convolution1dLayer
Description
A 1-D convolutional layer applies sliding convolutional filters to 1-D 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 1-D image input (data with three dimensions corresponding to the spatial pixels, channels, and observations), the layer convolves over the spatial dimension.
For 1-D 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 1-D convolutional layer and sets the layer = convolution1dLayer(filterSize,numFilters)FilterSize and NumFilters properties. 
                    sets optional properties using one or more name-value arguments.layer = convolution1dLayer(filterSize,numFilters,Name=Value)
Input Arguments
Width of the filters, specified as a positive integer.
Data Types: single | double | int8 | int16 | int32 | int64 | uint8 | uint16 | uint32 | uint64
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
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.
    
Example: convolution1dLayer(11,96,Padding=1) creates a 1-D
                    convolutional layer with 96 filters of size 11, and specifies padding of size 1
                    on the left and right of the layer input.
Step size for traversing the input, specified as a positive integer.
Data Types: single | double | int8 | int16 | int32 | int64 | uint8 | uint16 | uint32 | uint64
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 1-by-3 filter with a dilation factor of
                                    2 is equivalent to a 1-by-5 filter with zeros
                                between the elements.
Data Types: single | double | int8 | int16 | int32 | int64 | uint8 | uint16 | uint32 | uint64
Padding to apply to the input, specified as one of the following:
"same"— Apply padding such that the output size isceil(inputSize/stride), whereinputSizeis the length of the input. WhenStrideis1, the output is the same size as the input."causal"— Apply left padding to the input, equal to(FilterSize - 1) .* DilationFactor. WhenStrideis1, the output is the same size as the input.Nonnegative integer
sz— Add padding of sizeszto both ends of the input.Vector
[l r]of nonnegative integers — Add padding of sizelto the left andrto 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
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
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.
NumChannelsand the number of channels in the layer input data must match. For example, if the input is an RGB image, thenNumChannelsmust be 3. If the input is the output of a convolutional layer with 16 filters, thenNumChannelsmust be 16.
Data Types: single | double | int8 | int16 | int32 | int64 | uint8 | uint16 | uint32 | uint64 | char | string
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*NumChannelsandnumOut = 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."narrow-normal"— 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), whereszis 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
Function to initialize the biases, specified as one of these values:
"zeros"— Initialize the biases with zeros."ones"— Initialize the biases with ones."narrow-normal"— 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), whereszis the size of the biases.
The layer initializes the biases only when the
                                    Bias property is empty.
Data Types: char | string | function_handle
Layer weights for the transposed convolution operation, specified
                                as a
                                    FilterSize-by-NumChannels-by-numFilters
                                numeric array or [].
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.
Data Types: single | double
Layer biases for the transposed convolutional operation, specified
                                as a 1-by-NumFilters numeric array or
                                    [].
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.
Data Types: single | double
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
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
L2 regularization factor for the weights, specified as a nonnegative scalar.
The software multiplies this factor by the global
                                            L2
                                    regularization factor to determine the
                                            L2
                                    regularization for the weights in this layer. For example, if
                                        WeightL2Factor is 2,
                                    then the L2
                                    regularization for the weights in this layer is twice the global
                                            L2
                                    regularization factor. You can specify the global
                                            L2
                                    regularization factor using the trainingOptions
                                    function.
Data Types: single | double | int8 | int16 | int32 | int64 | uint8 | uint16 | uint32 | uint64
L2 regularization factor for the biases, specified as a nonnegative scalar.
The software multiplies this factor by the global
                                            L2
                                    regularization factor to determine the
                                            L2
                                    regularization for the biases in this layer. For example, if
                                        BiasL2Factor is 2,
                                    then the L2
                                    regularization for the biases in this layer is twice the global
                                            L2
                                    regularization factor. The software determines the global
                                            L2
                                    regularization factor based on the settings you specify using
                                    the trainingOptions
                                    function.
Data Types: single | double | int8 | int16 | int32 | int64 | uint8 | uint16 | uint32 | uint64
Properties
Convolution
This property is read-only.
Width of the filters, specified as a positive integer.
Data Types: single | double | int8 | int16 | int32 | int64 | uint8 | uint16 | uint32 | uint64
This property is read-only.
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
Step size for traversing the input, specified as a positive integer.
Data Types: single | double | int8 | int16 | int32 | int64 | uint8 | uint16 | uint32 | uint64
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 1-by-3 filter with a
                            dilation factor of 2 is equivalent to a 1-by-5 filter
                            with zeros between the elements.
Data Types: single | double | int8 | int16 | int32 | int64 | uint8 | uint16 | uint32 | uint64
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
            name-value argument to specify the padding size.
Data Types: double
This property is read-only.
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), whereinputSizeis the length of the input. WhenStrideis1, 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 name-value argument.
Data Types: char
This property is read-only.
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
This property is read-only.
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.
NumChannelsand the number of channels in the layer input data must match. For example, if the input is an RGB image, thenNumChannelsmust be 3. If the input is the output of a convolutional layer with 16 filters, thenNumChannelsmust be 16.
