## Define Custom Classification Output Layer

### Tip

To construct a classification output layer with cross entropy loss for k mutually exclusive classes, use classificationLayer. If you want to use a different loss function for your classification problems, then you can define a custom classification output layer using this example as a guide.

This example shows how to define a custom classification output layer with the sum of squares error (SSE) loss and use it in a convolutional neural network.

To define a custom classification output layer, you can use the template provided in this example, which takes you through the following steps:

1. Name the layer – Give the layer a name so it can be used in MATLAB®.

2. Declare the layer properties – Specify the properties of the layer.

3. Create a constructor function (optional) – Specify how to construct the layer and initialize its properties. If you do not specify a constructor function, then the software initializes the properties with '' at creation.

4. Create a forward loss function – Specify the loss between the predictions and the training targets.

5. Create a backward loss function (optional) – Specify the derivative of the loss with respect to the predictions. If you do not specify a backward loss function, then the forward loss function must support dlarray objects.

A classification SSE layer computes the sum of squares error loss for classification problems. SSE is an error measure between two continuous random variables. For predictions Y and training targets T, the SSE loss between Y and T is given by

$L=\frac{1}{N}\sum _{n=1}^{N}\text{​}\sum _{i=1}^{K}\text{​}{\left({Y}_{ni}-{T}_{ni}\right)}^{2},$

where N is the number of observations and K is the number of classes.

### Classification Output Layer Template

Copy the classification output layer template into a new file in MATLAB. This template outlines the structure of a classification output layer and includes the functions that define the layer behavior.

classdef myClassificationLayer < nnet.layer.ClassificationLayer

properties
% (Optional) Layer properties.

% Layer properties go here.
end

methods
function layer = myClassificationLayer()
% (Optional) Create a myClassificationLayer.

% Layer constructor function goes here.
end

function loss = forwardLoss(layer, Y, T)
% Return the loss between the predictions Y and the training
% targets T.
%
% Inputs:
%         layer - Output layer
%         Y     – Predictions made by network
%         T     – Training targets
%
% Output:
%         loss  - Loss between Y and T

% Layer forward loss function goes here.
end

function dLdY = backwardLoss(layer, Y, T)
% (Optional) Backward propagate the derivative of the loss
% function.
%
% Inputs:
%         layer - Output layer
%         Y     – Predictions made by network
%         T     – Training targets
%
% Output:
%         dLdY  - Derivative of the loss with respect to the
%                 predictions Y

% Layer backward loss function goes here.
end
end
end

### Name the Layer

First, give the layer a name. In the first line of the class file, replace the existing name myClassificationLayer with sseClassificationLayer.

classdef sseClassificationLayer < nnet.layer.ClassificationLayer
...
end

Next, rename the myClassificationLayer constructor function (the first function in the methods section) so that it has the same name as the layer.

methods
function layer = sseClassificationLayer()
...
end

...
end

#### Save the Layer

Save the layer class file in a new file named sseClassificationLayer.m. The file name must match the layer name. To use the layer, you must save the file in the current folder or in a folder on the MATLAB path.

### Declare Layer Properties

Declare the layer properties in the properties section.

By default, custom output layers have the following properties:

• NameLayer name, specified as a character vector or a string scalar. To include a layer in a layer graph, you must specify a nonempty unique layer name. If you train a series network with the layer and Name is set to '', then the software automatically assigns a name to the layer at training time.

• Description – One-line description of the layer, specified as a character vector or a string scalar. This description appears when the layer is displayed in a Layer array. If you do not specify a layer description, then the software displays "Classification Output" or "Regression Output".

• Type – Type of the layer, specified as a character vector or a string scalar. The value of Type appears when the layer is displayed in a Layer array. If you do not specify a layer type, then the software displays the layer class name.

Custom classification layers also have the following property:

• ClassesClasses of the output layer, specified as a categorical vector, string array, cell array of character vectors, or 'auto'. If Classes is 'auto', then the software automatically sets the classes at training time. If you specify the string array or cell array of character vectors str, then the software sets the classes of the output layer to categorical(str,str). The default value is 'auto'.

Custom regression layers also have the following property:

• ResponseNamesNames of the responses, specified a cell array of character vectors or a string array. At training time, the software automatically sets the response names according to the training data. The default is {}.

If the layer has no other properties, then you can omit the properties section.

In this example, the layer does not require any additional properties, so you can remove the properties section.

### Create Constructor Function

Create the function that constructs the layer and initializes the layer properties. Specify any variables required to create the layer as inputs to the constructor function.

Specify the input argument name to assign to the Name property at creation. Add a comment to the top of the function that explains the syntax of the function.

function layer = sseClassificationLayer(name)
% layer = sseClassificationLayer(name) creates a sum of squares
% error classification layer and specifies the layer name.

