Convolution1DLayer - 1-D convolutional layer - MATLAB (original) (raw)

1-D convolutional layer

Since R2021b

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

`layer` = convolution1dLayer([filterSize](#mw%5F20b4d6d9-c0af-404c-88b2-2d485865fbd3),[numFilters](#mw%5Fb770e561-b00c-4a3f-9f05-3325b05de3a5),[Name=Value](#namevaluepairarguments)) sets optional properties using one or more name-value arguments.

Input Arguments

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Width of the filters, specified as a positive integer.

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.

Name-Value Arguments

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Specify optional pairs of arguments asName1=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.

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 of2 is equivalent to a 1-by-5 filter with zeros between the elements.

Padding to apply to the input, specified as one of the following:

"same" — Apply padding such that the output size is ceil(inputSize/stride), where inputSize is the length of the input. When Stride is1, the output is the same size as the input.
"causal" — Apply left padding to the input, equal to (FilterSize - 1) .* DilationFactor. When Stride is 1, the output is the same size as the input.
Nonnegative integer sz — Add padding of size sz to both ends of the input.
Vector [l r] of nonnegative integers — Add padding of size l 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.

Value to pad data, specified as one of the following:

PaddingValue	Description	Example
Scalar	Pad with the specified scalar value.	[314]→[0031400]
"symmetric-include-edge"	Pad using mirrored values of the input, including the edge values.	[314]→[1331441]
"symmetric-exclude-edge"	Pad using mirrored values of the input, excluding the edge values.	[314]→[4131413]
"replicate"	Pad using repeated border elements of the input.	[314]→[3331444]

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, then NumChannels must be 16.

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 and numOut = 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, where numIn = 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), where sz is the size of the weights. For an example, see Specify Custom Weight Initialization Function.

The layer only initializes the weights when theWeights 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), where sz is the size of the biases.

The layer initializes the biases only when theBias property is empty.

Data Types: char | string | function_handle

Layer weights for the transposed convolution operation, specified as aFilterSize-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, ifWeightLearnRateFactor is2, 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.

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.

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, ifWeightL2Factor 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.

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, ifBiasL2Factor 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.

Layer name, specified as a character vector or a string scalar. For Layer array input, the trainnet and dlnetwork functions automatically assign names to layers with the name "".

This argument sets the Name property.

Data Types: char | string

Properties

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Convolution

This property is read-only.

Width of the filters, specified as a positive integer.

This property is read-only.

Step size for traversing the input, specified as a 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 1-by-3 filter with a dilation factor of 2 is equivalent to a 1-by-5 filter with zeros between the elements.

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 by Padding.
'same' – Apply padding such that the output size is ceil(inputSize/Stride), where inputSize is the length of the input. When Stride 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 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.	[314]→[0031400]
"symmetric-include-edge"	Pad using mirrored values of the input, including the edge values.	[314]→[1331441]
"symmetric-exclude-edge"	Pad using mirrored values of the input, excluding the edge values.	[314]→[4131413]
"replicate"	Pad using repeated border elements of the input.	[314]→[3331444]

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. NumChannels and the number of channels in the layer input data must match. For example, if the input is an RGB image, then NumChannels must be 3. If the input is the output of a convolutional layer with 16 filters, then NumChannels must be 16.

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 of 2/(numIn + numOut), where numIn = FilterSize*NumChannels and numOut = 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 of 2/numIn, where numIn = 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 formweights = func(sz), where sz 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

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 formbias = func(sz), where sz is 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 aFilterSize-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. IfBias 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.

Learning rate factor for the biases, specified as a nonnegative scalar.

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.

Layer

Data Types: char | string

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

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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

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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 withdlnetwork 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 aFunctionLayer 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
"SCB" (spatial, channel, batch)	"SCB" (spatial, channel, batch)
"CBT" (channel, batch, time)	"CBT" (channel, batch, time)
"SCBT" (spatial, channel, batch, time)	"SCBT" (spatial, channel, batch, time)

In dlnetwork objects, Convolution1DLayer objects also support these input and output format combinations.

Input Format	Output Format
"SC" (spatial, channel)	"SC" (spatial, channel)
"CT" (channel, time)	"CT" (channel, time)
"SCT" (spatial, channel, time)	"SCT" (spatial, channel, time)

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

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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