Specify Custom Layer Backward Function - MATLAB & Simulink (original) (raw)

If Deep Learning Toolbox™ does not provide the layer you require for your task, then you can define your own custom layer. For a list of built-in layers, see List of Deep Learning Layers.

The example Define Custom Deep Learning Layer with Learnable Parameters shows how to create a custom SReLU layer and goes through the following steps:

1. Name the layer — Give the layer a name so that you can use it in MATLAB®.
2. Declare the layer properties — Specify the properties of the layer, including learnable parameters and state parameters.
3. 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 theName, Description, andType properties with [] and sets the number of layer inputs and outputs to 1.
4. 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.
5. Create forward functions — Specify how data passes forward through the layer (forward propagation) at prediction time and at training time.
6. Create reset state function (optional) — Specify how to reset state parameters.
7. 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.

If the forward function only uses functions that support dlarray objects, then creating a backward function is optional. In this case, the software determines the derivatives automatically using automatic differentiation. For a list of functions that support dlarray objects, see List of Functions with dlarray Support. If you want to use functions that do not support dlarray objects, or want to use a specific algorithm for the backward function, then you can define a custom backward function using this example as a guide.

Create Custom Layer

The example Define Custom Deep Learning Layer with Learnable Parameters shows how to create a SReLU layer. A SReLU layer performs a thresholding operation, where for each channel, the layer scales values outside an interval. The interval thresholds and scaling factors are learnable parameters.[1]

The SReLU operation is given by

where xi is the input on channel i,tli and_tri_ are the left and right thresholds on channel i, respectively, and_ali_ and_ari_ are the left and right scaling factors on channel i, respectively. These threshold values and scaling factors are learnable parameter, which the layer learns during training.

View the layer created in the example Define Custom Deep Learning Layer with Learnable Parameters. This layer does not have a backward function.

classdef sreluLayer < nnet.layer.Layer ... & nnet.layer.Acceleratable % Example custom SReLU layer.

properties (Learnable)
% Layer learnable parameters

    LeftSlope
    RightSlope
    LeftThreshold
    RightThreshold
end

methods
    function layer = sreluLayer(args) 
        % layer = sreluLayer creates a SReLU layer.
        %
        % layer = sreluLayer(Name=name) also specifies the
        % layer name.

        arguments
            args.Name = "";
        end

        % Set layer name.
        layer.Name = args.Name;

        % Set layer description.
        layer.Description = "SReLU";
    end

    function layer = initialize(layer,layout)
        % layer = initialize(layer,layout) initializes the layer
        % learnable parameters using the specified input layout.

        % Find number of channels.
        idx = finddim(layout,"C");
        numChannels = layout.Size(idx);

        % Initialize empty learnable parameters.
        sz = ones(1,numel(layout.Size);
        sz(idx) = numChannels;
        
        if isempty(layer.LeftSlope)
            layer.LeftSlope = rand(sz);
        end
        
        if isempty(layer.RightSlope)
            layer.RightSlope = rand(sz);
        end
        
        if isempty(layer.LeftThreshold)
            layer.LeftThreshold = rand(sz);
        end
        
        if isempty(layer.RightThreshold)
            layer.RightThreshold = rand(sz);
        end
    end

    function Y = predict(layer, X)
        % Y = predict(layer, X) forwards the input data X through the
        % layer and outputs the result Y.
        
        tl = layer.LeftThreshold;
        al = layer.LeftSlope;
        tr = layer.RightThreshold;
        ar = layer.RightSlope;
        
        Y = (X <= tl) .* (tl + al.*(X-tl)) ...
            + ((tl < X) & (X < tr)) .* X ...
            + (tr <= X) .* (tr + ar.*(X-tr));
    end
end

end

Create Backward Function

Implement the backward function that returns the derivatives of the loss with respect to the input data and the learnable parameters.

The backward function syntax depends on the type of layer.

• dLdX = backward(layer,X,Y,dLdY,memory) returns the derivativesdLdX of the loss with respect to the layer input, wherelayer has a single input and a single output.Y corresponds to the forward function output anddLdY corresponds to the derivative of the loss with respect to Y. The function input memory corresponds to the memory output of the forward function.
• [dLdX,dLdW] = backward(layer,X,Y,dLdY,memory) also returns the derivative dLdW of the loss with respect to the learnable parameter, where layer has a single learnable parameter.
• [dLdX,dLdSin] = backward(layer,X,Y,dLdY,dLdSout,memory) also returns the derivative dLdSin of the loss with respect to the state input, where layer has a single state parameter anddLdSout corresponds to the derivative of the loss with respect to the layer state output.
• [dLdX,dLdW,dLdSin] = backward(layer,X,Y,dLdY,dLdSout,memory) also returns the derivative dLdW of the loss with respect to the learnable parameter and returns the derivative dLdSin of the loss with respect to the layer state input, where layer has a single state parameter and single learnable parameter.

