TransposedConvolution2DLayer - Transposed 2-D convolution layer - MATLAB (original) (raw)

Transposed 2-D convolution layer

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 is the transpose of convolution and does not perform deconvolution.

Properties

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Transposed Convolution

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.

This property is read-only.

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.

Step size for traversing the input vertically and horizontally, specified as a vector[a b] of two positive integers, where a is the vertical step size and b is the horizontal step size. When creating the layer, you can specify Stride as a scalar to use the same value for both step sizes.

Example: [2 3] specifies a vertical step size of 2 and a horizontal step size of 3.

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 and width of the layer input.

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

Output size reduction, specified as a vector of four nonnegative integers [t b l r], where t,b, l, r are the amounts to crop from the top, bottom, left, and right, respectively.

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

Example: [0 1 0 1]

Output size reduction, specified as a vector of two nonnegative integers [a b], where a corresponds to the cropping from the top and bottom andb corresponds to the cropping from the left and right.

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

Example: [0 1]

This property is read-only.

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.

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)*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 variance2/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 formweights = 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 these values:

"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 have the formbias = func(sz), where sz is the size of the biases.

The layer initializes the biases only when the Bias property is empty.

The TransposedConvolution2DLayer object stores this property as a character vector or a function handle.

Data Types: char | string | function_handle

Layer weights for the convolutional layer, specified as aFilterSize(1)-by-FilterSize(2)-by-NumFilters-by-NumChannels array.

The layer weights are learnable parameters. You can specify the initial value of 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 the trainnet function uses the Weights property as the initial value. If the Weights property is empty, then the software uses the initializer specified by the WeightsInitializer property of the layer.

Data Types: single | double

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

The layer biases are learnable parameters. When you train a neural network, if Bias is nonempty, then the trainnet function uses the Bias property as the initial value. IfBias is empty, then software uses the initializer specified by BiasInitializer.

At training time, Bias is a 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.

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.

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.

Layer

Data Types: char | string

This property is read-only.

Number of inputs to the layer, stored as 1. This layer accepts a single input only.

Data Types: double

This property is read-only.

Input names, stored as {'in'}. This layer accepts a single input only.

Data Types: cell

This property is read-only.

Number of outputs from the layer, stored as 1. This layer has a single output only.

Data Types: double

This property is read-only.

Output names, stored as {'out'}. This layer has a single output only.

Data Types: cell

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);

Algorithms

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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⊤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 3-by-3 filter upsampling 2-by-2 input. The lower map represents the input and the upper map represents the output. 1

Animation showing a sliding 3-by-3 transposed convolutional filter over an image. The input image is padded such that it is two pixels larger in each direction. When the filter slides over the input image, it can cover the padding regions. The input is a 2-by-2 image. The padded input is a 6-by-6 image. The output is a 4-by-4 image.

Layers in a layer array or layer graph pass data to subsequent layers as formatted dlarray objects. The format of a dlarray object is a string of characters in which each character describes the corresponding dimension of the data. The format consists of one or more of these characters:

"S" — Spatial
"C" — Channel
"B" — Batch
"T" — Time
"U" — Unspecified

For example, you can describe 2-D image data that is represented as a 4-D array, where the first two dimensions correspond to the spatial dimensions of the images, the third dimension corresponds to the channels of the images, and the fourth dimension corresponds to the batch dimension, as having the format "SSCB" (spatial, spatial, channel, batch).

You can interact with these dlarray objects in automatic differentiation workflows such as developing a custom layer, using a functionLayer object, or using the forward and predict functions withdlnetwork objects.

This table shows the supported input formats ofTransposedConvolution2DLayer objects and the corresponding output format. If the output of the layer is passed to a custom layer that does not inherit from the nnet.layer.Formattable class, or a FunctionLayer object with the Formattable property set to 0 (false), then the layer receives an unformatted dlarray object with dimensions ordered corresponding to the formats in this table.

Input Format	Output Format
"SSCB" (spatial, spatial, channel, batch)	"SSCB" (spatial, spatial, channel, batch)
"SSC" (spatial, spatial, channel)	"SSC" (spatial, spatial, channel)

In dlnetwork objects, TransposedConvolution2DLayer objects also support these input and output format combinations.

Input Format	Output Format
"SSCBT" (spatial, spatial, channel, batch, time)	"SSCBT" (spatial, spatial, channel, batch, time)
"SSCT" (spatial, spatial, channel, time)	"SSCT" (spatial, spatial, channel, time)

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 2015 IEEE International Conference on Computer Vision (ICCV), 1026–34. Santiago, Chile: IEEE, 2015. https://doi.org/10.1109/ICCV.2015.123

Version History

Introduced in R2017b

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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'.

Cropping property ofTransposedConvolution2DLayer will be removed, use CroppingSize instead. To update your code, replace all instances of the Cropping property withCroppingSize.

1 Image credit: Convolution arithmetic (License)