multiplyLayer - Perform a square operation ?

I'm building a deep learning network and need to perform a element-by-element square operation (that is x^2). I planned to use the multiplyLayer but it won't accept the same input twice. Is there a squaredLayer in the works, or is there a workaround in the short term?

Thank you,

• jz

Answer 1

[Meet]

Hi Jeffrey,

As of now, MATLAB's Deep Learning Toolbox does not have a built-in “squaredLayer”. However, you can create a custom layer to perform element-wise squaring. Follow the steps below to define a custom layer that squares its input and integrates it into a simple neural network:

Step 1: Create a custom class named “SquaredLayer”. Save this class in a file with the same name, “SquaredLayer.m”.

classdef SquaredLayer < nnet.layer.Layer
    % Custom layer to perform element-wise squaring
    methods
        function layer = SquaredLayer(name)
            % Create a SquaredLayer
            layer.Name = name;
            layer.Description = 'Element-wise square layer';
        end
        
        function Z = predict(layer, X)
            % Forward input data through the layer at prediction time
            Z = X .^ 2;
        end
        
        function [dLdX] = backward(layer, X, Z, dLdZ, memory)
            % Backward propagate the derivative of the loss function
            dLdX = 2 * X .* dLdZ;
        end
    end
end

Step 2: Define a neural network and while defining the layers you could use this custom class, in this case I have used built in classes “digitTrain4DArrayData” and “digitTest4DArrayData” provided by MATLAB.

% Load example data 
[XTrain,YTrain,anglesTrain] = digitTrain4DArrayData;
[XTest,YTest,anglesTest] = digitTest4DArrayData;

% Define the layers of the network
layers = [
    imageInputLayer([28 28 1], 'Name', 'input') % Example input layer for 28x28 grayscale images
    SquaredLayer('squared')                     % Custom squared layer
    fullyConnectedLayer(10, 'Name', 'fc')       
    softmaxLayer('Name', 'softmax') 
    classificationLayer('Name', 'output')      
];

% Specify training options
options = trainingOptions('adam', ...
    'MaxEpochs', 10, ...
    'InitialLearnRate', 0.01, ...
    'Verbose', false, ...
    'Plots', 'training-progress');

% Train the network
net = trainNetwork(XTrain, YTrain, layers, options);

% Test the network on the test data
YPred = classify(net, XTest);
accuracy = sum(YPred == YTest) / numel(YTest);
disp(['Test accuracy: ', num2str(accuracy)]);

You can refer to the documentation below for more information: Define Custom Deep Learning Layer with Multiple Inputs: https://www.mathworks.com/help/releases/R2021a/deeplearning/ug/define-custom-layer-with-multiple-inputs.html