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

• For layers with multiple inputs, replace X anddLdX with X1,...,XN anddLdX1,...,dLdXN, respectively, where N is the number of inputs.
• For layers with multiple outputs, replace Y anddLdY with Y1,...,YM anddLdY1,...,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 anddLdSout1,...,dLdSoutK, respectively, whereK is the number of state parameters.

To reduce memory usage by preventing unused variables being saved between the forward and backward pass, replace the corresponding input arguments with ~.

Tip

If the number of inputs to backward can vary, then usevarargin instead of the input arguments afterlayer. In this case, varargin is a cell array of the inputs, where the first N elements correspond to theN layer inputs, the next M elements correspond to the M layer outputs, the next M elements correspond to the derivatives of the loss with respect to the M layer outputs, the next K elements correspond to the K derivatives of the loss with respect to the K state outputs, and the last element corresponds to memory.

If the number of outputs can vary, then use varargout instead of the output arguments. In this case, varargout is a cell array of the outputs, where the first N elements correspond to theN the derivatives of the loss with respect to theN layer inputs, the next P elements correspond to the derivatives of the loss with respect to the P learnable parameters, and the next K elements correspond to the derivatives of the loss with respect to the K state inputs.

Because a SReLU layer has only one input, one output, four learnable parameters, and does not require the outputs of the layer forward function or a memory value, the syntax for backward for a SReLU layer is[dLdX,dLdLS,dLdRS,dldLT,dldRT] = backward(layer,X,~,dLdY,~). The dimensions of X are the same as in the forward function. The dimensions of dLdY are the same as the dimensions of the outputY of the forward function. The dimensions and data type ofdLdX are the same as the dimensions and data type ofX. The dimension and data type of dLdLS,dLdRS, dldLT, dldRT are the same as the dimension and data type of the learnable parametersLeftSlope, RightSlope,LeftThreshold, and RightThreshold, respectively.

During the backward pass, the layer automatically updates the learnable parameters using the corresponding derivatives.

To include a custom layer in a network, the layer forward functions must accept the outputs of the previous layer and forward propagate arrays with the size expected by the next layer. Similarly, when the layer specifies a backward function, it must accept inputs with the same size as the corresponding output of the forward function and backward propagate derivatives with the same size.

The derivative of the loss with respect to the input data is

where ∂L/∂f(xi) is the gradient propagated from the next layer, and the derivative of the activation is

The derivative of the loss with respect to the learnable parameter_tli_ is

where i indexes the channels, j indexes the remaining elements, and the gradient of the activation is

Similarly, for the other learnable parameters, the gradients are:

Create the backward function that returns these derivatives.

    function [dLdX,dLdLS,dLdRS,dLdLT,dLdRT] = backward(layer,X,~,dLdY,~)
        % [dLdX,dLdLS,dLdRS,dLdLT,dLdRT] = backward(layer,X,~,dLdY,~)
        % backward propagates the derivative of the loss function
        % through the layer.
        % Inputs:
        %         layer - Layer to backward propagate through
        %         X     - Input data
        %         dLdY  - Gradient propagated from the deeper layer
        % Outputs:
        %         dLdX  - Derivative of the loss with respect to the
        %                 input data
        %         dLdLS - Derivative of the loss with respect to the
        %                 learnable parameter LeftScale
        %         dLdRS - Derivative of the loss with respect to the
        %                 learnable parameter RightScale
        %         dLdLT - Derivative of the loss with respect to the
        %                 learnable parameter LeftThreshold
        %         dLdRT - Derivative of the loss with respect to the
        %                 learnable parameter RightThreshold

        ndims = numel(dims(X));
        idxC = finddim(X,"C");

        X = stripdims(X);
        dLdY = stripdims(dLdY);

        tl = layer.LeftThreshold;
        al = layer.LeftSlope;
        tr = layer.RightThreshold;
        ar = layer.RightSlope;

        dYdX = (X <= tl) .* al ...
            + (X > tl  & X < tr) ...
            + (X >= tr) .* ar;
        
        idx = setdiff(1:ndims,idxC);
        dLdLT = sum(dLdY .* (X <= tl) .* (1 - al),idx);
        dLdRT = sum(dLdY .* (tr <= X) .* (1 - ar),idx);
        dLdLS = sum(dLdY .* (X <= tl) .* (X - tl),idx);
        dLdRS = sum(dLdY .* (tr <= X) .* (X - tr),idx);
    end

