# transposedConv3dLayer

Transposed 3-D convolution layer

## Syntax

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

returns a 3-D transposed convolution layer and sets the `layer`

= transposedConv3dLayer(`filterSize`

,`numFilters`

)`FilterSize`

and
`NumFilters`

properties.

returns a 3-D transposed convolutional layer and specifies additional options using one or
more name-value pair arguments.`layer`

= transposedConv3dLayer(`filterSize`

,`numFilters`

,`Name,Value`

)

## Examples

### Create Transposed 3-D Convolutional Layer

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

## Input Arguments

`filterSize`

— Height, width, and depth of filters

positive integer | vector of three positive integers

Height, width, and depth of the filters, specified as a positive integer or a vector
of three positive integers `[h w d]`

, where `h`

is the
height, `w`

is the width, and `d`

is the depth. The
filter size defines the size of the local regions to which the neurons connect in the
input.

If `filterSize`

is a scalar, then the software uses the same
value for all three dimensions.

**Example: **
`[5 6 7]`

specifies filters with a height, width, and depth of
`5`

, `6`

, and `7`

respectively.

**Data Types: **`single`

| `double`

| `int8`

| `int16`

| `int32`

| `int64`

| `uint8`

| `uint16`

| `uint32`

| `uint64`

`numFilters`

— Number of filters

positive integer

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: **`transposedConv3dLayer(11,96,'Stride',4)`

creates a 3-D
transposed convolutional layer with 96 filters of size 11 and a stride of 4.

**Transposed Convolution**

`Stride`

— Step size for traversing input

`[1 1 1]`

(default) | vector of three positive integers

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`

`Cropping`

— Output size reduction

`0`

(default) | `"same"`

| vector of nonnegative integers | matrix of nonnegative integers

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, width, and depth 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, the left and right, and the front and back, 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. If the depth crop amount has an odd value, then the software trims an extra plane from the back.

A positive integer – Crop the specified amount of data from all the edges.

A vector of nonnegative integers

`[a b c]`

– Crop`a`

from the top and bottom, crop`b`

from the left and right, and crop`c`

from the front and back.a matrix of nonnegative integers

`[t l f; b r bk]`

of nonnegative integers — Crop`t`

,`l`

,`f`

,`b`

,`r`

,`bk`

from the top, left, front, bottom, right, and back 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 2]`

**Data Types: **`single`

| `double`

| `int8`

| `int16`

| `int32`

| `int64`

| `uint8`

| `uint16`

| `uint32`

| `uint64`

| `char`

| `string`

`NumChannels`

— Number of input channels

`"auto"`

(default) | positive integer

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**

`WeightsInitializer`

— Function to initialize weights

`'glorot'`

(default) | `'he'`

| `'narrow-normal'`

| `'zeros'`

| `'ones'`

| function handle

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`

`BiasInitializer`

— Function to initialize bias

`'zeros'`

(default) | `'narrow-normal'`

| `'ones'`

| 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`

`Weights`

— Layer weights

`[]`

(default) | numeric array

Layer weights for the transposed convolution operation, specified as a
`FilterSize(1)`

-by-`FilterSize(2)`

-by-`FilterSize(3)`

-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`

`Bias`

— Layer biases

`[]`

(default) | numeric array

Layer biases for the transposed convolutional operation, specified as a
1-by-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**

`WeightLearnRateFactor`

— Learning rate factor for weights

`1`

(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 you specify using
the `trainingOptions`

function.

**Data Types: **`single`

| `double`

| `int8`

| `int16`

| `int32`

| `int64`

| `uint8`

| `uint16`

| `uint32`

| `uint64`

`BiasLearnRateFactor`

— Learning rate factor for biases

`1`

(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 you specify using the `trainingOptions`

function.

**Data Types: **`single`

| `double`

| `int8`

| `int16`

| `int32`

| `int64`

| `uint8`

| `uint16`

| `uint32`

| `uint64`

`WeightL2Factor`

— *L*_{2} regularization factor for weights

1 (default) | nonnegative scalar

_{2}

*L _{2}* regularization factor for the weights,
specified as a nonnegative scalar.

The software multiplies this factor by the global
*L _{2}* regularization factor to determine the

*L*regularization for the weights in this layer. For example, if

_{2}`WeightL2Factor`

is `2`

,
then the *L*regularization for the weights in this layer is twice the global

_{2}*L*regularization factor. You can specify the global

_{2}*L*regularization factor using the

_{2}`trainingOptions`

function.**Data Types: **`single`

| `double`

| `int8`

| `int16`

| `int32`

| `int64`

| `uint8`

| `uint16`

| `uint32`

| `uint64`

`BiasL2Factor`

— *L*_{2} regularization factor for biases

`0`

(default) | nonnegative scalar

_{2}

*L _{2}* regularization factor for the biases,
specified as a nonnegative scalar.

The software multiplies this factor by the global
*L _{2}* regularization factor to determine the

*L*regularization for the biases in this layer. For example, if

_{2}`BiasL2Factor`

is `2`

, then the
*L*regularization for the biases in this layer is twice the global

_{2}*L*regularization factor. You can specify the global

_{2}*L*regularization factor using the

_{2}`trainingOptions`

function.**Data Types: **`single`

| `double`

| `int8`

| `int16`

| `int32`

| `int64`

| `uint8`

| `uint16`

| `uint32`

| `uint64`

**Layer**

`Name`

— Layer name

`''`

(default) | character vector | string scalar

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

`layer`

— Transposed 3-D convolution layer

`TransposedConvolution3DLayer`

object

Transposed 3-D convolution layer, returned as a `TransposedConvolution3dLayer`

object.

## Algorithms

### 3-D Transposed Convolutional Layer

A transposed 3-D convolution layer upsamples three-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.

## 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 R2019a**

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