convolution3dLayer

3-D convolutional layer

Description

A 3-D convolutional layer applies sliding cuboidal convolution filters to 3-D input. The layer convolves the input by moving the filters along the input vertically, horizontally, and along the depth, computing the dot product of the weights and the input, and then adding a bias term.

The dimensions that the layer convolves over depends on the layer input:

• For 3-D image input (data with five dimensions corresponding to pixels in three spatial dimensions, the channels, and the observations), the layer convolves over the spatial dimensions.

• For 3-D image sequence input (data with six dimensions corresponding to the pixels in three spatial dimensions, the channels, the observations, and the time steps), the layer convolves over the spatial dimensions.

• For 2-D image sequence input (data with five dimensions corresponding to the pixels in two spatial dimensions, the channels, the observations, and the time steps), the layer convolves over the spatial and time dimensions.

Creation

Syntax

layer = convolution3dLayer(filterSize,numFilters)

layer = convolution3dLayer(filterSize,numFilters,Name=Value)

Description

layer = convolution3dLayer(filterSize,numFilters) creates a 3-D convolutional layer and sets the FilterSize and NumFilters properties.

layer = convolution3dLayer(filterSize,numFilters,Name=Value) sets optional properties using one or more name-value arguments.

Input Arguments

filterSize — Height, width, and depth of filters

vector of three positive integers | positive integer

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 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 layer output.

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: convolution3dLayer(3,16,Padding="same") creates a 3-D convolutional layer with 16 filters of size [3 3 3] and "same" padding. At training time, the software calculates and sets the size of the padding so that the layer output has the same size as the input.

Stride — Step size for traversing input

[1 1 1] (default) | vector of three positive integers | positive integer

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

DilationFactor — Factor for dilated convolution

[1 1 1] (default) | vector of three positive integers | positive integer

Factor for dilated convolution (also known as atrous convolution), specified as a vector [h w d] of three positive integers, where h is the vertical dilation, w is the horizontal dilation, and d is the dilation along the depth. When creating the layer, you can specify DilationFactor as a scalar to use the same value for dilation in all three directions.

Use dilated convolutions to increase the receptive field (the area of the input which the layer can see) of the layer without increasing the number of parameters or computation.

The layer expands the filters by inserting zeros between each filter element. The dilation factor determines the step size for sampling the input or equivalently the upsampling factor of the filter. It corresponds to an effective filter size of (Filter Size – 1) .* Dilation Factor + 1. For example, a 3-by-3-by-3 filter with the dilation factor [2 2 2] is equivalent to a 5-by-5-by-5 filter with zeros between the elements.

Example: [2 3 1] dilates the filter vertically by a factor of 2, horizontally by a factor of 3, and along the depth by a factor of 1.

Padding — Input edge padding

0 (default) | array of nonnegative integers | "same"

Input edge padding, specified as one of these values:

• "same" — Add padding of size calculated by the software at training or prediction time so that the output has the same size as the input when the stride equals 1. If the stride is larger than 1, then the output size is ceil(inputSize/stride), where inputSize is the height, width, or depth of the input and stride is the stride in the corresponding dimension. The software adds the same amount of padding to the top and bottom, to the left and right, and to the front and back, if possible. If the padding in a given dimension has an odd value, then the software adds the extra padding to the input as postpadding. In other words, the software adds extra vertical padding to the bottom, extra horizontal padding to the right, and extra depth padding to the back of the input.

• Nonnegative integer p — Add padding of size p to all the edges of the input.

• Three-element vector [a b c] of nonnegative integers — Add padding of size a to the top and bottom, padding of size b to the left and right, and padding of size c to the front and back of the input.

• 2-by-3 matrix [t l f;b r k] of nonnegative integers — Add padding of size t to the top, b to the bottom, l to the left, r to the right, f to the front, and k to the back of the input. In other words, the top row specifies the prepadding and the second row defines the postpadding in the three dimensions.

