Transposed 3-D convolution layer

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.

Create a transposed convolution 3-D output layer using `transposedConv3dLayer`

.

`FilterSize`

— Height, width, and depth of filtersvector of three positive integers

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.

`NumFilters`

— Number of filterspositive integer

Number of filters, specified as a positive integer. This number corresponds to the number of neurons in the convolutional layer that connect to the same region in the input. This parameter determines the number of channels (feature maps) in the output of the convolutional layer.

**Example: **
`96`

`Stride`

— Step size for traversing input`[1 1 1]`

(default) | vector of three positive integersStep 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.

`CroppingMode`

— Method to determine cropping size`'manual'`

(default) | `'same'`

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`

.

`CroppingSize`

— Output size reduction`[0 0 0;0 0 0]`

(default) | matrix of nonnegative integersOutput 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]`

`NumChannels`

— Number of channels for each filter`'auto'`

(default) | integerNumber of channels for each filter, specified `'auto'`

or an
integer.

This parameter must be equal to the number of channels of the input to this convolutional layer. For example, if the input is a color image, then the number of channels for the input must be 3. If the number of filters for the convolutional layer prior to the current layer is 16, then the number of channels for this layer must be 16.

`WeightsInitializer`

— Function to initialize weights`'glorot'`

(default) | `'he'`

| `'narrow-normal'`

| `'zeros'`

| `'ones'`

| function handleFunction 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`

`BiasInitializer`

— Function to initialize bias`'zeros'`

(default) | `'narrow-normal'`

| `'ones'`

| function handleFunction 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 zero mean and standard deviation 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`

`Weights`

— Layer weights`[]`

(default) | numeric arrayLayer 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 training 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`

`Bias`

— Layer biases`[]`

(default) | numeric arrayLayer biases for the transposed convolutional layer, specified as a numeric array.

The layer biases are learnable parameters. When training 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-1-by-`NumFilters`

array.

**Data Types: **`single`

| `double`

`WeightLearnRateFactor`

— Learning rate factor for weights1 (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 specified with the `trainingOptions`

function.

**Example: **
`2`

`BiasLearnRateFactor`

— Learning rate factor for biases1 (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 specified with the `trainingOptions`

function.

**Example: **
`2`

`WeightL2Factor`

— L2 regularization factor for weights1 (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.

**Example: **
`2`

`BiasL2Factor`

— L2 regularization factor for biases0 (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. You can specify the global L2
regularization factor using the `trainingOptions`

function.

**Example: **
`2`

`Name`

— Layer name`''`

(default) | character vector | string scalar
Layer name, specified as a character vector or a string scalar.
To include a layer in a layer graph, you must specify a nonempty unique layer name. If you train
a series network with the layer and `Name`

is set to `''`

,
then the software automatically assigns a name to the layer at training time.

**Data Types: **`char`

| `string`

`NumInputs`

— Number of inputs1 (default)

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

**Data Types: **`double`

`InputNames`

— Input names`{'in'}`

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

**Data Types: **`cell`

`NumOutputs`

— Number of outputs1 (default)

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

**Data Types: **`double`

`OutputNames`

— Output names`{'out'}`

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

**Data Types: **`cell`

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

[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*, pp. 249-256. 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 IEEE international conference on computer vision*, pp. 1026-1034. 2015.

`averagePooling3dLayer`

| `convolution3dLayer`

| `maxPooling3dLayer`

| `transposedConv2dLayer`

| `transposedConv3dLayer`

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