Define Custom Deep Learning Layer with Multiple Inputs

If Deep Learning Toolbox™ does not provide the layer you require for your classification or regression problem, then you can define your own custom layer using this example as a guide. For a list of built-in layers, see List of Deep Learning Layers.

To define a custom deep learning layer, you can use the template provided in this example, which takes you through these steps:

Name the layer — Give the layer a name so that you can use it in MATLAB^®.
Declare the layer properties — Specify the properties of the layer, including learnable parameters and state parameters.
Create the constructor function (optional) — Specify how to construct the layer and initialize its properties. If you do not specify a constructor function, then at creation, the software initializes the Name, Description, and Type properties with [] and sets the number of layer inputs and outputs to 1.
Create initialize function (optional) — Specify how to initialize the learnable and state parameters when the software initializes the network. If you do not specify an initialize function, then the software does not initialize parameters when it initializes the network.
Create forward functions — Specify how data passes forward through the layer (forward propagation) at prediction time and at training time.
Create reset state function (optional) — Specify how to reset state parameters.
Create a backward function (optional) — Specify the derivatives of the loss with respect to the input data and the learnable parameters (backward propagation). If you do not specify a backward function, then the forward functions must support dlarray objects.

This example shows how to create a weighted addition layer, which is a layer with multiple inputs and learnable parameter, and use it in a convolutional neural network. A weighted addition layer scales and adds inputs from multiple neural network layers element-wise.

Custom Layer Template

Copy the custom layer template into a new file in MATLAB. This template gives the structure of a layer class definition. It outlines:

The optional properties blocks for the layer properties, learnable parameters, and state parameters.
The optional layer constructor function.
The optional initialize function.
The predict function and the optional forward function.
The optional resetState function for layers with state properties.
The optional backward function.

classdef myLayer < nnet.layer.Layer % ...
        % & nnet.layer.Formattable ... % (Optional) 
        % & nnet.layer.Acceleratable % (Optional)

    properties
        % (Optional) Layer properties.

        % Declare layer properties here.
    end

    properties (Learnable)
        % (Optional) Layer learnable parameters.

        % Declare learnable parameters here.
    end

    properties (State)
        % (Optional) Layer state parameters.

        % Declare state parameters here.
    end

    properties (Learnable, State)
        % (Optional) Nested dlnetwork objects with both learnable
        % parameters and state parameters.

        % Declare nested networks with learnable and state parameters here.
    end

    methods
        function layer = myLayer()
            % (Optional) Create a myLayer.
            % This function must have the same name as the class.

            % Define layer constructor function here.
        end

        function layer = initialize(layer,layout)
            % (Optional) Initialize layer learnable and state parameters.
            %
            % Inputs:
            %         layer  - Layer to initialize
            %         layout - Data layout, specified as a networkDataLayout
            %                  object
            %
            % Outputs:
            %         layer - Initialized layer
            %
            %  - For layers with multiple inputs, replace layout with 
            %    layout1,...,layoutN, where N is the number of inputs.
            
            % Define layer initialization function here.
        end
        

        function [Y,state] = predict(layer,X)
            % Forward input data through the layer at prediction time and
            % output the result and updated state.
            %
            % Inputs:
            %         layer - Layer to forward propagate through 
            %         X     - Input data
            % Outputs:
            %         Y     - Output of layer forward function
            %         state - (Optional) Updated layer state
            %
            %  - For layers with multiple inputs, replace X with X1,...,XN, 
            %    where N is the number of inputs.
            %  - For layers with multiple outputs, replace Y with 
            %    Y1,...,YM, where M is the number of outputs.
            %  - For layers with multiple state parameters, replace state 
            %    with state1,...,stateK, where K is the number of state 
            %    parameters.

            % Define layer predict function here.
        end

        function [Y,state,memory] = forward(layer,X)
            % (Optional) Forward input data through the layer at training
            % time and output the result, the updated state, and a memory
            % value.
            %
            % Inputs:
            %         layer - Layer to forward propagate through 
            %         X     - Layer input data
            % Outputs:
            %         Y      - Output of layer forward function 
            %         state  - (Optional) Updated layer state 
            %         memory - (Optional) Memory value for custom backward
            %                  function
            %
            %  - For layers with multiple inputs, replace X with X1,...,XN, 
            %    where N is the number of inputs.
            %  - For layers with multiple outputs, replace Y with 
            %    Y1,...,YM, where M is the number of outputs.
            %  - For layers with multiple state parameters, replace state 
            %    with state1,...,stateK, where K is the number of state 
            %    parameters.