Example: Padding=1 adds one row of padding to the top and bottom, one column of padding to the left and right, and one plane of padding to the front and back of the input.

Example: Padding="same" adds padding so that the output has the same size as the input (if the stride equals 1).

PaddingValue — Value to pad data

0 (default) | scalar | "symmetric-include-edge" | "symmetric-exclude-edge" | "replicate"

Value to pad data, specified as one of the following:

PaddingValue	Description	Example
Scalar	Pad with the specified scalar value.	$$\left[\begin{array}{ccc}3& 1& 4\\ 1& 5& 9\\ 2& 6& 5\end{array}\right]\to \left[\begin{array}{ccccccc}0& 0& 0& 0& 0& 0& 0\\ 0& 0& 0& 0& 0& 0& 0\\ 0& 0& 3& 1& 4& 0& 0\\ 0& 0& 1& 5& 9& 0& 0\\ 0& 0& 2& 6& 5& 0& 0\\ 0& 0& 0& 0& 0& 0& 0\\ 0& 0& 0& 0& 0& 0& 0\end{array}\right]$$
"symmetric-include-edge"	Pad using mirrored values of the input, including the edge values.	$$\left[\begin{array}{ccc}3& 1& 4\\ 1& 5& 9\\ 2& 6& 5\end{array}\right]\to \left[\begin{array}{ccccccc}5& 1& 1& 5& 9& 9& 5\\ 1& 3& 3& 1& 4& 4& 1\\ 1& 3& 3& 1& 4& 4& 1\\ 5& 1& 1& 5& 9& 9& 5\\ 6& 2& 2& 6& 5& 5& 6\\ 6& 2& 2& 6& 5& 5& 6\\ 5& 1& 1& 5& 9& 9& 5\end{array}\right]$$
"symmetric-exclude-edge"	Pad using mirrored values of the input, excluding the edge values.	$$\left[\begin{array}{ccc}3& 1& 4\\ 1& 5& 9\\ 2& 6& 5\end{array}\right]\to \left[\begin{array}{ccccccc}5& 6& 2& 6& 5& 6& 2\\ 9& 5& 1& 5& 9& 5& 1\\ 4& 1& 3& 1& 4& 1& 3\\ 9& 5& 1& 5& 9& 5& 1\\ 5& 6& 2& 6& 5& 6& 2\\ 9& 5& 1& 5& 9& 5& 1\\ 4& 1& 3& 1& 4& 1& 3\end{array}\right]$$
"replicate"	Pad using repeated border elements of the input	$$\left[\begin{array}{ccc}3& 1& 4\\ 1& 5& 9\\ 2& 6& 5\end{array}\right]\to \left[\begin{array}{ccccccc}3& 3& 3& 1& 4& 4& 4\\ 3& 3& 3& 1& 4& 4& 4\\ 3& 3& 3& 1& 4& 4& 4\\ 1& 1& 1& 5& 9& 9& 9\\ 2& 2& 2& 6& 5& 5& 5\\ 2& 2& 2& 6& 5& 5& 5\\ 2& 2& 2& 6& 5& 5& 5\end{array}\right]$$

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

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 biases

"zeros" (default) | "narrow-normal" | "ones" | 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 form bias = func(sz), where sz is the size of the biases.

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

Data Types: char | string | function_handle

Weights — Layer weights

[] (default) | numeric array

Initial layer weights for the convolutional layer, specified as a numeric 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.

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

Data Types: single | double

Bias — Layer biases

[] (default) | numeric array

Initial 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 and trainNetwork functions use the Bias property as the initial value. If Bias is empty, then software 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 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 — L₂ regularization factor for weights

1 (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.

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

BiasL2Factor — L₂ regularization factor for biases

0 (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. 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

Name — Layer name

"" (default) | character vector | string scalar

Layer name, specified as a character vector or a string scalar. For Layer array input, the trainnet and dlnetwork functions automatically assign names to layers with the name "".

