# transposedConv2dLayer

Transposed 2-D convolution layer

## Syntax

``layer = transposedConv2dLayer(filterSize,numFilters)``
``layer = transposedConv2dLayer(filterSize,numFilters,Name,Value)``

## 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 performs the transpose of convolution and does not perform deconvolution.

````layer = transposedConv2dLayer(filterSize,numFilters)` returns a 2-D transposed convolution layer and sets the `FilterSize` and `NumFilters` properties.```

example

````layer = transposedConv2dLayer(filterSize,numFilters,Name,Value)` returns a 2-D transposed convolutional layer and specifies additional options using one or more name-value pair arguments.```

## 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);`

## Input Arguments

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

If `filterSize` is a positive integer, then the software uses the same value for both dimensions.

Example: `[5 6]` specifies filters of height and width of `5` and `6`, respectively.

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.

Before R2021a, use commas to separate each name and value, and enclose `Name` in quotes.

Example: `transposedConv2dLayer(11,96,'Stride',4)` creates a 2-D transposed convolutional layer with 96 filters of size 11 and a stride of 4.

Transposed Convolution

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Up-sampling factor of the input, specified as one of the following:

• A vector of two positive integers ```[a b]```, where `a` is the vertical stride and `b` is the horizontal stride.

• A positive integer the corresponds to both the vertical and horizontal stride.

Example: `'Stride',[2 1]`

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 height and width of the layer input. If you set the `Cropping` option to `"same"`, then the software automatically sets the `CroppingMode` property of the layer to `'same'`.

The software trims an equal amount from the top and bottom, and the left and right, if possible. If the vertical crop amount has an odd value, then the software trims an extra row from the bottom. 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 all the edges.

• A vector of nonnegative integers `[a b]` - Crop `a` from the top and bottom and crop `b` from the left and right.

• A vector `[t b l r]` - Crop `t`, `b`, `l`, `r` from the top, bottom, left, and right of the input, respectively.

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

Example: `[1 2]`

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 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 transposed convolution operation, specified as a `filterSize(1)`-by-`filterSize(2)`-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-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. 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

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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 2-D convolution layer, returned as a `TransposedConvolution2DLayer` object.

## Algorithms

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### 2-D Transposed Convolutional Layer

A transposed 2-D convolution layer upsamples two-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.

This image shows a 4-by-4 filter upsampling 2-by-2 input. The lower map represents the input and the upper map represents the output. 1

## 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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1 Image credit: Convolution arithmetic (License)