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:

创建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.layerGraphconnects all the layers inlayerssequentially. Plot the layer graph.

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

创建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)

创建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.trainNetworkvalidates the network using the validation data everyValidationFrequencyiterations.

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

Display the properties of the trained network. The network is aDAGNetwork对象。

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