            % Define layer forward function here.
        end

        function layer = resetState(layer)
            % (Optional) Reset layer state.

            % Define reset state function here.
        end

        function [dLdX,dLdW,dLdSin] = backward(layer,X,Y,dLdY,dLdSout,memory)
            % (Optional) Backward propagate the derivative of the loss
            % function through the layer.
            %
            % Inputs:
            %         layer   - Layer to backward propagate through 
            %         X       - Layer input data 
            %         Y       - Layer output data 
            %         dLdY    - Derivative of loss with respect to layer 
            %                   output
            %         dLdSout - (Optional) Derivative of loss with respect 
            %                   to state output
            %         memory  - Memory value from forward function
            % Outputs:
            %         dLdX   - Derivative of loss with respect to layer input
            %         dLdW   - (Optional) Derivative of loss with respect to
            %                  learnable parameter 
            %         dLdSin - (Optional) Derivative of loss with respect to 
            %                  state input
            %
            %  - For layers with state parameters, the backward syntax must
            %    include both dLdSout and dLdSin, or neither.
            %  - For layers with multiple inputs, replace X and dLdX with
            %    X1,...,XN and dLdX1,...,dLdXN, respectively, where N is
            %    the number of inputs.
            %  - For layers with multiple outputs, replace Y and dLdY with
            %    Y1,...,YM and dLdY,...,dLdYM, respectively, where M is the
            %    number of outputs.
            %  - For layers with multiple learnable parameters, replace 
            %    dLdW with dLdW1,...,dLdWP, where P is the number of 
            %    learnable parameters.
            %  - For layers with multiple state parameters, replace dLdSin
            %    and dLdSout with dLdSin1,...,dLdSinK and 
            %    dLdSout1,...,dldSoutK, respectively, where K is the number
            %    of state parameters.

            % Define layer backward function here.
        end
    end
end

Name Layer and Specify Superclasses

First, give the layer a name. In the first line of the class file, replace the existing name myLayer with weightedAdditionLayer.

classdef weightedAdditionLayer < nnet.layer.Layer % ...
        % & nnet.layer.Formattable ... % (Optional) 
        % & nnet.layer.Acceleratable % (Optional)
    ...
end

If you do not specify a backward function, then the layer functions, by default, receive unformatted dlarray objects as input. To specify that the layer receives formatted dlarray objects as input and also outputs formatted dlarray objects, also inherit from the nnet.layer.Formattable class when defining the custom layer.

The layer functions support acceleration, so also inherit from nnet.layer.Acceleratable. For more information about accelerating custom layer functions, see Custom Layer Function Acceleration. The layer does not require formattable inputs, so remove the optional nnet.layer.Formattable superclass.

classdef weightedAdditionLayer < nnet.layer.Layer ...
        & nnet.layer.Acceleratable
    ...
end

Next, rename the myLayer constructor function (the first function in the methods section) so that it has the same name as the layer.

    methods
        function layer = weightedAdditionLayer()           
            ...
        end

        ...
     end

Save the Layer

Save the layer class file in a new file named weightedAdditionLayer.m. The file name must match the layer name. To use the layer, you must save the file in the current folder or in a folder on the MATLAB path.

Declare Properties and Learnable Parameters

Declare the layer properties in the properties section and declare learnable parameters by listing them in the properties (Learnable) section.

By default, custom layers have these properties. Do not declare these properties in the properties section.