The Convolution3DLayer object stores the Name property as a character vector.

Data Types: char | string

Properties

3-D Convolution

FilterSize — Height, width, and depth of filters

vector 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 filters

positive integer

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.

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

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

DilationFactor — Factor for dilated convolution

[1 1 1] (default) | vector of three positive integers

Factor for dilated convolution (also known as atrous convolution), specified as a vector [h w d] of three positive integers, where h is the vertical dilation, w is the horizontal dilation, and d is the dilation along the depth. When creating the layer, you can specify DilationFactor as a scalar to use the same value for dilation in all three directions.

Use dilated convolutions to increase the receptive field (the area of the input which the layer can see) of the layer without increasing the number of parameters or computation.

The layer expands the filters by inserting zeros between each filter element. The dilation factor determines the step size for sampling the input or equivalently the upsampling factor of the filter. It corresponds to an effective filter size of (Filter Size – 1) .* Dilation Factor + 1. For example, a 3-by-3-by-3 filter with the dilation factor [2 2 2] is equivalent to a 5-by-5-by-5 filter with zeros between the elements.

Example: [2 3 1] dilates the filter vertically by a factor of 2, horizontally by a factor of 3, and along the depth by a factor of 1.

PaddingSize — Size of padding

[0 0 0;0 0 0] (default) | 2-by-3 matrix of nonnegative integers

Size of padding to apply to input borders, specified as 2-by-3 matrix [t l f;b r k] of nonnegative integers, where t and b are the padding applied to the top and bottom in the vertical direction, l and r are the padding applied to the left and right in the horizontal direction, and f and k are the padding applied to the front and back along the depth. In other words, the top row specifies the prepadding and the second row defines the postpadding in the three dimensions.

When you create a layer, use the Padding name-value argument to specify the padding size.

Example: [1 2 4; 1 2 4] adds one row of padding to the top and bottom, two columns of padding to the left and right, and four planes of padding to the front and back of the input.

PaddingMode — Method to determine padding size

"manual" (default) | "same"

Method to determine padding size, specified as "manual" or "same".

The software automatically sets the value of PaddingMode based on the Padding argument value you specify when creating a layer.

• If you set the Padding argument to a scalar or a vector of nonnegative integers, then the software automatically sets PaddingMode to "manual".

• If you set the Padding argument to "same", then the software automatically sets PaddingMode to "same" and calculates the size of the padding at training time so that the output has the same size as the input when the stride equals 1. If the stride is larger than 1, then the output size is ceil(inputSize/stride), where inputSize is the height, width, or depth of the input and stride is the stride in the corresponding dimension. The software adds the same amount of padding to the top and bottom, to the left and right, and to the front and back, if possible. If the padding in a given dimension has an odd value, then the software adds the extra padding to the input as postpadding. In other words, the software adds extra vertical padding to the bottom, extra horizontal padding to the right, and extra depth padding to the back of the input.

The Convolution3DLayer object stores this property as a character vector.

PaddingValue — Value to pad data

0 (default) | scalar | "symmetric-include-edge" | "symmetric-exclude-edge" | "replicate"

Value to pad data, specified as one of these values:

PaddingValue	Description	Example
Scalar	Pad with the specified scalar value.	$$\left[\begin{array}{ccc}3& 1& 4\\ 1& 5& 9\\ 2& 6& 5\end{array}\right]\to \left[\begin{array}{ccccccc}0& 0& 0& 0& 0& 0& 0\\ 0& 0& 0& 0& 0& 0& 0\\ 0& 0& 3& 1& 4& 0& 0\\ 0& 0& 1& 5& 9& 0& 0\\ 0& 0& 2& 6& 5& 0& 0\\ 0& 0& 0& 0& 0& 0& 0\\ 0& 0& 0& 0& 0& 0& 0\end{array}\right]$$
"symmetric-include-edge"	Pad using mirrored values of the input, including the edge values.	$$\left[\begin{array}{ccc}3& 1& 4\\ 1& 5& 9\\ 2& 6& 5\end{array}\right]\to \left[\begin{array}{ccccccc}5& 1& 1& 5& 9& 9& 5\\ 1& 3& 3& 1& 4& 4& 1\\ 1& 3& 3& 1& 4& 4& 1\\ 5& 1& 1& 5& 9& 9& 5\\ 6& 2& 2& 6& 5& 5& 6\\ 6& 2& 2& 6& 5& 5& 6\\ 5& 1& 1& 5& 9& 9& 5\end{array}\right]$$
"symmetric-exclude-edge"	Pad using mirrored values of the input, excluding the edge values.	$$\left[\begin{array}{ccc}3& 1& 4\\ 1& 5& 9\\ 2& 6& 5\end{array}\right]\to \left[\begin{array}{ccccccc}5& 6& 2& 6& 5& 6& 2\\ 9& 5& 1& 5& 9& 5& 1\\ 4& 1& 3& 1& 4& 1& 3\\ 9& 5& 1& 5& 9& 5& 1\\ 5& 6& 2& 6& 5& 6& 2\\ 9& 5& 1& 5& 9& 5& 1\\ 4& 1& 3& 1& 4& 1& 3\end{array}\right]$$
"replicate"	Pad using repeated border elements of the input	$$\left[\begin{array}{ccc}3& 1& 4\\ 1& 5& 9\\ 2& 6& 5\end{array}\right]\to \left[\begin{array}{ccccccc}3& 3& 3& 1& 4& 4& 4\\ 3& 3& 3& 1& 4& 4& 4\\ 3& 3& 3& 1& 4& 4& 4\\ 1& 1& 1& 5& 9& 9& 9\\ 2& 2& 2& 6& 5& 5& 5\\ 2& 2& 2& 6& 5& 5& 5\\ 2& 2& 2& 6& 5& 5& 5\end{array}\right]$$

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

NumChannels — Number of input channels

"auto" (default) | positive integer

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.

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 biases

"zeros" (default) | "narrow-normal" | "ones" | 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 form bias = func(sz), where sz is the size of the biases.

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

The Convolution3DLayer object stores this property as a character vector or a function handle.

Data Types: char | string | function_handle

Weights — Layer weights

[] (default) | numeric array

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

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

Data Types: single | double

Bias — Layer biases

[] (default) | numeric array

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. If Bias is empty, then software 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

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 — L₂ regularization factor for weights

1 (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.

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

BiasL2Factor — L₂ regularization factor for biases

0 (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. 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

Name — Layer name

"" (default) | character vector | string scalar

Layer name, specified as a character vector or string scalar. For Layer array input, the trainnet and dlnetwork functions automatically assign names to layers with the name "".

The Convolution3DLayer object stores this property as a character vector.

Data Types: char | string

NumInputs — Number of inputs

1 (default)

This property is read-only.

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

Data Types: double

InputNames — Input names

{'in'} (default)

This property is read-only.

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

Data Types: cell

NumOutputs — Number of outputs

1 (default)

This property is read-only.

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

Data Types: double

OutputNames — Output names

{'out'} (default)

This property is read-only.

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

Data Types: cell

Examples

Create 3-D Convolution Layer

Create a 3-D convolution layer with 16 filters, each with a height, width, and depth of 5. Use a stride (step size) of 4 in all three directions.

layer = convolution3dLayer(5,16,Stride=4)

layer = 
  Convolution3DLayer with properties:

              Name: ''

   Hyperparameters
        FilterSize: [5 5 5]
       NumChannels: 'auto'
        NumFilters: 16
            Stride: [4 4 4]
    DilationFactor: [1 1 1]
       PaddingMode: 'manual'
       PaddingSize: [2x3 double]
      PaddingValue: 0

   Learnable Parameters
           Weights: []
              Bias: []

Use properties method to see a list of all properties.