...
end

#### Initialize Layer Properties

Replace the comment % Layer constructor function goes here with code that initializes the layer properties.

Give the layer a one-line description by setting the Description property of the layer. Set the Name property to the input argument name.

function layer = sseClassificationLayer(name)
% layer = sseClassificationLayer(name) creates a sum of squares
% error classification layer and specifies the layer name.

% Set layer name.
layer.Name = name;

% Set layer description.
layer.Description = 'Sum of squares error';
end

### Create Forward Loss Function

Create a function named forwardLoss that returns the SSE loss between the predictions made by the network and the training targets. The syntax for forwardLoss is loss = forwardLoss(layer, Y, T), where Y is the output of the previous layer and T represents the training targets.

For classification problems, the dimensions of T depend on the type of problem.

2-D image classification1-by-1-by-K-by-N, where K is the number of classes and N is the number of observations.4
3-D image classification1-by-1-by-1-by-K-by-N, where K is the number of classes and N is the number of observations.5
Sequence-to-label classificationK-by-N, where K is the number of classes and N is the number of observations.2
Sequence-to-sequence classificationK-by-N-by-S, where K is the number of classes, N is the number of observations, and S is the sequence length.2

The size of Y depends on the output of the previous layer. To ensure that Y is the same size as T, you must include a layer that outputs the correct size before the output layer. For example, to ensure that Y is a 4-D array of prediction scores for K classes, you can include a fully connected layer of size K followed by a softmax layer before the output layer.

A classification SSE layer computes the sum of squares error loss for classification problems. SSE is an error measure between two continuous random variables. For predictions Y and training targets T, the SSE loss between Y and T is given by

$L=\frac{1}{N}\sum _{n=1}^{N}\text{​}\sum _{i=1}^{K}\text{​}{\left({Y}_{ni}-{T}_{ni}\right)}^{2},$

where N is the number of observations and K is the number of classes.

The inputs Y and T correspond to Y and T in the equation, respectively. The output loss corresponds to L. Add a comment to the top of the function that explains the syntaxes of the function.

function loss = forwardLoss(layer, Y, T)
% loss = forwardLoss(layer, Y, T) returns the SSE loss between
% the predictions Y and the training targets T.

% Calculate sum of squares.
sumSquares = sum((Y-T).^2);

% Take mean over mini-batch.
N = size(Y,4);
loss = sum(sumSquares)/N;
end

Because the forwardLoss function only uses functions that support dlarray objects, defining the backwardLoss function is optional. For a list of functions that support dlarray objects, see List of Functions with dlarray Support.

### Completed Layer

View the completed classification output layer class file.

classdef sseClassificationLayer < nnet.layer.ClassificationLayer
% Example custom classification layer with sum of squares error loss.

methods
function layer = sseClassificationLayer(name)
% layer = sseClassificationLayer(name) creates a sum of squares
% error classification layer and specifies the layer name.

% Set layer name.
layer.Name = name;

% Set layer description.
layer.Description = 'Sum of squares error';
end

function loss = forwardLoss(layer, Y, T)
% loss = forwardLoss(layer, Y, T) returns the SSE loss between
% the predictions Y and the training targets T.

% Calculate sum of squares.
sumSquares = sum((Y-T).^2);

% Take mean over mini-batch.
N = size(Y,4);
loss = sum(sumSquares)/N;
end
end
end

### GPU Compatibility

If the layer forward functions fully support dlarray objects, then the layer is GPU compatible. Otherwise, to be GPU compatible, the layer functions must support inputs and return outputs of type gpuArray.

Many MATLAB built-in functions support gpuArray and dlarray input arguments. For a list of functions that support dlarray objects, see List of Functions with dlarray Support. For a list of functions that execute on a GPU, see Run MATLAB Functions on a GPU (Parallel Computing Toolbox). To use a GPU for deep learning, you must also have a CUDA® enabled NVIDIA® GPU with compute capability 3.0 or higher. For more information on working with GPUs in MATLAB, see GPU Computing in MATLAB (Parallel Computing Toolbox).

The MATLAB functions used in forwardLoss all support dlarray objects, so the layer is GPU compatible.

### Check Output Layer Validity

Check the layer validity of the custom classification output layer sseClassificationLayer.

Define a custom sum-of-squares error classification layer. To create this layer, save the file sseClassificationLayer.m in the current folder. Create an instance of the layer.

layer = sseClassificationLayer('sse');

Check the layer is valid using checkLayer. Specify the valid input size to be the size of a single observation of typical input to the layer. The layer expects a 1-by-1-by-K-by-N array inputs, where K is the number of classes, and N is the number of observations in the mini-batch.

validInputSize = [1 1 10];
checkLayer(layer,validInputSize,'ObservationDimension',4);
Skipping GPU tests. No compatible GPU device found.