Data Types: single | double | int8 | int16 | int32 | int64 | uint8 | uint16 | uint32 | uint64 | char | string
Parameters and Initialization
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*NumChannelsandnumOut = 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."narrow-normal"— 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), whereszis 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
Function to initialize the biases, specified as one of these values:
"zeros"— Initialize the biases with zeros."ones"— Initialize the biases with ones."narrow-normal"— 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), whereszis the size of the biases.
The layer initializes the biases only when the Bias property is
            empty.
The Convolution1DLayer object stores this property as a character vector or a
        function handle.
Data Types: char | string | function_handle
Layer weights for the transposed convolution operation, specified as a
                                FilterSize-by-NumChannels-by-numFilters
                            numeric array or [].
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
        function uses 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.
Data Types: single | double
Layer biases for the transposed convolutional operation, specified as a
                1-by-NumFilters numeric array or [].
The layer biases are learnable parameters. When you train a neural network, if Bias is nonempty, then the trainnet
        function uses the Bias property as the initial value. If
            Bias is empty, then software uses the initializer
        specified by BiasInitializer.
Data Types: single | double
Learning Rate and Regularization
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
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
L2 regularization factor for the weights, specified as a nonnegative scalar.
The software multiplies this factor by the global L2 regularization factor to determine the L2 regularization for the weights in this layer. For example, if WeightL2Factor is 2, then the L2 regularization for the weights in this layer is twice the global L2 regularization factor. You can specify the global L2 regularization factor using the trainingOptions function.
Data Types: single | double | int8 | int16 | int32 | int64 | uint8 | uint16 | uint32 | uint64
L2 regularization factor for the biases, specified as a nonnegative scalar.
The software multiplies this factor by the global L2 regularization factor to determine the L2 regularization for the biases in this layer. For example, if BiasL2Factor is 2, then the L2 regularization for the biases in this layer is twice the global L2 regularization factor. The software determines the global L2 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
This property is read-only.
Number of inputs to the layer, stored as 1. This layer accepts a
            single input only.
Data Types: double
This property is read-only.
Input names, stored as {'in'}. This layer accepts a single input
            only.
Data Types: cell
This property is read-only.
Number of outputs from the layer, stored as 1. This layer has a
            single output only.
Data Types: double
This property is read-only.
Output names, stored as {'out'}. This layer has a single output
            only.
Data Types: cell
Examples
Create a 1-D convolutional layer with 96 filters of width of 11.
layer = convolution1dLayer(11,96);
Include a 1-D convolutional layer in a Layer array.
layers = [
    sequenceInputLayer(3,MinLength=20)
    layer
    reluLayer
    globalMaxPooling1dLayer
    fullyConnectedLayer(10)
    softmaxLayer]layers = 
  6×1 Layer array with layers:
     1   ''   Sequence Input           Sequence input with 3 dimensions
     2   ''   1-D Convolution          96 11 convolutions with stride 1 and padding [0  0]
     3   ''   ReLU                     ReLU
     4   ''   1-D Global Max Pooling   1-D global max pooling
     5   ''   Fully Connected          10 fully connected layer
     6   ''   Softmax                  softmax
Algorithms
A 1-D convolutional layer applies sliding convolutional filters to 1-D 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 1-D image input (data with three dimensions corresponding to the spatial pixels, channels, and observations), the layer convolves over the spatial dimension.
For 1-D image sequence input (data with four dimensions corresponding to the spatial pixels, channels, observations, and time steps), the layer convolves over the spatial dimension.
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 format consists of one or
        more of these characters:
"S"— Spatial"C"— Channel"B"— Batch"T"— Time"U"— Unspecified
For example, you can represent vector sequence data as a 3-D array, in which the first
        dimension corresponds to the channel dimension, the second dimension corresponds to the
        batch dimension, and the third dimension corresponds to the time dimension. This
        representation is in the format "CBT" (channel, batch, time).
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 Convolution1DLayer 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, Convolution1DLayer objects also support
        these input and output format combinations.
| 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. https://proceedings.mlr.press/v9/glorot10a/glorot10a.pdf
[2] He, Kaiming, Xiangyu Zhang, Shaoqing Ren, and Jian Sun. "Delving Deep into Rectifiers: Surpassing Human-Level 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
Usage notes and limitations:
You can generate generic C/C++ code that does not depend on third-party libraries and deploy the generated code to hardware platforms.
Usage notes and limitations:
You can generate CUDA code that is independent of deep learning libraries and deploy the generated code to platforms that use NVIDIA® GPU processors.
Version History
Introduced in R2021b
See Also
trainnet | trainingOptions | dlnetwork | sequenceInputLayer | lstmLayer | bilstmLayer | gruLayer | maxPooling1dLayer | averagePooling1dLayer | globalMaxPooling1dLayer | globalAveragePooling1dLayer | transposedConv1dLayer | exportNetworkToSimulink | Convolution 1D
                Layer
Topics
- Sequence Classification Using 1-D Convolutions
 - Sequence-to-Sequence Classification Using 1-D Convolutions
 - Sequence Classification Using Deep Learning
 - Sequence-to-Sequence Classification Using Deep Learning
 - Sequence-to-Sequence Regression Using Deep Learning
 - Time Series Forecasting Using Deep Learning
 - Long Short-Term Memory Neural Networks
 - List of Deep Learning Layers
 - Deep Learning Tips and Tricks
 
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