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fullyConnectedLayer

Fully connected layer

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Description

A fully connected layer multiplies the input by a weight matrix and then adds a bias vector.

Creation

Syntax

layer = fullyConnectedLayer(outputSize)
layer = fullyConnectedLayer(outputSize,Name,Value)

Description

layer= fullyConnectedLayer(outputSize)returns a fully connected layer and specifies theOutputSizeproperty.

example

layer= fullyConnectedLayer(outputSize,Name,Value)sets the optionalParameters and Initialization,Learning Rate and Regularization, andNameproperties using name-value pairs. For example,fullyConnectedLayer(10,'Name','fc1')creates a fully connected layer with an output size of 10 and the name'fc1'。您可以指定多个名称-值对。Enclose each property name in single quotes.

Properties

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Fully Connected

Output size for the fully connected layer, specified as a positive integer.

Example:10

Input size for the fully connected layer, specified as a positive integer or'auto'。IfInputSizeis'auto', then the software automatically determines the input size during training.

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 variance2/(InputSize + OutputSize)。

  • 'he'– Initialize the weights with the He initializer[2]。The He initializer samples from a normal distribution with zero mean and variance2/InputSize。

  • 'orthogonal'– Initialize the input weights withQ, the orthogonal matrix given by the QR decomposition ofZ=QRfor a random matrixZsampled from a unit normal distribution.[3]

  • '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), whereszis the size of the weights. For an example, seeSpecify Custom Weight Initialization Function。

The layer only initializes the weights when theWeightsproperty is empty.

Data Types:char|string|function_handle

Function to initialize the bias, specified as one of the following:

  • 'zeros'— Initialize the bias with zeros.

  • 'ones'— Initialize the bias with ones.

  • 'narrow-normal'— Initialize the bias by independently sampling from a normal distribution with a mean of zero and a standard deviation of 0.01.

  • Function handle — Initialize the bias with a custom function. If you specify a function handle, then the function must be of the formbias = func(sz), whereszis the size of the bias.

The layer only initializes the bias when theBiasproperty is empty.

Data Types:char|string|function_handle

Layer weights, specified as a matrix.

The layer weights are learnable parameters. You can specify the initial value for the weights directly using theWeightsproperty of the layer. When you train a network, if theWeightsproperty of the layer is nonempty, thentrainNetworkuses theWeightsproperty as the initial value. If theWeightsproperty is empty, thentrainNetworkuses the initializer specified by theWeightsInitializerproperty of the layer.

At training time,Weightsis anOutputSize-by-InputSizematrix.

Data Types:single|double

Layer biases, specified as a matrix.

The layer biases are learnable parameters. When you train a network, ifBiasis nonempty, thentrainNetworkuses theBiasproperty as the initial value. IfBiasis empty, thentrainNetworkuses the initializer specified byBiasInitializer。

At training time,Biasis anOutputSize-by-1matrix.

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, ifWeightLearnRateFactoris2, 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 thetrainingOptionsfunction.

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

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, ifBiasLearnRateFactoris2, 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 thetrainingOptionsfunction.

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

L2regularization factor for the weights, specified as a nonnegative scalar.

The software multiplies this factor by the globalL2regularization factor to determine theL2regularization for the weights in this layer. For example, ifWeightL2Factoris2, then theL2regularization for the weights in this layer is twice the globalL2regularization factor. You can specify the globalL2regularization factor using thetrainingOptionsfunction.

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

L2regularization factor for the biases, specified as a nonnegative scalar.

The software multiplies this factor by the globalL2regularization factor to determine theL2在这一层正规化的偏见。对example, ifBiasL2Factoris2, then theL2regularization for the biases in this layer is twice the globalL2regularization factor. You can specify the globalL2regularization factor using thetrainingOptionsfunction.

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

Layer

Layer name, specified as a character vector or a string scalar. ForLayerarray input, thetrainNetwork,assembleNetwork,layerGraph, anddlnetworkfunctions automatically assign names to layers with name''。

Data Types:char|string

This property is read-only.

Number of inputs of the layer. This layer accepts a single input only.

Data Types:double

This property is read-only.

Input names of the layer. This layer accepts a single input only.

Data Types:cell

This property is read-only.

Number of outputs of the layer. This layer has a single output only.

Data Types:double

This property is read-only.

