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Train Network in Parallel with Custom Training Loop

This example shows how to set up a custom training loop to train a network in parallel. In this example, parallel workers train on portions of the overall mini-batch. If you have a GPU, then training happens on the GPU. During training, a DataQueue object sends training progress information back to the MATLAB client.

Load Data Set

Load the digit data set and create an image datastore for the data set. Split the datastore into training and test datastores in a randomized way.

digitDatasetPath = fullfile(matlabroot,'toolbox','nnet','nndemos', ...
imds = imageDatastore(digitDatasetPath, ...
    'IncludeSubfolders',true, ...

[imdsTrain,imdsTest] = splitEachLabel(imds,0.9,"randomized");

Determine the different classes in the training set.

classes = categories(imdsTrain.Labels);
numClasses = numel(classes);

Define Network

Define your network architecture and make it into a layer graph by using the layerGraph function. This network architecture includes batch normalization layers, which track the mean and variance statistics of the data set. When training in parallel, combine the statistics from all of the workers at the end of each iteration step, to ensure the network state reflects the whole mini-batch. Otherwise, the network state can diverge across the workers. If you are training stateful recurrent neural networks (RNNs), for example, using sequence data that has been split into smaller sequences to train networks containing LSTM or GRU layers, you must also manage the state between the workers.

layers = [
    imageInputLayer([28 28 1],'Name','input','Normalization','none')

lgraph = layerGraph(layers);

Create a dlnetwork object from the layer graph. dlnetwork objects allow for training with custom loops.

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

         Layers: [11×1 nnet.cnn.layer.Layer]
    Connections: [10×2 table]
     Learnables: [14×3 table]
          State: [6×3 table]
     InputNames: {'input'}
    OutputNames: {'fc'}
    Initialized: 1

Set Up Parallel Environment

Determine if GPUs are available for MATLAB to use with the canUseGPU function.

  • If there are GPUs available, then train on the GPUs. Create a parallel pool with as many workers as GPUs.

  • If there are no GPUs available, then train on the CPUs. Create a parallel pool with the default number of workers.

if canUseGPU
    executionEnvironment = "gpu";
    numberOfGPUs = gpuDeviceCount("available");
    pool = parpool(numberOfGPUs);
    executionEnvironment = "cpu";
    pool = parpool;

Get the number of workers in the parallel pool. Later in this example, you divide the workload according to this number.

N = pool.NumWorkers;

Train Model

Specify the training options.

numEpochs = 20;
miniBatchSize = 128;
velocity = [];

For GPU training, a recommended practice is to scale up the mini-batch size linearly with the number of GPUs, in order to keep the workload on each GPU constant. For more related advice, see Training with Multiple GPUs (Deep Learning Toolbox).

if executionEnvironment == "gpu"
    miniBatchSize = miniBatchSize .* N
miniBatchSize = 512

Calculate the mini-batch size for each worker by dividing the overall mini-batch size evenly among the workers. Distribute the remainder across the first workers.

workerMiniBatchSize = floor(miniBatchSize ./ repmat(N,1,N));
remainder = miniBatchSize - sum(workerMiniBatchSize);
workerMiniBatchSize = workerMiniBatchSize + [ones(1,remainder) zeros(1,N-remainder)]
workerMiniBatchSize = 1×4

   128   128   128   128

Initialize the training progress plot.

% Set up the training plot
lineLossTrain = animatedline('Color',[0.85 0.325 0.098]);
ylim([0 inf])
grid on

To send data back from the workers during training, create a DataQueue object. Use afterEach to set up a function, displayTrainingProgress, to call each time a worker sends data. displayTrainingProgress is a supporting function, defined at the end of this example, that displays the training progress information that comes from the workers.

Q = parallel.pool.DataQueue;
displayFcn = @(x) displayTrainingProgress(x,lineLossTrain);

Train the model using a custom parallel training loop, as detailed in the following steps. To execute the code simultaneously on all the workers, use an spmd block. Within the spmd block, labindex gives the index of the worker currently executing the code.

Before training, partition the datastore for each worker by using the partition function, and set ReadSize to the mini-batch size of the worker.