Complete Layer

View the completed layer class file.

classdef sreluLayer < nnet.layer.Layer % Example custom SReLU layer.

properties (Learnable)
% Layer learnable parameters

    LeftSlope
    RightSlope
    LeftThreshold
    RightThreshold
end

methods
    function layer = sreluLayer(args) 
        % layer = sreluLayer creates a SReLU layer.
        %
        % layer = sreluLayer(Name=name) also specifies the
        % layer name.

        arguments
            args.Name = "";
        end

        % Set layer name.
        layer.Name = args.Name;

        % Set layer description.
        layer.Description = "SReLU";
    end

    function layer = initialize(layer,layout)
        % layer = initialize(layer,layout) initializes the layer
        % learnable parameters using the specified input layout.

        % Find number of channels.
        idx = finddim(layout,"C");
        numChannels = layout.Size(idx);

        % Initialize empty learnable parameters.
        sz = ones(1,numel(layout.Size);
        sz(idx) = numChannels;
        
        if isempty(layer.LeftSlope)
            layer.LeftSlope = rand(sz);
        end
        
        if isempty(layer.RightSlope)
            layer.RightSlope = rand(sz);
        end
        
        if isempty(layer.LeftThreshold)
            layer.LeftThreshold = rand(sz);
        end
        
        if isempty(layer.RightThreshold)
            layer.RightThreshold = rand(sz);
        end
    end

    function Y = predict(layer, X)
        % Y = predict(layer, X) forwards the input data X through the
        % layer and outputs the result Y.
        
        tl = layer.LeftThreshold;
        al = layer.LeftSlope;
        tr = layer.RightThreshold;
        ar = layer.RightSlope;
        
        Y = (X <= tl) .* (tl + al.*(X-tl)) ...
            + ((tl < X) & (X < tr)) .* X ...
            + (tr <= X) .* (tr + ar.*(X-tr));
    end
    
    function [dLdX,dLdLS,dLdRS,dLdLT,dLdRT] = backward(layer,X,~,dLdY,~)
        % [dLdX,dLdLS,dLdRS,dLdLT,dLdRT] = backward(layer,X,~,dLdY,~)
        % backward propagates the derivative of the loss function
        % through the layer.
        % Inputs:
        %         layer - Layer to backward propagate through
        %         X     - Input data
        %         dLdY  - Gradient propagated from the deeper layer
        % Outputs:
        %         dLdX  - Derivative of the loss with respect to the
        %                 input data
        %         dLdLS - Derivative of the loss with respect to the
        %                 learnable parameter LeftScale
        %         dLdRS - Derivative of the loss with respect to the
        %                 learnable parameter RightScale
        %         dLdLT - Derivative of the loss with respect to the
        %                 learnable parameter LeftThreshold
        %         dLdRT - Derivative of the loss with respect to the
        %                 learnable parameter RightThreshold

        ndims = numel(dims(X));
        idxC = finddim(X,"C");

        X = stripdims(X);
        dLdY = stripdims(dLdY);

        tl = layer.LeftThreshold;
        al = layer.LeftSlope;
        tr = layer.RightThreshold;
        ar = layer.RightSlope;

        dYdX = (X <= tl) .* al ...
            + (X > tl  & X < tr) ...
            + (X >= tr) .* ar;
        
        idx = setdiff(1:ndims,idxC);
        dLdLT = sum(dLdY .* (X <= tl) .* (1 - al),idx);
        dLdRT = sum(dLdY .* (tr <= X) .* (1 - ar),idx);
        dLdLS = sum(dLdY .* (X <= tl) .* (X - tl),idx);
        dLdRS = sum(dLdY .* (tr <= X) .* (X - tr),idx);
    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, seeGPU Computing Requirements (Parallel Computing Toolbox). For more information on working with GPUs in MATLAB, see GPU Computing in MATLAB (Parallel Computing Toolbox).

See Also

trainnet | trainingOptions | dlnetwork | functionLayer | checkLayer | setLearnRateFactor | setL2Factor | getLearnRateFactor | getL2Factor | findPlaceholderLayers | replaceLayer | PlaceholderLayer | networkDataLayout

Related Topics

• Define Custom Deep Learning Layers
• Define Custom Deep Learning Layer with Learnable Parameters
• Define Custom Deep Learning Layer with Multiple Inputs
• Define Custom Deep Learning Layer with Formatted Inputs
• Define Custom Recurrent Deep Learning Layer
• Define Custom Deep Learning Layer for Code Generation
• Define Nested Deep Learning Layer Using Network Composition
• Check Custom Layer Validity