# dlnetwork

Deep learning network for custom training loops

## Description

A dlnetwork object enables support for custom training loops using automatic differentiation.

### Tip

For most deep learning tasks, you can use a pretrained network and adapt it to your own data. For an example showing how to use transfer learning to retrain a convolutional neural network to classify a new set of images, see Train Deep Learning Network to Classify New Images. Alternatively, you can create and train networks from scratch using layerGraph objects with the trainNetwork and trainingOptions functions.

If the trainingOptions function does not provide the training options that you need for your task, then you can create a custom training loop using automatic differentiation. To learn more, see Define Custom Training Loops.

## Creation

### Description

example

dlnet = dlnetwork(lgraph) converts a layer graph to a dlnetwork object representing a deep neural network for custom training loops.

### Input Arguments

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Network architecture, specified as a layer graph.

The layer graph must not contain output layers. When training the network, calculate the loss separately.

For a list of layers supported by dlnetwork, see Supported Layers.

## Properties

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Network layers, specified as a Layer array.

Layer connections, specified as a table with two columns.

Each table row represents a connection in the layer graph. The first column, Source, specifies the source of each connection. The second column, Destination, specifies the destination of each connection. The connection sources and destinations are either layer names or have the form 'layerName/IOName', where 'IOName' is the name of the layer input or output.

Data Types: table

Network learnable parameters, specified as 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 dlarray.

The network learnable parameters contain the features learned by the network. For example, the weights of convolution and fully connected layers.

Data Types: table

Network state, specified 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.

During training or inference, you can update the network state using the output of the forward and predict functions.

Data Types: table

Network input layer names, specified as a cell array of character vectors.

Data Types: cell

Network output layer names, specified as a cell array of character vectors. This property includes all layers with disconnected outputs. If a layer has multiple outputs, then the disconnected outputs are specified as 'layerName/outputName'.

Data Types: cell

## Object Functions

 forward Compute deep learning network output for training predict Compute deep learning network output for inference layerGraph Graph of network layers for deep learning

## Examples

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To implement a custom training loop for your network, first convert it to a dlnetwork object. Do not include output layers in a dlnetwork object. Instead, you must specify the loss function in the custom training loop.

Convert the network to a layer graph and remove the layers used for classification using removeLayers.

lgraph = layerGraph(net);
lgraph = removeLayers(lgraph,["prob" "output"]);

Convert the network to a dlnetwork object.

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

Layers: [142x1 nnet.cnn.layer.Layer]
Connections: [168x2 table]
Learnables: [116x3 table]
State: [0x3 table]
InputNames: {'data'}
OutputNames: {'loss3-classifier'}

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.

[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')
batchNormalizationLayer('Name','bn1')
reluLayer('Name', 'relu1')
convolution2dLayer(3, 20, 'Padding', 1, 'Name', 'conv2')
batchNormalizationLayer('Name','bn2')
reluLayer('Name', 'relu2')
convolution2dLayer(3, 20, 'Padding', 1, 'Name', 'conv3')
batchNormalizationLayer('Name','bn3')
reluLayer('Name', 'relu3')
fullyConnectedLayer(numClasses, 'Name', 'fc')
softmaxLayer('Name','softmax')];
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'}

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"
figure
lineLossTrain = animatedline('Color',[0.85 0.325 0.098]);
ylim([0 inf])
xlabel("Iteration")
ylabel("Loss")
grid on
end

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;
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, state, and loss using dlfeval and the
% modelGradients function and update the network state.
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))
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

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

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.

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

loss = crossentropy(dlYPred,Y);

end

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));
end

end