convolution1dLayer

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

layer = convolution1dLayer(filterSize,numFilters)

layer = convolution1dLayer(filterSize,numFilters,Name=Value)

Description

layer = convolution1dLayer(filterSize,numFilters) creates a 1-D convolutional layer and sets the FilterSize and NumFilters properties.

layer = convolution1dLayer(filterSize,numFilters,Name=Value) also sets the optional Stride, DilationFactor, NumChannels, Parameters and Initialization, Learning Rate and Regularization, and Name properties using one or more name-value arguments. To specify input padding, use the Padding name-value argument. For 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.

Input Arguments

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.

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 is ceil(inputSize/stride), where inputSize is the length of the input. When Stride is 1, 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 and r 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 read-only.

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 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

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 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

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 name-value argument to specify the padding size.

Data Types: double

PaddingMode — Method to determine padding size

'manual' (default) | 'same' | 'causal'

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 is 1, 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

PaddingValue — Value to pad data

0 (default) | scalar | 'symmetric-include-edge' | 'symmetric-exclude-edge' | 'replicate'

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.	$$\left[\begin{array}{ccc}3& 1& 4\end{array}\right]\to \left[\begin{array}{ccccccc}0& 0& 3& 1& 4& 0& 0\end{array}\right]$$
'symmetric-include-edge'	Pad using mirrored values of the input, including the edge values.	$$\left[\begin{array}{ccc}3& 1& 3\end{array}\right]\to \left[\begin{array}{ccccccc}1& 3& 3& 1& 4& 4& 1\end{array}\right]$$
'symmetric-exclude-edge'	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 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.

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' | 'narrow-normal' | '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 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 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 the Weights property is empty.

Data Types: char | string | function_handle

BiasInitializer — Function to initialize biases

'zeros' (default) | 'narrow-normal' | 'ones' | function handle

Function to initialize the biases, specified as one of the following:

• '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 be of the form bias = func(sz), where sz is the size of the biases.

The layer only initializes the biases 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-by-NumChannels-by-numFilters 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 1-by-NumFilters numeric array or [].

The layer biases are learnable parameters. When you train a neural 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 — L₂ regularization factor for weights

1 (default) | nonnegative scalar

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

BiasL2Factor — L₂ regularization factor for biases

0 (default) | 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.

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 read-only.

Number of inputs of the layer. This layer accepts a single input only.

Data Types: double

InputNames — Input names

{"in"} (default)

This property is read-only.

Input names of the layer. This layer accepts a single input only.

Data Types: cell

NumOutputs — Number of outputs

1 (default)

This property is read-only.

Number of outputs of the layer. This layer has a single output only.

Data Types: double

OutputNames — Output names

{'out'} (default)

This property is read-only.

Output names of the layer. This layer has a single output only.

Data Types: cell

Examples

Create 1-D Convolutional Layer

Create a 1-D 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 1-D convolutional layer in a Layer array.

layers = [
    sequenceInputLayer(3,MinLength=20)
    convolution1dLayer(11,96)
    reluLayer
    globalMaxPooling1dLayer
    fullyConnectedLayer(10)
    softmaxLayer
    classificationLayer]

layers = 
  7x1 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
     7   ''   Classification Output    crossentropyex

Algorithms

1-D Convolutional Layer

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.

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, 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 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 property set to 0 (false), then the layer receives an unformatted dlarray object with dimensions ordered corresponding to the formats in this table.

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 Proceedings of the 2015 IEEE International Conference on Computer Vision, 1026–1034. Washington, DC: IEEE Computer Vision Society, 2015. https://doi.org/10.1109/ICCV.2015.123

Version History

Introduced in R2021b