Property	Description
`Name`	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 `""`.
`Description`	One-line description of the layer, specified as a string scalar or a character vector. This description appears when the layer is displayed in a `Layer` array. If you do not specify a layer description, then the software displays the layer class name.
`Type`	Type of the layer, specified as a character vector or a string scalar. The value of `Type` appears when the layer is displayed in a `Layer` array. If you do not specify a layer type, then the software displays the layer class name.
`NumInputs`	Number of inputs of the layer, specified as a positive integer. If you do not specify this value, then the software automatically sets `NumInputs` to the number of names in `InputNames`. The default value is 1.
`InputNames`	Input names of the layer, specified as a cell array of character vectors. If you do not specify this value and `NumInputs` is greater than 1, then the software automatically sets `InputNames` to `{'in1',...,'inN'}`, where `N` is equal to `NumInputs`. The default value is `{'in'}`.
`NumOutputs`	Number of outputs of the layer, specified as a positive integer. If you do not specify this value, then the software automatically sets `NumOutputs` to the number of names in `OutputNames`. The default value is 1.
`OutputNames`	Output names of the layer, specified as a cell array of character vectors. If you do not specify this value and `NumOutputs` is greater than 1, then the software automatically sets `OutputNames` to `{'out1',...,'outM'}`, where `M` is equal to `NumOutputs`. The default value is `{'out'}`.

If the layer has no other properties, then you can omit the properties section.

Tip

If you are creating a layer with multiple inputs, then you must set either the NumInputs or InputNames properties in the layer constructor. If you are creating a layer with multiple outputs, then you must set either the NumOutputs or OutputNames properties in the layer constructor.

A weighted addition layer does not require any additional properties, so you can remove the properties section.

A weighted addition layer has only one learnable parameter, the weights. Declare this learnable parameter in the properties (Learnable) section and call the parameter Weights.

    properties (Learnable)
        % Layer learnable parameters
            
        % Scaling coefficients
        Weights
    end

Create Constructor Function

Create the function that constructs the layer and initializes the layer properties. Specify any variables required to create the layer as inputs to the constructor function.

The weighted addition layer constructor function requires two inputs: the number of inputs to the layer and the layer name. This number of inputs to the layer specifies the size of the learnable parameter Weights. Specify two input arguments named numInputs and name in the weightedAdditionLayer function. Add a comment to the top of the function that explains the syntax of the function.

        function layer = weightedAdditionLayer(numInputs,name)
            % layer = weightedAdditionLayer(numInputs,name) creates a
            % weighted addition layer and specifies the number of inputs
            % and the layer name.
            
            ...
        end

Initialize Layer Properties

Initialize the layer properties, including learnable parameters, in the constructor function. Replace the comment % Layer constructor function goes here with code that initializes the layer properties.

Set the NumInputs property to the input argument numInputs.

            % Set number of inputs.
            layer.NumInputs = numInputs;

Set the Name property to the input argument name.

            % Set layer name.
            layer.Name = name;

Give the layer a one-line description by setting the Description property of the layer. Set the description to describe the type of layer and its size.

            % Set layer description.
            layer.Description = "Weighted addition of " + numInputs + ...
                " inputs";

A weighted addition layer multiplies each layer input by the corresponding coefficient in Weights and adds the resulting values together. Initialize the learnable parameter Weights to be a random vector of size 1-by-numInputs. Weights is a property of the layer object, so you must assign the vector to layer.Weights.

            % Initialize layer weights
            layer.Weights = rand(1,numInputs);

View the completed constructor function.

        function layer = weightedAdditionLayer(numInputs,name) 
            % layer = weightedAdditionLayer(numInputs,name) creates a
            % weighted addition layer and specifies the number of inputs
            % and the layer name.

            % Set number of inputs.
            layer.NumInputs = numInputs;

            % Set layer name.
            layer.Name = name;

            % Set layer description.
            layer.Description = "Weighted addition of " + numInputs +  ... 
                " inputs";
        
            % Initialize layer weights.
            layer.Weights = rand(1,numInputs); 
        end

With this constructor function, the command weightedAdditionLayer(3,'add') creates a weighted addition layer with three inputs and the name 'add'.

Because the constructor function does not require information from the layer input data to initialize the learnable parameters, defining the initialize function is optional. For layers that require information from the input data to initialize the learnable parameters, for example, the weights of a SReLU layer must have the same number of channels as the input data, you can implement a custom initialize function. For an example, see Define Custom Deep Learning Layer with Learnable Parameters.

