# TransposedConvolution3dLayer

Transposed 3-D convolution layer

Since R2019a

## Description

A transposed 3-D convolution layer upsamples three-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 3-D layer using `transposedConv3dLayer`.

## Properties

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### Transposed Convolution

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

When creating the layer, you can specify `FilterSize` as a scalar to use the same value for the height, width, and depth.

Example: `[5 5 5]` specifies filters with a height, width, and depth of 5.

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 in three dimensions, specified as a vector `[a b c]` of three positive integers, where `a` is the vertical step size, `b` is the horizontal step size, and `c` is the step size along the depth. When creating the layer, you can specify `Stride` as a scalar to use the same value for step sizes in all three directions.

Example: `[2 3 1]` specifies a vertical step size of 2, a horizontal step size of 3, and a step size along the depth of 1.

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

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, width, and depth of the layer input.

To specify the cropping size, use the `'Cropping'` option of `transposedConv3dLayer`.

Output size reduction, specified as a matrix of nonnegative integers ```[t l f; b r bk]```, `t`, `l`, `f`, `b`, `r`, `bk` are the amounts to crop from the top, left, front, bottom, right, and back of the input, respectively.

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

Example: `[0 1 0 1 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)*FilterSize(3)*NumChannels``` and ```numOut = FilterSize(1)*FilterSize(2)*FilterSize(3)*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)*FilterSize(3)*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 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`

Layer weights for the transposed convolutional layer, specified as a numeric 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.

At training time, `Weights` is a `FilterSize(1)`-by-`FilterSize(2)`-by-`FilterSize(3)`-by-`NumFilters`-by-`NumChannels` array.

Data Types: `single` | `double`

Layer biases for the transposed convolutional layer, specified as a numeric array.

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`.

At training time, `Bias` is a 1-by-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. 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

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`

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 3-D convolutional layer with 32 filters, each with a height, width, and depth of 11. Use a stride of 4 in the horizontal and vertical directions and 2 along the depth.

`layer = transposedConv3dLayer(11,32,'Stride',[4 4 2])`
```layer = TransposedConvolution3DLayer with properties: Name: '' Hyperparameters FilterSize: [11 11 11] NumChannels: 'auto' NumFilters: 32 Stride: [4 4 2] CroppingMode: 'manual' CroppingSize: [2x3 double] Learnable Parameters Weights: [] Bias: [] Show all properties ```

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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. 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 R2019a