Specify Custom Weight Initialization Function

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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 $σ^{2} = \frac{2}{(1 + a^{2}) n}$ , whereais the scale of the leaky ReLU layer that follows the convolution layer andn = FilterSize(1) * FilterSize(2) * NumChannels.

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

Load Data

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

数字DatasetPath = 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.splitEachLabelsplits 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 theleakyHefunction. TheleakyHefunction, listed at the end of the example, takes the inputsz(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,trainNetworkuses 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, seeGPU Support by Release(Parallel Computing Toolbox). You can also specify the execution environment by using the'ExecutionEnvironment'name-value pair argument oftrainingOptions.

maxEpochs = 4; miniBatchSize = 128; numObservations = numel(imdsTrain.Files); numIterationsPerEpoch = floor(numObservations / miniBatchSize); options = trainingOptions('sgdm',...“MaxEpochs”,maxEpochs,...'MiniBatchSize',miniBatchSize,...'GradientThreshold',2,...'ValidationData',imdsValidation,...'ValidationFrequency',numIterationsPerEpoch,...'Verbose',false,...“阴谋”,'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

Specify Additional Options

TheleakyHefunction accepts the optional input argumentscale. To input extra variables into the custom weight initialization function, specify the function as an anonymous function that accepts a single inputsz. To do this, replace instances of@leakyHewith@(sz) leakyHe(sz,scale). Here, the anonymous function accepts the single input argumentszonly and calls theleakyHefunction with the specifiedscaleinput 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 theleakyHefunction 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 thetrainNetworkfunction.

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

The vectors of validation accuracy containNaNfor iterations that the validation accuracy was not computed. Remove theNaNvalues.

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

TheleakyHe函数的输入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 argumentscalewhich specifies the scale multiplier for the leaky ReLU layer.

functionweights = leakyHe(sz,scale)% If not specified, then use default scale = 0.1ifnargin < 2 scale = 0.1;endfilterSize = [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

开明,他象屿张任Shaoqing和剑Sun. "Delving deep into rectifiers: Surpassing human-level performance on imagenet classification." InProceedings of the IEEE international conference on computer vision, pp. 1026-1034. 2015.