## Specify Custom Output Layer Backward Loss Function

If Deep Learning Toolbox™ does not provide the layer you require for your classification or regression problem, then you can define your own custom layer. For a list of built-in layers, see List of Deep Learning Layers.

The example Define Custom Classification Output Layer shows how to define and create a custom classification output layer with sum of squares error (SSE) loss and goes 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.

Creating a backward loss function is optional. If the forward loss function only uses functions that support dlarray objects, then software determines the derivatives automatically using automatic differentiation. For a list of functions that support dlarray objects, see List of Functions with dlarray Support. If you want to use functions that do not support dlarray objects, or want to use a specific algorithm for the backward loss function, then you can define a custom backward function using this example as a guide.

### Create Custom Layer

The example Define Custom Classification Output Layer shows how to create a SSE classification 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.

View the layer created in the example Define Custom Classification Output Layer. This layer does not have a backwardLoss function.

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

### Create Backward Loss Function

Implement the backwardLoss function that returns the derivatives of the loss with respect to the input data and the learnable parameters.

The syntax for backwardLoss is dLdY = backwardLoss(layer, Y, T). The input Y contains the predictions made by the network and T contains the training targets. The output dLdY is the derivative of the loss with respect to the predictions Y. The output dLdY must be the same size as the layer input Y.

The dimensions of Y and T are the same as the inputs in forwardLoss.

The derivative of the SSE loss with respect to the predictions Y is given by

$\frac{\delta L}{\delta {Y}_{i}}=\frac{2}{N}\left({Y}_{i}-{T}_{i}\right),$

where N is the number of observations in the input.

Create the backward loss function that returns these derivatives.

function dLdY = backwardLoss(layer, Y, T)
% dLdY = backwardLoss(layer, Y, T) returns the derivatives of
% the SSE loss with respect to the predictions Y.

N = size(Y,4);
dLdY = 2*(Y-T)/N;
end

### Complete Layer

View the completed 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

function dLdY = backwardLoss(layer, Y, T)
% dLdY = backwardLoss(layer, Y, T) returns the derivatives of
% the SSE loss with respect to the predictions Y.

N = size(Y,4);
dLdY = 2*(Y-T)/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 (Parallel Computing Toolbox).

Many MATLAB built-in functions support gpuArray (Parallel Computing Toolbox) 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 supported GPU device. For information on supported devices, see GPU Support by Release (Parallel Computing Toolbox). For more information on working with GPUs in MATLAB, see GPU Computing in MATLAB (Parallel Computing Toolbox).