# forward

Compute deep learning network output for training

## Description

Some deep learning layers behave differently during training and inference (prediction). For example, during training, dropout layers randomly set input elements to zero to help prevent overfitting, but during inference, dropout layers do not change the input.

To compute network outputs for training, use the forward function. To compute network outputs for inference, use the predict function.

example

dlY = forward(dlnet,dlX) computes the network output dlY during training given the input data dlX.

[dlY1,...,dlYN] = forward(dlnet,dlX,'Outputs',layerNames) returns the outputs dlY1, …, dlYN for the specified layers.

[dlY1,...,dlYN,state] = forward(___) also returns the updated network state using any of the previous syntaxes.

## Examples

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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 ${\rho }_{\mathit{t}}=\frac{{\rho }_{0}}{1+\mathit{k}\text{\hspace{0.17em}}\mathit{t}}$, where t is the iteration number, ${\rho }_{0}$ is the initial learning rate, and k is the decay.

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: [8×1 nnet.cnn.layer.Layer]
Connections: [7×2 table]
Learnables: [8×3 table]
State: [0×3 table]

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

Specify the training options.

velocity = [];
numEpochs = 20;
miniBatchSize = 128;
numObservations = numel(YTrain);
numIterationsPerEpoch = floor(numObservations./miniBatchSize);
initialLearnRate = 0.01;
momentum = 0.9;
decay = 0.01;

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 and loss using dlfeval and the modelGradients function.

• 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.

plots = "training-progress";
if plots == "training-progress"
figure
lineLossTrain = animatedline;
xlabel("Iteration")
ylabel("Loss")
end

Train the network.

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;
end

% 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);
end

% Evaluate the model gradients and loss using dlfeval and the

% Determine learning rate for time-based decay learning rate schedule.
learnRate = initialLearnRate/(1 + decay*iteration);

% Update the network parameters using the SGDM optimizer.
[dlnet.Learnables, velocity] = sgdmupdate(dlnet.Learnables, 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))
drawnow
end
end
end

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);
end

To classify images using a dlnetwork object, use the predict function and find the classes with the highest scores.

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

Evaluate the classification accuracy.

accuracy = mean(YPred==YTest)
accuracy = 0.9780

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 and the corresponding loss. To compute the gradients automatically, use the dlgradient function.

dlYPred = forward(dlnet,dlX);
dlYPred = softmax(dlYPred);

loss = crossentropy(dlYPred,Y);

end

## Input Arguments

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Network for custom training loops, specified as a dlnetwork object.

Input data, specified as a formatted dlarray. For more information about dlarray formats, see the fmt input argument of dlarray.

Layers to extract outputs from, specified as a string array or a cell array of character vectors containing the layer names.

• If layerNames(i) corresponds to a layer with a single output, then layerNames(i) is the name of the layer.

• If layerNames(i) corresponds to a layer with multiple outputs, then layerNames(i) is the layer name followed by the character "/" and the name of the layer output: 'layerName/outputName'.

## Output Arguments

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Output data, returned as a formatted dlarray. For more information about dlarray formats, see the fmt input argument of dlarray.

Updated network state, returned as a table.

The network state is a table with three columns:

• Layer – Layer name, specified as a string scalar.

• Parameter – Parameter name, specified as a string scalar.

• Value – Value of parameter, specified as a numeric array object.

The network state contains information remembered by the network between iterations. For example, the state of LSTM and batch normalization layers.

Update the state of a dlnetwork using the State property.