convolution3dLayer
3D convolutional layer
Description
A 3D convolutional layer applies sliding cuboidal convolution filters to 3D 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 3D 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 3D 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 2D 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
Description
creates a 3D convolutional layer and sets the layer
= convolution3dLayer(filterSize
,numFilters
)FilterSize
and NumFilters
properties.
sets the optional layer
= convolution3dLayer(filterSize
,numFilters
,Name,Value
)Stride
, DilationFactor
, NumChannels
, Parameters and Initialization, Learning Rate and Regularization, and Name
properties
using namevalue pairs. To specify input padding, use the 'Padding'
namevalue pair argument. For example,
convolution3dLayer(11,96,'Stride',4,'Padding',1)
creates a 3D
convolutional layer with 96 filters of size [11 11 11]
, a stride of
[4 4 4]
, and padding of size 1 along all edges of the layer input.
You can specify multiple namevalue pairs. Enclose each property name in single
quotes.
Input Arguments
Specify optional pairs of arguments as
Name1=Value1,...,NameN=ValueN
, where Name
is
the argument name and Value
is the corresponding value.
Namevalue 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 3D
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.
Padding
— Input edge padding
0
(default)  array of nonnegative integers  'same'
Input edge padding, specified as the commaseparated pair consisting of
'Padding'
and 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 isceil(inputSize/stride)
, whereinputSize
is the height, width, or depth of the input andstride
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 sizep
to all the edges of the input.Threeelement vector
[a b c]
of nonnegative integers — Add padding of sizea
to the top and bottom, padding of sizeb
to the left and right, and padding of sizec
to the front and back of the input.2by3 matrix
[t l f;b r k]
of nonnegative integers — Add padding of sizet
to the top,b
to the bottom,l
to the left,r
to the right,f
to the front, andk
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).
Properties
3D 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 readonly.
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 3by3by3 filter with the dilation factor [2 2 2]
is
equivalent to a 5by5by5 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)  2by3 matrix of nonnegative integers
Size of padding to apply to input borders, specified as 2by3 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'
namevalue pair 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' value you specify when creating a layer.
If you set the
'Padding'
option to a scalar or a vector of nonnegative integers, then the software automatically setsPaddingMode
to'manual'
.If you set the
'Padding'
option to'same'
, then the software automatically setsPaddingMode
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 isceil(inputSize/stride)
, whereinputSize
is the height, width, or depth of the input andstride
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.
PaddingValue
— Value to pad data
0 (default)  scalar  'symmetricincludeedge'
 'symmetricexcludeedge'
 'replicate'
Value to pad data, specified as one of the following:
PaddingValue  Description  Example 

Scalar  Pad with the specified scalar value. 
$$\left[\begin{array}{ccc}3& 1& 4\\ 1& 5& 9\\ 2& 6& 5\end{array}\right]\to \left[\begin{array}{ccccccc}0& 0& 0& 0& 0& 0& 0\\ 0& 0& 0& 0& 0& 0& 0\\ 0& 0& 3& 1& 4& 0& 0\\ 0& 0& 1& 5& 9& 0& 0\\ 0& 0& 2& 6& 5& 0& 0\\ 0& 0& 0& 0& 0& 0& 0\\ 0& 0& 0& 0& 0& 0& 0\end{array}\right]$$ 
'symmetricincludeedge'  Pad using mirrored values of the input, including the edge values. 
$$\left[\begin{array}{ccc}3& 1& 4\\ 1& 5& 9\\ 2& 6& 5\end{array}\right]\to \left[\begin{array}{ccccccc}5& 1& 1& 5& 9& 9& 5\\ 1& 3& 3& 1& 4& 4& 1\\ 1& 3& 3& 1& 4& 4& 1\\ 5& 1& 1& 5& 9& 9& 5\\ 6& 2& 2& 6& 5& 5& 6\\ 6& 2& 2& 6& 5& 5& 6\\ 5& 1& 1& 5& 9& 9& 5\end{array}\right]$$ 
'symmetricexcludeedge'  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 readonly.
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, thenNumChannels
must be 3. If the input is the output of a convolutional layer with 16 filters, thenNumChannels
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'
 'narrownormal'
 '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 variance2/(numIn + numOut)
, wherenumIn = FilterSize(1)*FilterSize(2)*FilterSize(3)*NumChannels
andnumOut = 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 variance2/numIn
, wherenumIn = FilterSize(1)*FilterSize(2)*FilterSize(3)*NumChannels
.'narrownormal'
– 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)
, wheresz
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)  'narrownormal'
 '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.'narrownormal'
— 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)
, wheresz
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 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 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.
At training time, Weights
is a
FilterSize(1)
byFilterSize(2)
byFilterSize(3)
byNumChannels
byNumFilters
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
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
1by1by1byNumFilters
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
— L_{2} regularization factor for weights
1 (default)  nonnegative scalar
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_{2} regularization for the weights in
this layer. For example, if WeightL2Factor
is 2
,
then the L_{2} regularization for the weights in
this layer is twice the global L_{2}
regularization factor. You can specify the global
L_{2} regularization factor using the
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
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_{2} regularization for the biases in this
layer. For example, if BiasL2Factor
is 2
, then the
L_{2} regularization for the biases in this layer
is twice the global L_{2} regularization factor. You can
specify the global L_{2} regularization factor 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 a string scalar.
For Layer
array input, the trainNetwork
,
assembleNetwork
, layerGraph
, and
dlnetwork
functions automatically assign names to layers with name
''
.
Data Types: char
 string
NumInputs
— Number of inputs
1
(default)
This property is readonly.
Number of inputs of the layer. This layer accepts a single input only.
Data Types: double
InputNames
— Input names
{'in'}
(default)
This property is readonly.
Input names of the layer. This layer accepts a single input only.
Data Types: cell
NumOutputs
— Number of outputs
1
(default)
This property is readonly.
Number of outputs of the layer. This layer has a single output only.
Data Types: double
OutputNames
— Output names
{'out'}
(default)
This property is readonly.
Output names of the layer. This layer has a single output only.
Data Types: cell
Examples
Create 3D Convolution Layer
Create a 3D 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: [] Show all properties
Include a 3D 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 classificationLayer]
layers = 7x1 Layer array with layers: 1 '' 3D Image Input 28x28x28x3 images with 'zerocenter' normalization 2 '' Convolution 16 5x5x5 convolutions with stride [4 4 4] and padding [0 0 0; 0 0 0] 3 '' ReLU ReLU 4 '' 3D 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 7 '' Classification Output crossentropyex
Specify Initial Weights and Biases in 3D 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 3D 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: [] Show 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: [] Show 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 3D 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: [5D double] Bias: [1x1x1x32 double] Show all properties
Here, the Weights
and Bias
properties contain the specified values. At training time, if these properties are nonempty, 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 3D Input
Suppose the size of the input is 28by28by28by1. Create a 3D 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 ith 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 2by3 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: [] Show all properties
Algorithms
3D Convolutional Layer
A convolutional layer applies sliding convolutional filters to the
input. A 3D convolutional layer extends the functionality of a 2D 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 3D 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 3D 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 2D 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 specified as formatted dlarray
objects.
You can interact with these dlarray
objects in automatic differentiation workflows such as when 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 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
option set
to false
, then the layer receives an unformatted dlarray
object with dimensions ordered corresponding to the formats outlined in this table.
Input Format  Output Format 







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 HumanLevel Performance on ImageNet Classification." In Proceedings of the 2015 IEEE International Conference on Computer Vision, 1026–1034. Washington, DC: IEEE Computer Vision Society, 2015.
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