Create Forward Functions

Create the layer forward functions to use at prediction time and training time.

Create a function named predict that propagates the data forward through the layer at prediction time and outputs the result.

The predict function syntax depends on the type of layer.

Y = predict(layer,X) forwards the input data X through the layer and outputs the result Y, where layer has a single input and a single output.
[Y,state] = predict(layer,X) also outputs the updated state parameter state, where layer has a single state parameter.

You can adjust the syntaxes for layers with multiple inputs, multiple outputs, or multiple state parameters:

For layers with multiple inputs, replace X with X1,...,XN, where N is the number of inputs. The NumInputs property must match N.
For layers with multiple outputs, replace Y with Y1,...,YM, where M is the number of outputs. The NumOutputs property must match M.
For layers with multiple state parameters, replace state with state1,...,stateK, where K is the number of state parameters.

Tip

If the number of inputs to the layer can vary, then use varargin instead of X1,…,XN. In this case, varargin is a cell array of the inputs, where varargin{i} corresponds to Xi.

If the number of outputs can vary, then use varargout instead of Y1,…,YM. In this case, varargout is a cell array of the outputs, where varargout{j} corresponds to Yj.

Tip

If the custom layer has a dlnetwork object for a learnable parameter, then in the predict function of the custom layer, use the predict function for the dlnetwork. When you do so, the dlnetwork object predict function uses the appropriate layer operations for prediction. If the dlnetwork has state parameters, then also return the network state.

Because a weighted addition layer has only one output and a variable number of inputs, the syntax for predict for a weighted addition layer is Y = predict(layer,varargin), where varargin{i} corresponds to Xi for positive integers i less than or equal to NumInputs.

By default, the layer uses predict as the forward function at training time. To use a different forward function at training time, or retain a value required for the backward function, you must also create a function named forward.

The dimensions of the inputs depend on the type of data and the output of the connected layers:

Layer Input	Example
Layer Input	Shape	Data Format
2-D images	h-by-w-by-c-by-N numeric array, where h, w, c and N are the height, width, number of channels of the images, and number of observations, respectively.	`"SSCB"`
3-D images	h-by-w-by-d-by-c-by-N numeric array, where h, w, d, c and N are the height, width, depth, number of channels of the images, and number of image observations, respectively.	`"SSSCB"`
Vector sequences	c-by-N-by-s matrix, where c is the number of features of the sequence, N is the number of sequence observations, and s is the sequence length.	`"CBT"`
2-D image sequences	h-by-w-by-c-by-N-by-s array, where h, w, and c correspond to the height, width, and number of channels of the image, respectively, N is the number of image sequence observations, and s is the sequence length.	`"SSCBT"`
3-D image sequences	h-by-w-by-d-by-c-by-N-by-s array, where h, w, d, and c correspond to the height, width, depth, and number of channels of the image, respectively, N is the number of image sequence observations, and s is the sequence length.	`"SSSCBT"`
Features	c-by-N array, where c is the number of features, and N is the number of observations.	`"CB"`

For layers that output sequences, the layers can output sequences of any length or output data with no time dimension.

The forward function propagates the data forward through the layer at training time and also outputs a memory value.

The forward function syntax depends on the type of layer:

Y = forward(layer,X) forwards the input data X through the layer and outputs the result Y, where layer has a single input and a single output.
[Y,state] = forward(layer,X) also outputs the updated state parameter state, where layer has a single state parameter.
[__,memory] = forward(layer,X) also returns a memory value for a custom backward function using any of the previous syntaxes. If the layer has both a custom forward function and a custom backward function, then the forward function must return a memory value.

You can adjust the syntaxes for layers with multiple inputs, multiple outputs, or multiple state parameters:

For layers with multiple inputs, replace X with X1,...,XN, where N is the number of inputs. The NumInputs property must match N.
For layers with multiple outputs, replace Y with Y1,...,YM, where M is the number of outputs. The NumOutputs property must match M.
For layers with multiple state parameters, replace state with state1,...,stateK, where K is the number of state parameters.

Tip

If the number of inputs to the layer can vary, then use varargin instead of X1,…,XN. In this case, varargin is a cell array of the inputs, where varargin{i} corresponds to Xi.