For each epoch, reset and shuffle the datastore with the reset and shuffle functions. For each iteration in the epoch:

  • Ensure that all workers have data available before beginning processing it in parallel, by performing a global and operation (gop) on the result of the hasdata function.

  • Read a mini-batch from the datastore by using the read function, and concatenate the retrieved images into a four-dimensional array of images. Normalize the images so that the pixels take values between 0 and 1.

  • Convert the labels to a matrix of dummy variables that puts labels against observations. Dummy variables contain 1 for the label of the observation and 0 otherwise.

  • Convert the mini-batch of data to a dlarray object with the underlying type single and specify the dimension labels 'SSCB' (spatial, spatial, channel, batch). For GPU training, convert the data to gpuArray.

  • Compute the gradients and the loss of the network on each worker by calling dlfeval on the modelGradients function. The dlfeval function evaluates the helper function modelGradients with automatic differentiation enabled, so modelGradients can compute the gradients with respect to the loss in an automatic way. modelGradients is defined at the end of the example and returns loss and gradients given a network, mini-batch of data, and true labels.

  • To obtain the overall loss, aggregate the losses on all workers. This example uses cross entropy for the loss function, and the aggregated loss is the sum of all losses. Before aggregating, normalize each loss by multiplying by the proportion of the overall mini-batch that the worker is working on. Use gplus to add all losses together and replicate the results across workers.

  • To aggregate and update the gradients of all workers, use the dlupdate function with the aggregateGradients function. aggregateGradients is a supporting function defined at the end of this example. This function uses gplus to add together and replicate gradients across workers, following normalization according to the proportion of the overall mini-batch that each worker is working on.

  • Aggregate the state of the network on all workers using the aggregateState function. aggregateState is a supporting function defined at the end of this example. The batchnormalization layers in the network track the mean and variance of the data. Since the complete mini-batch is spread across multiple workers, aggregate the network state after each iteration to compute the mean and variance of the whole minibatch.

  • After computing the final gradients, update the network learnable parameters with the sgdmupdate function.

  • Send training progress information back to the client by using the send function with the DataQueue. Use only one worker to send data, because all workers have the same loss information. To ensure that data is on the CPU, so that a client machine without a GPU can access it, use gather on the dlarray before sending it.

start = tic;
    % Partition datastore.
    workerImds = partition(imdsTrain,N,labindex);
    workerImds.ReadSize = workerMiniBatchSize(labindex);
    workerVelocity = velocity;
    iteration = 0;
    for epoch = 1:numEpochs
        % Reset and shuffle the datastore.
        workerImds = shuffle(workerImds);
        % Loop over mini-batches.
        while gop(@and,hasdata(workerImds))
            iteration = iteration + 1;
            % Read a mini-batch of data.
            [workerXBatch,workerTBatch] = read(workerImds);
            workerXBatch = cat(4,workerXBatch{:});
            workerNumObservations = numel(workerTBatch.Label);

            % Normalize the images.
            workerXBatch =  single(workerXBatch) ./ 255;
            % Convert the labels to dummy variables.
            workerY = zeros(numClasses,workerNumObservations,'single');
            for c = 1:numClasses
                workerY(c,workerTBatch.Label==classes(c)) = 1;
            % Convert the mini-batch of data to dlarray.
            dlworkerX = dlarray(workerXBatch,'SSCB');
            % If training on GPU, then convert data to gpuArray.
            if executionEnvironment == "gpu"
                dlworkerX = gpuArray(dlworkerX);
            % Evaluate the model gradients and loss on the worker.
            [workerGradients,dlworkerLoss,workerState] = dlfeval(@modelGradients,dlnet,dlworkerX,workerY);
            % Aggregate the losses on all workers.
            workerNormalizationFactor = workerMiniBatchSize(labindex)./miniBatchSize;
            loss = gplus(workerNormalizationFactor*extractdata(dlworkerLoss));
            % Aggregate the network state on all workers
            dlnet.State = aggregateState(workerState,workerNormalizationFactor);
            % Aggregate the gradients on all workers.
            workerGradients.Value = dlupdate(@aggregateGradients,workerGradients.Value,{workerNormalizationFactor});
            % Update the network parameters using the SGDM optimizer.
            [dlnet.Learnables,workerVelocity] = sgdmupdate(dlnet.Learnables,workerGradients,workerVelocity);
       % Display training progress information.
       if labindex == 1
           data = [epoch loss iteration toc(start)];

Test Model

After you train the network, you can test its accuracy.

