Create an addition layer with two inputs and the name 'add_1'.

add = additionLayer(2,'Name','add_1')

add = 
  AdditionLayer with properties:

          Name: 'add_1'
     NumInputs: 2
    InputNames: {'in1'  'in2'}

Create two ReLU layers and connect them to the addition layer. The addition layer sums the outputs from the ReLU layers.

relu_1 = reluLayer('Name','relu_1');
relu_2 = reluLayer('Name','relu_2');

lgraph = layerGraph;
lgraph = addLayers(lgraph,relu_1);
lgraph = addLayers(lgraph,relu_2);
lgraph = addLayers(lgraph,add);

lgraph = connectLayers(lgraph,'relu_1','add_1/in1');
lgraph = connectLayers(lgraph,'relu_2','add_1/in2');

plot(lgraph)

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. To easily add connections later, specify names for the first ReLU layer and the addition layer.

layers = [
    imageInputLayer([28 28 1])
    
    convolution2dLayer(5,16,'Padding','same')
    batchNormalizationLayer
    reluLayer('Name','relu_1')
    
    convolution2dLayer(3,32,'Padding','same','Stride',2)
    batchNormalizationLayer
    reluLayer
    convolution2dLayer(3,32,'Padding','same')
    batchNormalizationLayer
    reluLayer
    
    additionLayer(2,'Name','add')
    
    averagePooling2dLayer(2,'Stride',2)
    fullyConnectedLayer(10)
    softmaxLayer
    classificationLayer];

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 third ReLU layer. This arrangement enables the addition layer to add the outputs of the third ReLU layer and the 1-by-1 convolutional layer. 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 third ReLU 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 third ReLU layer and the 'skipConv' layer. 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: [16x1 nnet.cnn.layer.Layer]
    Connections: [16x2 table]
     InputNames: {'imageinput'}
    OutputNames: {'classoutput'}

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

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

accuracy = 0.9934