Include a 3-D convolution layer in a Layer array.

layers = [ ...
    image3dInputLayer([28 28 28 3])
    convolution3dLayer(5,16,Stride=4)
    reluLayer
    maxPooling3dLayer(2,Stride=4)
    fullyConnectedLayer(10)
    softmaxLayer]

layers = 
  6x1 Layer array with layers:

     1   ''   3-D Image Input   28x28x28x3 images with 'zerocenter' normalization
     2   ''   3-D Convolution   16 5x5x5 convolutions with stride [4  4  4] and padding [0  0  0; 0  0  0]
     3   ''   ReLU              ReLU
     4   ''   3-D Max Pooling   2x2x2 max pooling with stride [4  4  4] and padding [0  0  0; 0  0  0]
     5   ''   Fully Connected   10 fully connected layer
     6   ''   Softmax           softmax

Specify Initial Weights and Biases in 3-D Convolutional Layer

To specify the weights and bias initializer functions, use the WeightsInitializer and BiasInitializer properties respectively. To specify the weights and biases directly, use the Weights and Bias properties respectively.

Specify Initialization Functions

Create a 3-D convolutional layer with 32 filters, each with a height, width, and depth of 5. Specify the weights initializer to be the He initializer.

filterSize = 5;
numFilters = 32;
layer = convolution3dLayer(filterSize,numFilters, ...
    'WeightsInitializer','he')

layer = 
  Convolution3DLayer with properties:

              Name: ''

   Hyperparameters
        FilterSize: [5 5 5]
       NumChannels: 'auto'
        NumFilters: 32
            Stride: [1 1 1]
    DilationFactor: [1 1 1]
       PaddingMode: 'manual'
       PaddingSize: [2x3 double]
      PaddingValue: 0

   Learnable Parameters
           Weights: []
              Bias: []

Use properties method to see a list of all properties.

Note that the Weights and Bias properties are empty. At training time, the software initializes these properties using the specified initialization functions.

Specify Custom Initialization Functions

To specify your own initialization function for the weights and biases, set the WeightsInitializer and BiasInitializer properties to a function handle. For these properties, specify function handles that take the size of the weights and biases as input and output the initialized value.

Create a convolutional layer with 32 filters, each with a height, width, and depth of 5. Specify initializers that sample the weights and biases from a Gaussian distribution with a standard deviation of 0.0001.

filterSize = 5;
numFilters = 32;

layer = convolution3dLayer(filterSize,numFilters, ...
    'WeightsInitializer', @(sz) rand(sz) * 0.0001, ...
    'BiasInitializer', @(sz) rand(sz) * 0.0001)

layer = 
  Convolution3DLayer with properties:

              Name: ''

   Hyperparameters
        FilterSize: [5 5 5]
       NumChannels: 'auto'
        NumFilters: 32
            Stride: [1 1 1]
    DilationFactor: [1 1 1]
       PaddingMode: 'manual'
       PaddingSize: [2x3 double]
      PaddingValue: 0

   Learnable Parameters
           Weights: []
              Bias: []

Use properties method to see a list of all properties.

Again, the Weights and Bias properties are empty. At training time, the software initializes these properties using the specified initialization functions.

Specify Weights and Bias Directly

Create a 3-D convolutional layer compatible with color images. Set the weights and bias to W and b in the MAT file Conv3dWeights.mat respectively.

filterSize = 5;
numFilters = 32;
load Conv3dWeights

layer = convolution3dLayer(filterSize,numFilters, ...
    'Weights',W, ...
    'Bias',b)

layer = 
  Convolution3DLayer with properties:

              Name: ''

   Hyperparameters
        FilterSize: [5 5 5]
       NumChannels: 3
        NumFilters: 32
            Stride: [1 1 1]
    DilationFactor: [1 1 1]
       PaddingMode: 'manual'
       PaddingSize: [2x3 double]
      PaddingValue: 0

   Learnable Parameters
           Weights: [5-D double]
              Bias: [1x1x1x32 double]

Use properties method to see a list of all properties.