If the number of outputs can vary, then use varargout instead of Y1,…,YM. In this case, varargout is a cell array of the outputs, where varargout{j} corresponds to Yj.

Tip

If the custom layer has a dlnetwork object for a learnable parameter, then in the forward function of the custom layer, use the forward function of the dlnetwork object. When you do so, the dlnetwork object forward function uses the appropriate layer operations for training.

The forward function of a weighted addition layer is

$f (X^{(1)}, \dots, X^{(n)}) = \sum_{i = 1}^{n} W_{i} X^{(i)}$

where X⁽¹⁾, …, X⁽ⁿ⁾ correspond to the layer inputs and W₁,…,W_n are the layer weights.

Implement the forward function in predict. In predict, the output Y corresponds to $f (X^{(1)}, \dots, X^{(n)})$ . The weighted addition layer does not require memory or a different forward function for training, so you can remove the forward function from the class file. Add a comment to the top of the function that explains the syntaxes of the function.

Tip

If you preallocate arrays using functions such as zeros, then you must ensure that the data types of these arrays are consistent with the layer function inputs. To create an array of zeros of the same data type as another array, use the "like" option of zeros. For example, to initialize an array of zeros of size sz with the same data type as the array X, use Y = zeros(sz,"like",X).

        function Y = predict(layer, varargin)
            % Y = predict(layer, X1, ..., Xn) forwards the input data X1,
            % ..., Xn through the layer and outputs the result Y.
            
            X = varargin;
            W = layer.Weights;
            
            % Initialize output
            X1 = X{1};
            sz = size(X1);
            Y = zeros(sz,'like',X1);
            
            % Weighted addition
            for i = 1:layer.NumInputs
                Y = Y + W(i)*X{i};
            end
        end

Because the predict function uses only functions that support dlarray objects, defining the backward function is optional. For a list of functions that support dlarray objects, see List of Functions with dlarray Support.

Completed Layer

View the completed layer class file.

classdef weightedAdditionLayer < nnet.layer.Layer ...
        & nnet.layer.Acceleratable
    % Example custom weighted addition layer.

    properties (Learnable)
        % Layer learnable parameters
            
        % Scaling coefficients
        Weights
    end
    
    methods
        function layer = weightedAdditionLayer(numInputs,name) 
            % layer = weightedAdditionLayer(numInputs,name) creates a
            % weighted addition layer and specifies the number of inputs
            % and the layer name.

            % Set number of inputs.
            layer.NumInputs = numInputs;

            % Set layer name.
            layer.Name = name;

            % Set layer description.
            layer.Description = "Weighted addition of " + numInputs +  ... 
                " inputs";
        
            % Initialize layer weights.
            layer.Weights = rand(1,numInputs); 
        end
        
        function Y = predict(layer, varargin)
            % Y = predict(layer, X1, ..., Xn) forwards the input data X1,
            % ..., Xn through the layer and outputs the result Y.
            
            X = varargin;
            W = layer.Weights;
            
            % Initialize output
            X1 = X{1};
            sz = size(X1);
            Y = zeros(sz,'like',X1);
            
            % Weighted addition
            for i = 1:layer.NumInputs
                Y = Y + W(i)*X{i};
            end
        end
    end
end

GPU Compatibility

If the layer forward functions fully support dlarray objects, then the layer is GPU compatible. Otherwise, to be GPU compatible, the layer functions must support inputs and return outputs of type gpuArray (Parallel Computing Toolbox).

Many MATLAB built-in functions support gpuArray (Parallel Computing Toolbox) and dlarray input arguments. For a list of functions that support dlarray objects, see List of Functions with dlarray Support. For a list of functions that execute on a GPU, see Run MATLAB Functions on a GPU (Parallel Computing Toolbox). To use a GPU for deep learning, you must also have a supported GPU device. For information on supported devices, see GPU Computing Requirements (Parallel Computing Toolbox). For more information on working with GPUs in MATLAB, see GPU Computing in MATLAB (Parallel Computing Toolbox).

In this example, the MATLAB functions used in predict all support dlarray objects, so the layer is GPU compatible.

