# Specify Custom Weight Initialization Function

This example shows how to create a custom He weight initialization function for convolution layers followed by leaky ReLU layers.

The He initializer for convolution layers followed by leaky ReLU layers samples from a normal distribution with zero mean and variance ${\sigma }^{2}=\frac{2}{\left(1+{\mathit{a}}^{2}\right)\mathit{n}}$, where a is the scale of the leaky ReLU layer that follows the convolution layer and n = FilterSize(1) * FilterSize(2) * NumChannels.

For learnable layers, when setting the options 'WeightsInititializer', 'InputWeightsInitializer', or 'RecurrentWeightsInitializer' to 'he', the software uses a=0. To set a to different value, create a custom function to use as a weights initializer.

Load the digit sample data as an image datastore. The imageDatastore function automatically labels the images based on folder names.

digitDatasetPath = fullfile(matlabroot,'toolbox','nnet','nndemos', ...
'nndatasets','DigitDataset');
imds = imageDatastore(digitDatasetPath, ...
'IncludeSubfolders',true, ...
'LabelSource','foldernames');

Divide the data into training and validation data sets, so that each category in the training set contains 750 images, and the validation set contains the remaining images from each label. splitEachLabel splits the datastore into two new datastores for training and validation.

numTrainFiles = 750;
[imdsTrain,imdsValidation] = splitEachLabel(imds,numTrainFiles,'randomize');

### Define Network Architecture

Define the convolutional neural network architecture:

• Image input layer size of [28 28 1], the size of the input images

• Three 2-D convolution layers with filter size 3 and with 8, 16, and 32 filters respectively

• A leaky ReLU layer following each convolutional layer

• Fully connected layer of size 10, the number of classes

• Softmax layer

• Classification layer

For each of the convolutional layers, set the weights initializer to the leakyHe function. The leakyHe function, listed at the end of the example, takes the input sz (the size of the layer weights) and returns an array of weights given by the He Initializer for convolution layers followed by a leaky ReLU layer.

inputSize = [28 28 1];
numClasses = 10;

layers = [
imageInputLayer(inputSize)
convolution2dLayer(3,8,'WeightsInitializer',@leakyHe)
leakyReluLayer
convolution2dLayer(3,16,'WeightsInitializer',@leakyHe)
leakyReluLayer
convolution2dLayer(3,32,'WeightsInitializer',@leakyHe)
leakyReluLayer
fullyConnectedLayer(numClasses)
softmaxLayer
classificationLayer];

### Train Network

Specify the training options and train the network. Train for four epochs. To prevent the gradients from exploding, set the gradient threshold to 2. Validate the network once per epoch. View the training progress plot.

By default, trainNetwork uses a GPU if one is available, otherwise, it uses a CPU. Training on a GPU requires Parallel Computing Toolbox™ and a supported GPU device. For information on supported devices, see GPU Support by Release (Parallel Computing Toolbox). You can also specify the execution environment by using the 'ExecutionEnvironment' name-value pair argument of trainingOptions.

maxEpochs = 4;
miniBatchSize = 128;
numObservations = numel(imdsTrain.Files);
numIterationsPerEpoch = floor(numObservations / miniBatchSize);

options = trainingOptions('sgdm', ...
'MaxEpochs',maxEpochs, ...
'MiniBatchSize',miniBatchSize, ...
'ValidationData',imdsValidation, ...
'ValidationFrequency',numIterationsPerEpoch, ...
'Verbose',false, ...
'Plots','training-progress');

[netDefault,infoDefault] = trainNetwork(imdsTrain,layers,options);

### Test Network

Classify the validation data and calculate the classification accuracy.

YPred = classify(netDefault,imdsValidation);
YValidation = imdsValidation.Labels;
accuracy = mean(YPred == YValidation)
accuracy = 0.9684

The leakyHe function accepts the optional input argument scale. To input extra variables into the custom weight initialization function, specify the function as an anonymous function that accepts a single input sz. To do this, replace instances of @leakyHe with @(sz) leakyHe(sz,scale). Here, the anonymous function accepts the single input argument sz only and calls the leakyHe function with the specified scale input argument.

Create and train the same network as before with the following changes:

• For the leaky ReLU layers, specify a scale multiplier of 0.01.

• Initialize the weights of the convolutional layers with the leakyHe function and also specify the scale multiplier.

scale = 0.01;

layers = [
imageInputLayer(inputSize)
convolution2dLayer(3,8,'WeightsInitializer',@(sz) leakyHe(sz,scale))
leakyReluLayer(scale)
convolution2dLayer(3,16,'WeightsInitializer',@(sz) leakyHe(sz,scale))
leakyReluLayer(scale)
convolution2dLayer(3,32,'WeightsInitializer',@(sz) leakyHe(sz,scale))
leakyReluLayer(scale)
fullyConnectedLayer(numClasses)
softmaxLayer
classificationLayer];

[netCustom,infoCustom] = trainNetwork(imdsTrain,layers,options);

Classify the validation data and calculate the classification accuracy.

YPred = classify(netCustom,imdsValidation);
YValidation = imdsValidation.Labels;
accuracy = mean(YPred == YValidation)
accuracy = 0.9456

### Compare Results

Extract the validation accuracy from the information structs output from the trainNetwork function.

validationAccuracy = [
infoDefault.ValidationAccuracy;
infoCustom.ValidationAccuracy];

The vectors of validation accuracy contain NaN for iterations that the validation accuracy was not computed. Remove the NaN values.

idx = all(isnan(validationAccuracy));
validationAccuracy(:,idx) = [];

For each of the networks, plot the epoch numbers against the validation accuracy.

figure
epochs = 0:maxEpochs;
plot(epochs,validationAccuracy)
title("Validation Accuracy")
xlabel("Epoch")
ylabel("Validation Accuracy")
legend(["Leaky He (Default)" "Leaky He (Custom)"],'Location','southeast')

### Custom Weight Initialization Function

The leakyHe function takes the input sz (the size of the layer weights) and returns an array of weights given by the He Initializer for convolution layers followed by a leaky ReLU layer. The function also accepts the optional input argument scale which specifies the scale multiplier for the leaky ReLU layer.

function weights = leakyHe(sz,scale)

% If not specified, then use default scale = 0.1
if nargin < 2
scale = 0.1;
end

filterSize = [sz(1) sz(2)];
numChannels = sz(3);
numIn = filterSize(1) * filterSize(2) * numChannels;

varWeights = 2 / ((1 + scale^2) * numIn);
weights = randn(sz) * sqrt(varWeights);

end

### Bibliography

1. He, Kaiming, Xiangyu Zhang, Shaoqing Ren, and Jian Sun. "Delving deep into rectifiers: Surpassing human-level performance on imagenet classification." In Proceedings of the IEEE international conference on computer vision, pp. 1026-1034. 2015.