Running nnet.checklayer.TestOutputLayerWithoutBackward
........
Done nnet.checklayer.TestOutputLayerWithoutBackward
__________

Test Summary:
8 Passed, 0 Failed, 0 Incomplete, 2 Skipped.
Time elapsed: 0.23691 seconds.

The test summary reports the number of passed, failed, incomplete, and skipped tests.

### Include Custom Classification Output Layer in Network

You can use a custom output layer in the same way as any other output layer in Deep Learning Toolbox. This section shows how to create and train a network for classification using the custom classification output layer that you created earlier.

[XTrain,YTrain] = digitTrain4DArrayData;

Define a custom sum-of-squares error classification layer. To create this layer, save the file sseClassificationLayer.m in the current folder. Create an instance of the layer. Create a layer array including the custom classification output layer sseClassificationLayer.

layers = [
imageInputLayer([28 28 1])
convolution2dLayer(5,20)
batchNormalizationLayer
reluLayer
fullyConnectedLayer(10)
softmaxLayer
sseClassificationLayer('sse')]
layers =
7x1 Layer array with layers:

1   ''      Image Input             28x28x1 images with 'zerocenter' normalization
2   ''      Convolution             20 5x5 convolutions with stride [1  1] and padding [0  0  0  0]
3   ''      Batch Normalization     Batch normalization
4   ''      ReLU                    ReLU
5   ''      Fully Connected         10 fully connected layer
6   ''      Softmax                 softmax
7   'sse'   Classification Output   Sum of squares error

Set the training options and train the network.

options = trainingOptions('sgdm');
net = trainNetwork(XTrain,YTrain,layers,options);
Training on single CPU.
Initializing input data normalization.
|========================================================================================|
|  Epoch  |  Iteration  |  Time Elapsed  |  Mini-batch  |  Mini-batch  |  Base Learning  |
|         |             |   (hh:mm:ss)   |   Accuracy   |     Loss     |      Rate       |
|========================================================================================|
|       1 |           1 |       00:00:01 |        9.38% |       0.9944 |          0.0100 |
|       2 |          50 |       00:00:07 |       75.00% |       0.3561 |          0.0100 |
|       3 |         100 |       00:00:11 |       92.97% |       0.1316 |          0.0100 |
|       4 |         150 |       00:00:16 |       96.88% |       0.0915 |          0.0100 |
|       6 |         200 |       00:00:21 |       95.31% |       0.0738 |          0.0100 |
|       7 |         250 |       00:00:26 |       96.88% |       0.0485 |          0.0100 |
|       8 |         300 |       00:00:32 |       99.22% |       0.0203 |          0.0100 |
|       9 |         350 |       00:00:37 |       99.22% |       0.0264 |          0.0100 |
|      11 |         400 |       00:00:41 |      100.00% |       0.0069 |          0.0100 |
|      12 |         450 |       00:00:45 |      100.00% |       0.0045 |          0.0100 |
|      13 |         500 |       00:00:50 |      100.00% |       0.0078 |          0.0100 |
|      15 |         550 |       00:00:55 |      100.00% |       0.0059 |          0.0100 |
|      16 |         600 |       00:01:00 |      100.00% |       0.0021 |          0.0100 |
|      17 |         650 |       00:01:04 |      100.00% |       0.0040 |          0.0100 |
|      18 |         700 |       00:01:10 |      100.00% |       0.0024 |          0.0100 |
|      20 |         750 |       00:01:16 |      100.00% |       0.0028 |          0.0100 |
|      21 |         800 |       00:01:20 |      100.00% |       0.0020 |          0.0100 |
|      22 |         850 |       00:01:25 |      100.00% |       0.0017 |          0.0100 |
|      24 |         900 |       00:01:30 |      100.00% |       0.0020 |          0.0100 |
|      25 |         950 |       00:01:35 |      100.00% |       0.0013 |          0.0100 |
|      26 |        1000 |       00:01:40 |      100.00% |       0.0012 |          0.0100 |
|      27 |        1050 |       00:01:45 |       99.22% |       0.0104 |          0.0100 |
|      29 |        1100 |       00:01:53 |      100.00% |       0.0013 |          0.0100 |
|      30 |        1150 |       00:01:59 |      100.00% |       0.0012 |          0.0100 |
|      30 |        1170 |       00:02:02 |       99.22% |       0.0077 |          0.0100 |
|========================================================================================|

Evaluate the network performance by making predictions on new data and calculating the accuracy.

[XTest,YTest] = digitTest4DArrayData;
YPred = classify(net, XTest);
accuracy = mean(YTest == YPred)
accuracy = 0.9844