Check Validity of Layer with Multiple Inputs

Open Live Script

Check the layer validity of the custom layer weightedAdditionLayer.

Create an instance of the layer weightedAdditionLayer, attached to this example as a supporting file, and check its validity using checkLayer. Specify the valid input sizes to be the typical sizes of a single observation for each input to the layer. The layer expects 4-D array inputs, where the first three dimensions correspond to the height, width, and number of channels of the previous layer output, and the fourth dimension corresponds to the observations.

Specify the typical size of the input of an observation and set 'ObservationDimension' to 4.

layer = weightedAdditionLayer(2,'add');
validInputSize = {[24 24 20],[24 24 20]};
checkLayer(layer,validInputSize,'ObservationDimension',4)

Skipping initialization tests. The layer does not have an initialize function.
 
Skipping GPU tests. No compatible GPU device found.
 
Skipping code generation compatibility tests. To check validity of the layer for code generation, specify the CheckCodegenCompatibility and ObservationDimension options.
 
Running nnet.checklayer.TestLayerWithoutBackward
.......... ........
Done nnet.checklayer.TestLayerWithoutBackward
__________

Test Summary:
	 18 Passed, 0 Failed, 0 Incomplete, 16 Skipped.
	 Time elapsed: 0.55093 seconds.

Here, the function does not detect any issues with the layer.

Use Custom Weighted Addition Layer in Network

Open Live Script

You can use a custom layer in the same way as any other layer in Deep Learning Toolbox. This section shows how to create and train a network for digit classification using the weighted addition layer you created earlier.

Load the example training data.

load DigitsDataTrain

Create a dlnetwork object.

net = dlnetwork;

Define the neural network architecture including the custom layer weightedAdditionLayer, attached to this example as a supporting file.

layers = [
    imageInputLayer([28 28 1])
    convolution2dLayer(5,20)
    reluLayer(Name="relu1")
    convolution2dLayer(3,20,Padding=1)
    reluLayer
    convolution2dLayer(3,20,Padding=1)
    reluLayer
    weightedAdditionLayer(2,"add")
    fullyConnectedLayer(10)
    softmaxLayer];

net = addLayers(net,layers);
net = connectLayers(net,"relu1","add/in2");

Specify the training options. Choosing among the options requires empirical analysis. To explore different training option configurations by running experiments, you can use the Experiment Manager app.

Train using the Adam optimizer.
Train for 10 epochs.
Monitor the accuracy.

options = trainingOptions("adam",MaxEpochs=10,Metrics="accuracy");

Train the neural network using the trainnet function. For classification, use cross-entropy loss. By default, the trainnet function uses a GPU if one is available. Training on a GPU requires a Parallel Computing Toolbox™ license and a supported GPU device. For information on supported devices, see GPU Computing Requirements (Parallel Computing Toolbox). Otherwise, the trainnet function uses the CPU. To specify the execution environment, use the ExecutionEnvironment training option.

net = trainnet(XTrain,labelsTrain,net,"crossentropy",options);

    Iteration    Epoch    TimeElapsed    LearnRate    TrainingLoss    TrainingAccuracy
    _________    _____    ___________    _________    ____________    ________________
            1        1       00:00:00        0.001          2.3021                12.5
           50        2       00:00:06        0.001         0.90036              67.969
          100        3       00:00:11        0.001         0.34059                87.5
          150        4       00:00:17        0.001         0.10723              98.438
          200        6       00:00:22        0.001        0.042721              99.219
          250        7       00:00:28        0.001        0.020463                 100
          300        8       00:00:33        0.001        0.033737              99.219
          350        9       00:00:38        0.001       0.0052703                 100
          390       10       00:00:42        0.001       0.0033437                 100
Training stopped: Max epochs completed

View the weights learned by the weighted addition layer.

net.Layers(8).Weights

ans = 1x2 single row vector

    1.0256    0.9973

Load the test data.

load DigitsDataTest

Test the neural network using the testnet function. For single-label classification, evaluate the accuracy. By default, the testnet function uses a GPU if one is available. To select the execution environment manually, use the ExecutionEnvironment argument of the testnet function.

accuracy = testnet(net,XTest,labelsTest,"accuracy")

accuracy = 
98.7800