## Define Custom Deep Learning Intermediate Layers

Tip

This topic explains how to define custom deep learning layers for your problems. For a list of built-in layers in Deep Learning Toolbox™, see List of Deep Learning Layers.

To learn how to define custom output layers, see Define Custom Deep Learning Output Layers.

If Deep Learning Toolbox does not provide the layer that you require for your task, then you can define your own custom layer using this topic as a guide. After defining the custom layer, you can automatically check that the layer is valid and GPU compatible, and outputs correctly defined gradients.

### Intermediate Layer Architecture

When you train a network, the software iteratively performs forward and backward passes through the network.

During a forward pass through the network, each layer takes the outputs of the previous layers, applies a function, and then outputs (forward propagates) the results to the next layers. Stateful layers, such as LSTM layers, also update the layer state.

Layers can have multiple inputs or outputs. For example, a layer can take X1, …, XN from multiple previous layers and forward propagate the outputs Z1, …, ZM to subsequent layers.

At the end of a forward pass of the network, the output layer calculates the loss L between the predictions Y and the targets T.

During the backward pass through the network, each layer takes the derivatives of the loss with respect to the outputs of the layer, computes the derivatives of the loss L with respect to the inputs, and then backward propagates the results. If the layer has learnable parameters, then the layer also computes the derivatives of the layer weights (learnable parameters). The layer uses the derivatives of the weights to update the learnable parameters.

The following figure describes the flow of data through a deep neural network and highlights the data flow through a layer with a single input X, a single output Z, and a learnable parameter W.

### Intermediate Layer Template

To define a custom intermediate layer, use this class definition template. This template gives the structure of an intermediate layer class definition. It outlines:

• The optional `properties` blocks for the layer properties, learnable parameters, and state parameters. For more information, see Intermediate Layer Properties.

• The layer constructor function.

• The `predict` function and the optional `forward` function. For more information, see Forward Functions.

• The optional `resetState` function for layers with state properties. For more information, see Reset State Function.

