad using mirrored values of the input, including the edge values. 
$$\left[\begin{array}{ccc}3& 1& 3\end{array}\right]\to \left[\begin{array}{ccccccc}1& 3& 3& 1& 4& 4& 1\end{array}\right]$$ 
'symmetricexcludeedge'  Pad using mirrored values of the input, excluding the edge values. 
$$\left[\begin{array}{ccc}3& 1& 4\end{array}\right]\to \left[\begin{array}{ccccccc}4& 1& 3& 1& 4& 1& 3\end{array}\right]$$ 
'replicate'  Pad using repeated border elements of the input. 
$$\left[\begin{array}{ccc}3& 1& 3\end{array}\right]\to \left[\begin{array}{ccccccc}3& 3& 3& 1& 4& 4& 4\end{array}\right]$$ 
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 [1] (also known as the Xavier initializer). The Glorot initializer independently samples from a uniform distribution with a mean of zero and a variance of2/(numIn + numOut)
, wherenumIn = FilterSize*NumChannels
andnumOut = FilterSize*NumFilters
.'he'
– Initialize the weights with the He initializer [2]. The He initializer samples from a normal distribution with a mean of zero and a variance of2/numIn
, wherenumIn = FilterSize*NumChannels
.'narrownormal'
— Initialize the weights by independently sampling from a normal distribution with a mean of zero and a standard deviation of 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)  'narrownormal'
 '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.'narrownormal'
— 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 transposed convolution operation, specified as a
FilterSize
byNumChannels
bynumFilters
numeric array or []
.
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 transposed convolutional operation, specified as a
1byNumFilters
numeric array or []
.
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
.
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. 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
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 the name
''
.
Data Types: char
 string
NumInputs
— Number of inputs
1
(default)
This property is readonly.
Number of inputs of the layer. This layer accepts a single input only.
Data Types: double
InputNames
— Input names
{'in'}
(default)
This property is readonly.
Input names of the layer. This layer accepts a single input only.
Data Types: cell
NumOutputs
— Number of outputs
1
(default)
This property is readonly.
Number of outputs of the layer. This layer has a single output only.
Data Types: double
OutputNames
— Output names
{'out'}
(default)
This property is readonly.
Output names of the layer. This layer has a single output only.
Data Types: cell
Examples
Create 1D Convolutional Layer
Create a 1D convolutional layer with 96 filters of width of 11.
layer = convolution1dLayer(11,96)
layer = Convolution1DLayer with properties: Name: '' Hyperparameters FilterSize: 11 NumChannels: 'auto' NumFilters: 96 Stride: 1 DilationFactor: 1 PaddingMode: 'manual' PaddingSize: [0 0] PaddingValue: 0 Learnable Parameters Weights: [] Bias: [] Show all properties
Include a 1D convolutional layer in a Layer
array.
layers = [ sequenceInputLayer(3,MinLength=12) convolution1dLayer(11,96) reluLayer globalMaxPooling1dLayer fullyConnectedLayer(10) softmaxLayer classificationLayer]
layers = 7x1 Layer array with layers: 1 '' Sequence Input Sequence input with 3 dimensions 2 '' 1D Convolution 96 11 convolutions with stride 1 and padding [0 0] 3 '' ReLU ReLU 4 '' 1D Global Max Pooling 1D global max pooling 5 '' Fully Connected 10 fully connected layer 6 '' Softmax softmax 7 '' Classification Output crossentropyex
Algorithms
1D Convolutional Layer
A 1D convolutional layer applies sliding convolutional filters to 1D input. The layer convolves the input by moving the filters along the input and computing the dot product of the weights and the input, then adding a bias term.
The dimension that the layer convolves over depends on the layer input:
For time series and vector sequence input (data with three dimensions corresponding to the channels, observations, and time steps), the layer convolves over the time dimension.
For 1D image input (data with three dimensions corresponding to the spatial pixels, channels, and observations), the layer convolves over the spatial dimension.
For 1D image sequence input (data with four dimensions corresponding to the spatial pixels, channels, observations, and time steps), the layer convolves over the spatial dimension.
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 consists of one or more of these characters:
"S"
— Spatial"C"
— Channel"B"
— Batch"T"
— Time"U"
— Unspecified
For example, 2D image data 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 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 Convolution1DLayer
objects and
the corresponding output format. If the output of the layer is passed to a custom layer that
does not inherit from the nnet.layer.Formattable
class, or a
FunctionLayer
object with the Formattable
option set
to false
, then the layer receives an unformatted dlarray
object with dimensions ordered corresponding to the formats outlined in this table.
Input Format  Output Format 







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 HumanLevel 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 R2021b
See Also
trainingOptions
 trainNetwork
 sequenceInputLayer
 lstmLayer
 bilstmLayer
 gruLayer
 maxPooling1dLayer
 averagePooling1dLayer
 globalMaxPooling1dLayer
 globalAveragePooling1dLayer
 transposedConv1dLayer
Topics
 Sequence Classification Using 1D Convolutions
 SequencetoSequence Classification Using 1D Convolutions
 Sequence Classification Using Deep Learning
 SequencetoSequence Classification Using Deep Learning
 SequencetoSequence Regression Using Deep Learning
 Time Series Forecasting Using Deep Learning
 Long ShortTerm Memory Networks
 List of Deep Learning Layers
 Deep Learning Tips and Tricks
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