Transposed 2-D convolution layer

A transposed 2-D convolution layer upsamples 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.

returns a transposed 2-D convolution layer and sets the
`layer`

= transposedConv2dLayer(`filterSize`

,`numFilters`

)`filterSize`

and `numFilters`

properties.

returns a transposed 2-D convolutional layer and specifies additional options using
one or more name-value pair arguments.`layer`

= transposedConv2dLayer(`filterSize`

,`numFilters`

,`Name,Value`

)

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);`

`filterSize`

— Height and width of filtersvector of two positive integers

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.

`numFilters`

— Number of filterspositive 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 convolutional layer.

**Example: **
`96`

Specify optional
comma-separated pairs of `Name,Value`

arguments. `Name`

is
the argument name and `Value`

is the corresponding value.
`Name`

must appear inside quotes. You can specify several name and value
pair arguments in any order as
`Name1,Value1,...,NameN,ValueN`

.

`'Cropping',1`

`'Stride'`

— Up-sampling factor`1`

(default) | vector of two positive integers | positive integerUp-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]`

`'Cropping'`

— Output size reduction`0`

(default) | `'same'`

| nonnegative integer | vector of two nonnegative integersOutput 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]`

`'NumChannels'`

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

(default) | positive integerNumber of channels for each filter, specified as
'`NumChannels`

' and `'auto'`

or
a positive 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)*NumChannels`

,`numOut = filterSize(1)*filterSize(2)*numFilters`

, and`NumChannels`

is the number of input channels.`'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`

and`NumChannels`

is the number of input channels.`'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 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-`numFilters`

-by-`NumChannels`

array.

**Data Types: **`single`

| `double`

`'Bias'`

— Layer biases`[]`

(default) | numeric arrayLayer biases for the 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-`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`

`layer`

— Transposed 2-D convolution layer`TransposedConvolution2DLayer`

objectTransposed 2-D convolution layer, returned as a `TransposedConvolution2DLayer`

object.

*Behavior changed in R2019a*

Starting in R2019a, the software, by default, initializes the layer weights of this layer using the Glorot initializer. This behavior helps stabilize training and usually reduces the training time of deep networks.

In previous releases, the software, by default, initializes the layer weights by sampling from
a normal distribution with zero mean and variance 0.01. To reproduce this behavior, set the
`'WeightsInitializer'`

option of the layer to
`'narrow-normal'`

.

[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.

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