• The optional `backward` function. For more information, see Backward Function.

```classdef myLayer < nnet.layer.Layer % ... % & nnet.layer.Formattable ... % (Optional) % & nnet.layer.Acceleratable % (Optional) properties % (Optional) Layer properties. % Declare layer properties here. end properties (Learnable) % (Optional) Layer learnable parameters. % Declare learnable parameters here. end properties (State) % (Optional) Layer state parameters. % Declare state parameters here. end properties (Learnable, State) % (Optional) Nested dlnetwork objects with both learnable % parameters and state parameters. % Declare nested networks with learnable and state parameters here. end methods function layer = myLayer() % (Optional) Create a myLayer. % This function must have the same name as the class. % Define layer constructor function here. end function layer = initialize(layer,layout) % (Optional) Initialize layer learnable and state parameters. % % Inputs: % layer - Layer to initialize % layout - Data layout, specified as a networkDataLayout % object % % Outputs: % layer - Initialized layer % % - For layers with multiple inputs, replace layout with % layout1,...,layoutN, where N is the number of inputs. % Define layer initialization function here. end function [Z,state] = predict(layer,X) % Forward input data through the layer at prediction time and % output the result and updated state. % % Inputs: % layer - Layer to forward propagate through % X - Input data % Outputs: % Z - Output of layer forward function % state - (Optional) Updated layer state % % - For layers with multiple inputs, replace X with X1,...,XN, % where N is the number of inputs. % - For layers with multiple outputs, replace Z with % Z1,...,ZM, where M is the number of outputs. % - For layers with multiple state parameters, replace state % with state1,...,stateK, where K is the number of state % parameters. % Define layer predict function here. end function [Z,state,memory] = forward(layer,X) % (Optional) Forward input data through the layer at training % time and output the result, the updated state, and a memory % value. % % Inputs: % layer - Layer to forward propagate through % X - Layer input data % Outputs: % Z - Output of layer forward function % state - (Optional) Updated layer state % memory - (Optional) Memory value for custom backward % function % % - For layers with multiple inputs, replace X with X1,...,XN, % where N is the number of inputs. % - For layers with multiple outputs, replace Z with % Z1,...,ZM, where M is the number of outputs. % - For layers with multiple state parameters, replace state % with state1,...,stateK, where K is the number of state % parameters. % Define layer forward function here. end function layer = resetState(layer) % (Optional) Reset layer state. % Define reset state function here. end function [dLdX,dLdW,dLdSin] = backward(layer,X,Z,dLdZ,dLdSout,memory) % (Optional) Backward propagate the derivative of the loss % function through the layer. % % Inputs: % layer - Layer to backward propagate through % X - Layer input data % Z - Layer output data % dLdZ - Derivative of loss with respect to layer % output % dLdSout - (Optional) Derivative of loss with respect % to state output % memory - Memory value from forward function % Outputs: % dLdX - Derivative of loss with respect to layer input % dLdW - (Optional) Derivative of loss with respect to % learnable parameter % dLdSin - (Optional) Derivative of loss with respect to % state input % % - For layers with state parameters, the backward syntax must % include both dLdSout and dLdSin, or neither. % - For layers with multiple inputs, replace X and dLdX with % X1,...,XN and dLdX1,...,dLdXN, respectively, where N is % the number of inputs. % - For layers with multiple outputs, replace Z and dlZ with % Z1,...,ZM and dLdZ,...,dLdZM, respectively, where M is the % number of outputs. % - For layers with multiple learnable parameters, replace % dLdW with dLdW1,...,dLdWP, where P is the number of % learnable parameters. % - For layers with multiple state parameters, replace dLdSin % and dLdSout with dLdSin1,...,dLdSinK and % dLdSout1,...,dldSoutK, respectively, where K is the number % of state parameters. % Define layer backward function here. end end end```

### Formatted Inputs and Outputs

Using `dlarray` objects makes working with high dimensional data easier by allowing you to label the dimensions. For example, you can label which dimensions correspond to spatial, time, channel, and batch dimensions using the `"S"`, `"T"`, `"C"`, and `"B"` labels, respectively. For unspecified and other dimensions, use the `"U"` label. For `dlarray` object functions that operate over particular dimensions, you can specify the dimension labels by formatting the `dlarray` object directly, or by using the `DataFormat` option.

Using formatted `dlarray` objects in custom layers also allows you to define layers where the inputs and outputs have different formats, such as layers that permute, add, or remove dimensions. For example, you can define a layer that takes as input a mini-batch of images with the format `"SSCB"` (spatial, spatial, channel, batch) and output a mini-batch of sequences with the format `"CBT"` (channel, batch, time). Using formatted `dlarray` objects also allows you to define layers that can operate on data with different input formats, for example, layers that support inputs with the formats `"SSCB"` (spatial, spatial, channel, batch) and `"CBT"` (channel, batch, time).

If you do not specify a backward function, then the layer functions, by default, receive unformatted `dlarray` objects as input. To specify that the layer receives formatted `dlarray` objects as input and also outputs formatted `dlarray` objects, also inherit from the `nnet.layer.Formattable` class when defining the custom layer.

For an example showing how to define a custom layer with formatted inputs, see Define Custom Deep Learning Layer with Formatted Inputs.

### Custom Layer Acceleration

If you do not specify a backward function when you define a custom layer, then the software automatically determines the gradients using automatic differentiation.

When you train a network with a custom layer without a backward function, the software traces each input `dlarray` object of the custom layer forward function to determine the computation graph used for automatic differentiation. This tracing process can take some time and can end up recomputing the same trace. By optimizing, caching, and reusing the traces, you can speed up gradient computation when training a network. The software can also reuse these traces to speed up network predictions after training.

The trace depends on the size, format, and underlying data type of the layer inputs. That is, the layer triggers a new trace for inputs with a size, format, or underlying data type not contained in the cache. Any inputs differing only by value to a previously cached trace do not trigger a new trace.

To indicate that the custom layer supports acceleration, also inherit from the `nnet.layer.Acceleratable` class when defining the custom layer. When a custom layer inherits from `nnet.layer.Acceleratable`, the software automatically caches traces when passing data through a `dlnetwork` object.

For example, to indicate that the custom layer `myLayer` supports acceleration, use this syntax

```classdef myLayer < nnet.layer.Layer & nnet.layer.Acceleratable ... end```

#### Acceleration Considerations

Because of the nature of caching traces, not all functions support acceleration.

The caching process can cache values or code structures that you might expect to change or that depend on external factors. You must take care when accelerating custom layers that:

• Generate random numbers.

• Use `if` statements and `while` loops with conditions that depend on the values of `dlarray` objects.

Because the caching process requires extra computation, acceleration can lead to longer running code in some cases. This scenario can happen when the software spends time creating new caches that do not get reused often. For example, when you pass multiple mini-batches of different sequence lengths to the function, the software triggers a new trace for each unique sequence length.

When custom layer acceleration causes slowdown, you can disable acceleration by removing the `Acceleratable` mixin or by disabling acceleration of the `dlnetwork` object functions `predict` and `forward` by setting the `Acceleration` option to `"none"`.

### Intermediate Layer Properties

Declare the layer properties in the `properties` section of the class definition.

By default, custom intermediate layers have these properties. Do not declare these properties in the `properties` section.