Load the test images into memory by using readall on the test datastore, concatenate them, and normalize them.

XTest = readall(imdsTest);
XTest = cat(4,XTest{:});
XTest = single(XTest) ./ 255;
YTest = imdsTest.Labels;

After the training is complete, all workers have the same complete trained network. Retrieve any of them.

dlnetFinal = dlnet{1};

To classify images using a dlnetwork object, use the predict function on a dlarray.

dlYPredScores = predict(dlnetFinal,dlarray(XTest,'SSCB'));

From the predicted scores, find the class with the highest score with the max function. Before you do that, extract the data from the dlarray with the extractdata function.

[~,idx] = max(extractdata(dlYPredScores),[],1);
YPred = classes(idx);

To obtain the classification accuracy of the model, compare the predictions on the test set against the true labels.

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

Model Gradients Functions

Define a function, modelGradients, to compute the gradients of the loss with respect to the learnable parameters of the network. This function computes the network outputs for a mini-batch X with forward and softmax and calculates the loss, given the true outputs, using cross entropy. When you call this function with dlfeval, automatic differentiation is enabled, and dlgradient can compute the gradients of the loss with respect to the learnables automatically.

function [dlgradients,dlloss,state] = modelGradients(dlnet,dlX,dlY)
    [dlYPred,state] = forward(dlnet,dlX);
    dlYPred = softmax(dlYPred);
    dlloss = crossentropy(dlYPred,dlY);
    dlgradients = dlgradient(dlloss,dlnet.Learnables);

Display Training Progress Function

Define a function to display training progress information that comes from the workers. The DataQueue in this example calls this function every time a worker sends data.

function displayTrainingProgress (data,line)
     D = duration(0,0,data(4),'Format','hh:mm:ss');
     title("Epoch: " + data(1) + ", Elapsed: " + string(D))

Aggregate Gradients Function

Define a function that aggregates the gradients on all workers by adding them together. gplus adds together and replicates all the gradients on the workers. Before adding them together, normalize them by multiplying them by a factor that represents the proportion of the overall mini-batch that the worker is working on. To retrieve the contents of a dlarray, use extractdata.

function gradients = aggregateGradients(dlgradients,factor)
    gradients = extractdata(dlgradients);
    gradients = gplus(factor*gradients);

Aggregate State Function

Define a function that aggregates the network state on all workers. The network state contains the trained batch normalization statistics of the data set. Since each worker only sees a portion of the mini-batch, aggregate the network state so that the statistics are representative of the statistics across all the data. For each mini-batch, the combined mean is calculated as a weighted average of the mean across the workers for each iteration. The combined variance is calculated according to the following formula:


where Nis the total number of workers, Mis the total number of observations in a mini-batch, mj is the number of observations processed on the jth worker, xj and sj2 are the mean and variance statistics calculated on that worker, and xc is the combined mean across all workers.

function state = aggregateState(state,factor)

    numrows = size(state,1);
    for j = 1:numrows
        isBatchNormalizationState = state.Parameter(j) =="TrainedMean"...
            && state.Parameter(j+1) =="TrainedVariance"...
            && state.Layer(j) == state.Layer(j+1);
        if isBatchNormalizationState
            meanVal = state.Value{j};
            varVal = state.Value{j+1};
            % Calculate combined mean
            combinedMean = gplus(factor*meanVal);
            % Caclulate combined variance terms to sum
            combinedVarTerm = factor.*(varVal + (meanVal - combinedMean).^2);        
            % Update state
            state.Value(j) = {combinedMean};
            state.Value(j+1) = {gplus(combinedVarTerm)};

See Also

| | | | | | | (Deep Learning Toolbox) | (Deep Learning Toolbox) | (Deep Learning Toolbox) | (Deep Learning Toolbox)

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