# TransposedConvolution2DLayer

Transposed 2-D convolution layer

## Description

A transposed 2-D convolution layer upsamples two-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.

## Creation

Create a transposed convolution 2-D layer using transposedConv2dLayer.

## Properties

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### Transposed Convolution

Height and width of the filters, specified as a vector of two positive integers [h w], where h is the height and w is the width. FilterSize defines the size of the local regions to which the neurons connect in the input.

If you set FilterSize using an input argument, then you can specify FilterSize as scalar to use the same value for both dimensions.

Example: [5 5] specifies filters of height 5 and width 5.

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

Step size for traversing the input vertically and horizontally, specified as a vector [a b] of two positive integers, where a is the vertical step size and b is the horizontal step size. When creating the layer, you can specify Stride as a scalar to use the same value for both step sizes.

Example: [2 3] specifies a vertical step size of 2 and a horizontal step size of 3.

Method to determine cropping size, specified as 'manual' or same.

The software automatically sets the value of CroppingMode based on the 'Cropping' value you specify when creating the layer.

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

• If you set the 'Cropping' option to 'same', then the software automatically sets the CroppingMode property of the layer to 'same' and set the cropping so that the output size equals inputSize .* Stride, where inputSize is the height and width of the layer input.

To specify the cropping size, use the 'Cropping' option of transposedConv2dLayer.

Output size reduction, specified as a vector of four nonnegative integers [t b l r], where t, b, l, r are the amounts to crop from the top, bottom, left, and right, respectively.

To specify the cropping size manually, use the 'Cropping' option of transposedConv2dLayer.

Example: [0 1 0 1]

Note

Cropping property will be removed in a future release. Use CroppingSize instead. To specify the cropping size manually, use the 'Cropping' option of transposedConv2dLayer.

Output size reduction, specified as a vector of two nonnegative integers [a b], where a corresponds to the cropping from the top and bottom and b corresponds to the cropping from the left and right.

To specify the cropping size manually, use the 'Cropping' option of transposedConv2dLayer.

Example: [0 1]

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

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

• 'glorot' – Initialize the weights with the Glorot initializer [1] (also known as Xavier initializer). The Glorot initializer independently samples from a uniform distribution with zero mean and variance 2/(numIn + numOut), where numIn = FilterSize(1)*FilterSize(2)*NumChannels and numOut = FilterSize(1)*FilterSize(2)*NumFilters.

• 'he' – Initialize the weights with the He initializer [2]. The He initializer samples from a normal distribution with zero mean and variance 2/numIn, where numIn = FilterSize(1)*FilterSize(2)*NumChannels.

• 'narrow-normal' – Initialize the weights by independently sampling from a normal distribution with zero mean and standard deviation 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 convolutional layer, specified as a FilterSize(1)-by-FilterSize(2)-by-NumFilters-by-NumChannels array.

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 convolutional layer, specified as a numeric array.

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.

At training time, Bias is a 1-by-1-by-NumFilters array.

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. You can specify the global L2 regularization factor using the trainingOptions function.

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

### Layer

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 name ''.

Data Types: char | string

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

Data Types: double

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

Data Types: cell

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

Data Types: double

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

Data Types: cell

## Examples

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Create a transposed convolutional layer with 96 filters, each with a height and width of 11. Use a stride of 4 in the horizontal and vertical directions.

layer = transposedConv2dLayer(11,96,'Stride',4);

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## 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 R2017b

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Behavior changed in R2019a

Not recommended starting in R2019a

1 Image credit: Convolution arithmetic (License)