Output names of the layer. This layer has a single output only.

Data Types:cell

Examples

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Open Live Script

Create a fully connected layer with an output size of 10 and the name'fc1'。

layer = fullyConnectedLayer(10,'Name','fc1')
layer = FullyConnectedLayer with properties: Name: 'fc1' Hyperparameters InputSize: 'auto' OutputSize: 10 Learnable Parameters Weights: [] Bias: [] Show all properties

Include a fully connected layer in aLayerarray.

layers = [。..imageInputLayer([28 28 1]) convolution2dLayer(5,20) reluLayer maxPooling2dLayer(2,'Stride',2) fullyConnectedLayer(10) softmaxLayer classificationLayer]
layers = 7x1 Layer array with layers: 1 '' Image Input 28x28x1 images with 'zerocenter' normalization 2 '' Convolution 20 5x5 convolutions with stride [1 1] and padding [0 0 0 0] 3 '' ReLU ReLU 4 '' Max Pooling 2x2 max pooling with stride [2 2] and padding [0 0 0 0] 5 '' Fully Connected 10 fully connected layer 6 '' Softmax softmax 7 '' Classification Output crossentropyex
Open Live Script

To specify the weights and bias initializer functions, use theWeightsInitializerandBiasInitializerproperties respectively. To specify the weights and biases directly, use theWeightsandBiasproperties respectively.

Specify Initialization Function

Create a fully connected layer with an output size of 10 and specify the weights initializer to be the He initializer.

outputSize = 10; layer = fullyConnectedLayer(outputSize,'WeightsInitializer','he')
layer = FullyConnectedLayer with properties: Name: '' Hyperparameters InputSize: 'auto' OutputSize: 10 Learnable Parameters Weights: [] Bias: [] Show all properties

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

Specify Custom Initialization Function

To specify your own initialization function for the weights and biases, set theWeightsInitializerandBiasInitializerproperties 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 fully connected layer with output size 10 and specify initializers that sample the weights and biases from a Gaussian distribution with a standard deviation of 0.0001.

outputSize = 10; weightsInitializationFcn = @(sz) rand(sz) * 0.0001; biasInitializationFcn = @(sz) rand(sz) * 0.0001; layer = fullyConnectedLayer(outputSize,。..'WeightsInitializer',@(sz) rand(sz) * 0.0001,。..'BiasInitializer',@(sz) rand(sz) * 0.0001)
layer = FullyConnectedLayer with properties: Name: '' Hyperparameters InputSize: 'auto' OutputSize: 10 Learnable Parameters Weights: [] Bias: [] Show all properties

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

Specify Weights and Bias Directly

Create a fully connected layer with an output size of 10 and set the weights and bias toWandbin the MAT fileFCWeights.matrespectively.

outputSize = 10; loadFCWeightslayer = fullyConnectedLayer(outputSize,。..'Weights',W,。..'Bias',b)
layer = FullyConnectedLayer with properties: Name: '' Hyperparameters InputSize: 720 OutputSize: 10 Learnable Parameters Weights: [10x720 double] Bias: [10x1 double] Show all properties

Here, theWeightsandBiasproperties 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.

Algorithms

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References

[1] Glorot, Xavier, and Yoshua Bengio. "Understanding the Difficulty of Training Deep Feedforward Neural Networks." InProceedings of the Thirteenth International Conference on Artificial Intelligence and Statistics, 249–356. Sardinia, Italy: AISTATS, 2010.

[2] He, Kaiming, Xiangyu Zhang, Shaoqing Ren, and Jian Sun. "Delving Deep into Rectifiers: Surpassing Human-Level Performance on ImageNet Classification." InProceedings of the 2015 IEEE International Conference on Computer Vision, 1026–1034. Washington, DC: IEEE Computer Vision Society, 2015.

[3]萨克斯,安德鲁·M。詹姆斯L. McClelland, and Surya Ganguli. "Exact solutions to the nonlinear dynamics of learning in deep linear neural networks."arXiv preprint arXiv:1312.6120(2013).

Extended Capabilities

C/C++ Code Generation
Generate C and C++ code using MATLAB® Coder™.

GPU Code Generation
Generate CUDA® code for NVIDIA® GPUs using GPU Coder™.

Version History

Introduced in R2016a

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Behavior changed in R2019a

See Also

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