Here, the Weights and Bias properties contain the specified values. At training time, if these properties are non-empty, then the software uses the specified values as the initial weights and biases. In this case, the software does not use the initializer functions.

Create Convolutional Layer That Fully Covers 3-D Input

Suppose the size of the input is 28-by-28-by-28-by-1. Create a 3-D convolutional layer with 16 filters, each with a height of 6, a width of 4, and a depth of 5. Set the stride in all dimensions to 4.

Make sure the convolution covers the input completely. For the convolution to fully cover the input, the output dimensions must be integer numbers. When there is no dilation, the i-th output dimension is calculated as (imageSize(i) - filterSize(i) + padding(i)) / stride(i) + 1.

• For the horizontal output dimension to be an integer, two rows of padding are required: (28 – 6 + 2)/4 + 1 = 7. Distribute the padding symmetrically by adding one row of padding at the top and bottom of the image.

• For the vertical output dimension to be an integer, no padding is required: (28 – 4+ 0)/4 + 1 = 7.

• For the depth output dimension to be an integer, one plane of padding is required: (28 – 5 + 1)/4 + 1 = 7. You must distribute the padding asymmetrically across the front and back of the image. This example adds one plane of padding to the back of the image.

Construct the convolutional layer. Specify 'Padding' as a 2-by-3 matrix. The first row specifies prepadding and the second row specifies postpadding in the three dimensions.

layer = convolution3dLayer([6 4 5],16,'Stride',4,'Padding',[1 0 0;1 0 1])

layer = 
  Convolution3DLayer with properties:

              Name: ''

   Hyperparameters
        FilterSize: [6 4 5]
       NumChannels: 'auto'
        NumFilters: 16
            Stride: [4 4 4]
    DilationFactor: [1 1 1]
       PaddingMode: 'manual'
       PaddingSize: [2x3 double]
      PaddingValue: 0

   Learnable Parameters
           Weights: []
              Bias: []

Use properties method to see a list of all properties.

Algorithms

3-D Convolutional Layer

A convolutional layer applies sliding convolutional filters to the input. A 3-D convolutional layer extends the functionality of a 2-D convolutional layer to a third dimension, depth. The layer convolves the input by moving the filters along the input vertically, horizontally, and along the depth, computing the dot product of the weights and the input, and then adding a bias term. To learn more, see the definition of convolutional layer on the convolution2dLayer reference page.

The dimensions that the layer convolves over depends on the layer input:

• For 3-D image input (data with five dimensions corresponding to pixels in three spatial dimensions, the channels, and the observations), the layer convolves over the spatial dimensions.

• For 3-D image sequence input (data with six dimensions corresponding to the pixels in three spatial dimensions, the channels, the observations, and the time steps), the layer convolves over the spatial dimensions.

• For 2-D image sequence input (data with five dimensions corresponding to the pixels in two spatial dimensions, the channels, the observations, and the time steps), the layer convolves over the spatial and time dimensions.

Layer Input and Output Formats

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 formats consist 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 those for developing a custom layer, using a functionLayer object, or using the forward and predict functions with dlnetwork objects.

This table shows the supported input formats of Convolution3DLayer objects and the corresponding output format. If the software passes the output of the layer 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 according to the formats in this table. The formats listed here are only a subset. The layer may support additional formats such as formats with additional "S" (spatial) or "U" (unspecified) dimensions.

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

In dlnetwork objects, Convolution3DLayer objects also support these input and output format combinations.

Input Format	Output Format
"SSSC" (spatial, spatial, spatial, channel)	"SSSC" (spatial, spatial, spatial, channel)
"SSCT" (spatial, spatial, channel, time)	"SSCT" (spatial, spatial, channel, time)
"SSSCT" (spatial, spatial, spatial, channel, time)	"SSSCT" (spatial, 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 R2019a