# transposedConv1dLayer

Transposed 1-D convolution layer

## Description

A transposed 1-D convolution layer upsamples one-dimensional feature maps.

This layer is sometimes incorrectly known as a "deconvolution" or "deconv" layer. This layer is the transpose of convolution and does not perform deconvolution.

layer = transposedConv1dLayer(filterSize,numFilters) returns a 1-D transposed convolution layer and sets the FilterSize and NumFilters properties.

example

layer = transposedConv1dLayer(filterSize,numFilters,Name=Value) returns a 1-D transposed convolutional layer and specifies additional options using one or more name-value arguments.

## Examples

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Create a 1-D transposed convolutional layer with 96 filters of length 11 and a stride of 4.

layer = transposedConv1dLayer(11,96,Stride=4)
layer =
TransposedConvolution1DLayer with properties:

Name: ''

Hyperparameters
FilterSize: 11
NumChannels: 'auto'
NumFilters: 96
Stride: 4
CroppingMode: 'manual'
CroppingSize: [0 0]

Learnable Parameters
Weights: []
Bias: []

Show all properties

## Input Arguments

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Length of the filters, specified as a positive integer. The filter size defines the size of the local regions to which the neurons connect in the input.

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 output of the layer.

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: transposedConv1dLayer(11,96,Stride=4) creates a 1-D transposed convolutional layer with 96 filters of length 11 and a stride of 4.

Transposed Convolution

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Upsampling factor of the input, specified as a positive integer that corresponds to the horizontal stride.

Data Types: single | double | int8 | int16 | int32 | int64 | uint8 | uint16 | uint32 | uint64

Output size reduction, specified as one of the following:

• "same" — Set the cropping so that the output size equals inputSize.*Stride, where inputSize is the length of the layer input. If Cropping is "same", then the software automatically sets the CroppingMode property of the layer to 'same'.

The software trims an equal amount from the left and right, when possible. If the horizontal crop amount has an odd value, then the software trims an extra column from the right.

• A positive integer — Crop the specified amount of data from the left and right edges.

• A vector of nonnegative integers [l r] — Crop l and r from the left and right, respectively.

If you set the Cropping option to a numeric value, then the software automatically sets the CroppingMode property of the layer to 'manual'.

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. 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

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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

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

• 'zeros' — Initialize the bias with zeros.

• 'ones' — Initialize the bias with ones.

• 'narrow-normal' — 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), where sz is the size of the bias.

The layer only initializes the bias when the Bias property is empty.

Data Types: char | string | function_handle

Layer weights for the transposed convolution operation, specified as a FilterSize-by-NumFilters-by-NumChannels 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

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 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

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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

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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

## Output Arguments

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Transposed 1-D convolution layer, returned as a TransposedConvolution1DLayer object.

## Algorithms

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### 1-D Transposed Convolutional Layer

A transposed 1-D convolution layer upsamples one-dimensional feature maps.

The standard convolution operation downsamples the input by applying sliding convolutional filters to the input. By flattening the input and output, you can express the convolution operation as $Y=CX+B$ for the convolution matrix C and bias vector B that can be derived from the layer weights and biases.

Similarly, the transposed convolution operation upsamples the input by applying sliding convolutional filters to the input. To upsample the input instead of downsampling using sliding filters, the layer zero-pads each edge of the input with padding that has the size of the corresponding filter edge size minus 1.

By flattening the input and output, the transposed convolution operation is equivalent to $Y={C}^{\top }X+B$, where C and B denote the convolution matrix and bias vector for standard convolution derived from the layer weights and biases, respectively. This operation is equivalent to the backward function of a standard convolution layer.

A 1-D transposed convolution layer upsamples a single dimension only. The dimension that the layer upsamples 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 upsamples the time dimension.

• For 1-D image input (data with three dimensions corresponding to the spatial pixels, channels, and observations), the layer upsamples 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 upsamples 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, 2-D image data represented as a 4-D 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 TransposedConvolution1DLayer 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 FormatOutput 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)

## 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 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.

## Version History

Introduced in R2022a