Train Network Using Custom Training Loop

This example shows how to train a network that classifies handwritten digits with a custom learning rate schedule.

If trainingOptions does not provide the options you need (for example, a custom learning rate schedule), then you can define your own custom training loop using automatic differentiation.

This example trains a network to classify handwritten digits with the time-based decay learning rate schedule: for each iteration, the solver uses the learning rate given by ρt=ρ01+kt, where t is the iteration number, ρ0 is the initial learning rate, and k is the decay.

Load Training Data

Load the digits data.

[XTrain,YTrain] = digitTrain4DArrayData;
classes = categories(YTrain);
numClasses = numel(classes);

Define Network

Define the network and specify the average image using the 'Mean' option in the image input layer.

layers = [
    imageInputLayer([28 28 1], 'Name', 'input', 'Mean', mean(XTrain,4))
    convolution2dLayer(5, 20, 'Name', 'conv1')
    reluLayer('Name', 'relu1')
    convolution2dLayer(3, 20, 'Padding', 1, 'Name', 'conv2')
    reluLayer('Name', 'relu2')
    convolution2dLayer(3, 20, 'Padding', 1, 'Name', 'conv3')
    reluLayer('Name', 'relu3')
    fullyConnectedLayer(numClasses, 'Name', 'fc')
lgraph = layerGraph(layers);

Create a dlnetwork object from the layer graph.

dlnet = dlnetwork(lgraph)
dlnet = 
  dlnetwork with properties:

         Layers: [12×1 nnet.cnn.layer.Layer]
    Connections: [11×2 table]
     Learnables: [14×3 table]
          State: [6×3 table]
     InputNames: {'input'}
    OutputNames: {'softmax'}

Define Model Gradients Function

Create the function modelGradients, listed at the end of the example, that takes a dlnetwork object dlnet, a mini-batch of input data dlX with corresponding labels Y and returns the gradients of the loss with respect to the learnable parameters in dlnet and the corresponding loss.

Specify Training Options

Train with a minibatch size of 128 for 5 epochs.

numEpochs = 5;
miniBatchSize = 128;

Specify the options for SGDM optimization. Specify an initial learn rate of 0.01 with a decay of 0.01, and momentum 0.9.

initialLearnRate = 0.01;
decay = 0.01;
momentum = 0.9;

Visualize the training progress in a plot.

plots = "training-progress";

Train on a GPU if one is available. Using a GPU requires Parallel Computing Toolbox™ and a CUDA® enabled NVIDIA® GPU with compute capability 3.0 or higher.

executionEnvironment = "auto";

Train Model

Train the model using a custom training loop.

For each epoch, shuffle the data and loop over mini-batches of data. At the end of each epoch, display the training progress.

For each mini-batch:

  • Convert the labels to dummy variables.

  • Convert the data to dlarray objects with underlying type single and specify the dimension labels 'SSCB' (spatial, spatial, channel, batch).

  • For GPU training, convert to gpuArray objects.

  • Evaluate the model gradients, state, and loss using dlfeval and the modelGradients function and update the network state.

  • Determine the learning rate for the time-based decay learning rate schedule.

  • Update the network parameters using the sgdmupdate function.

Initialize the training progress plot.

if plots == "training-progress"
    lineLossTrain = animatedline('Color',[0.85 0.325 0.098]);
    ylim([0 inf])
    grid on

Initialize the velocity parameter for the SGDM solver.

velocity = [];

Train the network.

numObservations = numel(YTrain);
numIterationsPerEpoch = floor(numObservations./miniBatchSize);

iteration = 0;
start = tic;

% Loop over epochs.
for epoch = 1:numEpochs
    % Shuffle data.
    idx = randperm(numel(YTrain));
    XTrain = XTrain(:,:,:,idx);
    YTrain = YTrain(idx);
    % Loop over mini-batches.
    for i = 1:numIterationsPerEpoch
        iteration = iteration + 1;
        % Read mini-batch of data and convert the labels to dummy
        % variables.
        idx = (i-1)*miniBatchSize+1:i*miniBatchSize;
        X = XTrain(:,:,:,idx);
        Y = zeros(numClasses, miniBatchSize, 'single');
        for c = 1:numClasses
            Y(c,YTrain(idx)==classes(c)) = 1;
        % Convert mini-batch of data to dlarray.
        dlX = dlarray(single(X),'SSCB');
        % If training on a GPU, then convert data to gpuArray.
        if (executionEnvironment == "auto" && canUseGPU) || executionEnvironment == "gpu"
            dlX = gpuArray(dlX);
        % Evaluate the model gradients, state, and loss using dlfeval and the
        % modelGradients function and update the network state.
        [gradients,state,loss] = dlfeval(@modelGradients,dlnet,dlX,Y);
        dlnet.State = state;
        % Determine learning rate for time-based decay learning rate schedule.
        learnRate = initialLearnRate/(1 + decay*iteration);
        % Update the network parameters using the SGDM optimizer.
        [dlnet, velocity] = sgdmupdate(dlnet, gradients, velocity, learnRate, momentum);
        % Display the training progress.
        if plots == "training-progress"
            D = duration(0,0,toc(start),'Format','hh:mm:ss');
            title("Epoch: " + epoch + ", Elapsed: " + string(D))

Test Model

Test the classification accuracy of the model by comparing the predictions on a test set with the true labels.

[XTest, YTest] = digitTest4DArrayData;

Convert the data to a dlarray object with dimension format 'SSCB'. For GPU prediction, also convert the data to gpuArray.

dlXTest = dlarray(XTest,'SSCB');
if (executionEnvironment == "auto" && canUseGPU) || executionEnvironment == "gpu"
    dlXTest = gpuArray(dlXTest);

Classify the images using modelPredictions function, listed at the end of the example and find the classes with the highest scores.

dlYPred = modelPredictions(dlnet,dlXTest,miniBatchSize);
[~,idx] = max(extractdata(dlYPred),[],1);
YPred = classes(idx);

Evaluate the classification accuracy.

accuracy = mean(YPred == YTest)
accuracy = 0.9910

Model Gradients Function

The modelGradients function takes a dlnetwork object dlnet, a mini-batch of input data dlX with corresponding labels Y and returns the gradients of the loss with respect to the learnable parameters in dlnet, the network state, and the loss. To compute the gradients automatically, use the dlgradient function.

function [gradients,state,loss] = modelGradients(dlnet,dlX,Y)

[dlYPred,state] = forward(dlnet,dlX);

loss = crossentropy(dlYPred,Y);
gradients = dlgradient(loss,dlnet.Learnables);


Model Predictions Function

The modelPredictions function takes a dlnetwork object dlnet, an array of input data dlX, and a mini-batch size, and outputs the model predictions by iterating over mini-batches of the specified size.

function dlYPred = modelPredictions(dlnet,dlX,miniBatchSize)

numObservations = size(dlX,4);
numIterations = ceil(numObservations / miniBatchSize);

numClasses = dlnet.Layers(11).OutputSize;
dlYPred = zeros(numClasses,numObservations,'like',dlX);

for i = 1:numIterations
    idx = (i-1)*miniBatchSize+1:min(i*miniBatchSize,numObservations);
    dlYPred(:,idx) = predict(dlnet,dlX(:,:,:,idx));


See Also

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