Create an empty layer graph and an array of layers. Add the layers to the layer graph and plot the graph. addLayers connects the layers sequentially.

lgraph = layerGraph;

layers = [
    imageInputLayer([32 32 3],'Name','input')  
    convolution2dLayer(3,16,'Padding','same','Name','conv_1')
    batchNormalizationLayer('Name','BN_1')
    reluLayer('Name','relu_1')];

lgraph = addLayers(lgraph,layers);
figure
plot(lgraph)

Create an array of layers.

layers = [
    imageInputLayer([28 28 1],'Name','input')  
    convolution2dLayer(3,16,'Padding','same','Name','conv_1')
    batchNormalizationLayer('Name','BN_1')
    reluLayer('Name','relu_1')];

Create a layer graph from the layer array. layerGraph connects all the layers in layers sequentially. Plot the layer graph.

lgraph = layerGraph(layers);
figure
plot(lgraph)

Load a pretrained SqueezeNet network. You can use this trained network for classification and prediction.

net = squeezenet;

To modify the network structure, first extract the structure of the DAG network by using layerGraph. You can then use the object functions of LayerGraph to modify the network architecture.

lgraph = layerGraph(net)

lgraph = 
  LayerGraph with properties:

         Layers: [68x1 nnet.cnn.layer.Layer]
    Connections: [75x2 table]
     InputNames: {'data'}
    OutputNames: {'ClassificationLayer_predictions'}

Create a simple directed acyclic graph (DAG) network for deep learning. Train the network to classify images of digits. The simple network in this example consists of:

Create the main branch of the network as a layer array. The addition layer sums multiple inputs element-wise. Specify the number of inputs for the addition layer to sum. All layers must have names and all names must be unique.

layers = [
    imageInputLayer([28 28 1],'Name','input')
    
    convolution2dLayer(5,16,'Padding','same','Name','conv_1')
    batchNormalizationLayer('Name','BN_1')
    reluLayer('Name','relu_1')
    
    convolution2dLayer(3,32,'Padding','same','Stride',2,'Name','conv_2')
    batchNormalizationLayer('Name','BN_2')
    reluLayer('Name','relu_2')
    convolution2dLayer(3,32,'Padding','same','Name','conv_3')
    batchNormalizationLayer('Name','BN_3')
    reluLayer('Name','relu_3')
    
    additionLayer(2,'Name','add')
    
    averagePooling2dLayer(2,'Stride',2,'Name','avpool')
    fullyConnectedLayer(10,'Name','fc')
    softmaxLayer('Name','softmax')
    classificationLayer('Name','classOutput')];

Create a layer graph from the layer array. layerGraph connects all the layers in layers sequentially. Plot the layer graph.

lgraph = layerGraph(layers);
figure
plot(lgraph)

Create the 1-by-1 convolutional layer and add it to the layer graph. Specify the number of convolutional filters and the stride so that the activation size matches the activation size of the 'relu_3' layer. This arrangement enables the addition layer to add the outputs of the 'skipConv' and 'relu_3' layers. To check that the layer is in the graph, plot the layer graph.

skipConv = convolution2dLayer(1,32,'Stride',2,'Name','skipConv');
lgraph = addLayers(lgraph,skipConv);
figure
plot(lgraph)

Create the shortcut connection from the 'relu_1' layer to the 'add' layer. Because you specified two as the number of inputs to the addition layer when you created it, the layer has two inputs named 'in1' and 'in2'. The 'relu_3' layer is already connected to the 'in1' input. Connect the 'relu_1' layer to the 'skipConv' layer and the 'skipConv' layer to the 'in2' input of the 'add' layer. The addition layer now sums the outputs of the 'relu_3' and 'skipConv' layers. To check that the layers are connected correctly, plot the layer graph.

lgraph = connectLayers(lgraph,'relu_1','skipConv');
lgraph = connectLayers(lgraph,'skipConv','add/in2');
figure
plot(lgraph);

Load the training and validation data, which consists of 28-by-28 grayscale images of digits.

[XTrain,YTrain] = digitTrain4DArrayData;
[XValidation,YValidation] = digitTest4DArrayData;

Specify training options and train the network. trainNetwork validates the network using the validation data every ValidationFrequency iterations.

options = trainingOptions('sgdm', ...
    'MaxEpochs',8, ...
    'Shuffle','every-epoch', ...
    'ValidationData',{XValidation,YValidation}, ...
    'ValidationFrequency',30, ...
    'Verbose',false, ...
    'Plots','training-progress');
net = trainNetwork(XTrain,YTrain,lgraph,options);

Display the properties of the trained network. The network is a DAGNetwork object.

net

net = 
  DAGNetwork with properties:

         Layers: [16×1 nnet.cnn.layer.Layer]
    Connections: [16×2 table]
     InputNames: {'input'}
    OutputNames: {'classOutput'}

Classify the validation images and calculate the accuracy. The network is very accurate.

YPredicted = classify(net,XValidation);
accuracy = mean(YPredicted == YValidation)

accuracy = 0.9930