PropertyDescription
`Name`Layer name, specified as a character vector or a string scalar. For `Layer` array input, the `trainNetwork`, `assembleNetwork`, `layerGraph`, and `dlnetwork` functions automatically assign names to layers with the name `''`.
`Description`

One-line description of the layer, specified as a string scalar or a character vector. This description appears when the layer is displayed in a `Layer` array.

If you do not specify a layer description, then the software displays the layer class name.

`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.

`NumInputs`Number of inputs of the layer, specified as a positive integer. If you do not specify this value, then the software automatically sets `NumInputs` to the number of names in `InputNames`. The default value is 1.
`InputNames`Input names of the layer, specified as a cell array of character vectors. If you do not specify this value and `NumInputs` is greater than 1, then the software automatically sets `InputNames` to `{'in1',...,'inN'}`, where `N` is equal to `NumInputs`. The default value is `{'in'}`.
`NumOutputs`Number of outputs of the layer, specified as a positive integer. If you do not specify this value, then the software automatically sets `NumOutputs` to the number of names in `OutputNames`. The default value is 1.
`OutputNames`Output names of the layer, specified as a cell array of character vectors. If you do not specify this value and `NumOutputs` is greater than 1, then the software automatically sets `OutputNames` to `{'out1',...,'outM'}`, where `M` is equal to `NumOutputs`. The default value is `{'out'}`.

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

Tip

If you are creating a layer with multiple inputs, then you must set either the `NumInputs` or `InputNames` properties in the layer constructor. If you are creating a layer with multiple outputs, then you must set either the `NumOutputs` or `OutputNames` properties in the layer constructor. For an example, see Define Custom Deep Learning Layer with Multiple Inputs.

#### Learnable Parameters

Declare the layer learnable parameters in the ```properties (Learnable)``` section of the class definition.

You can specify numeric arrays or `dlnetwork` objects as learnable parameters. If the `dlnetwork` object has both learnable and state parameters (for example, a `dlnetwork` object that contains an LSTM layer), then you must specify it in the ```properties (Learnable, State)``` section. If the layer has no learnable parameters, then you can omit the `properties` sections with the `Learnable` attribute.

Optionally, you can specify the learning rate factor and the L2 factor of the learnable parameters. By default, each learnable parameter has its learning rate factor and L2 factor set to `1`. For both built-in and custom layers, you can set and get the learning rate factors and L2 regularization factors using the following functions.

FunctionDescription
`setLearnRateFactor`Set the learning rate factor of a learnable parameter.
`setL2Factor`Set the L2 regularization factor of a learnable parameter.
`getLearnRateFactor`Get the learning rate factor of a learnable parameter.
`getL2Factor`Get the L2 regularization factor of a learnable parameter.

To specify the learning rate factor and the L2 factor of a learnable parameter, use the syntaxes ```layer = setLearnRateFactor(layer,parameterName,value)``` and ```layer = setL2Factor(layer,parameterName,value)```, respectively.

To get the value of the learning rate factor and the L2 factor of a learnable parameter, use the syntaxes `getLearnRateFactor(layer,parameterName)` and `getL2Factor(layer,parameterName)`, respectively.

For example, this syntax sets the learning rate factor of the learnable parameter `"Alpha"` to `0.1`.

`layer = setLearnRateFactor(layer,"Alpha",0.1);`

#### State Parameters

For stateful layers, such as recurrent layers, declare the layer state parameters in the `properties (State)` section of the class definition. If the learnable parameter is a `dlnetwork` object that has both learnable and state parameters (for example, a `dlnetwork` object that contains an LSTM layer), then you must specify the corresponding property in the `properties (Learnable, State)` section. If the layer has no state parameters, then you can omit the `properties` sections with the `State` attribute.

If the layer has state parameters, then the forward functions must also return the updated layer state. For more information, see Forward Functions.

To specify a custom reset state function, include a function with syntax `layer = resetState(layer)` in the class definition. For more information, see Reset State Function.

Parallel training of networks containing custom layers with state parameters using the `trainNetwork` function is not supported. When you train a network with custom layers with state parameters, the `ExecutionEnvironment` training option must be `"auto"`, `"gpu"`, or `"cpu"`.

#### Learnable and State Parameter Initialization

You can specify to initialize the layer learnable parameters and states in the layer constructor function or in a custom `initialize` function:

• If the learnable or state parameter initialization does not require size information from the layer input, for example, the learnable weights of a weighted addition layer is a vector with size matching the number of layer inputs, then you can initialize the weights in the layer constructor function. For an example, see Define Custom Deep Learning Layer with Multiple Inputs.

• If the learnable or state parameter initialization requires size information from the layer input, for example, the learnable weights of a PReLU layer is a vector with size matching the number of channels of the input data, then you can initialize the weights in a custom initialize function that utilizes the information about the input data layout. For an example, see Define Custom Deep Learning Layer with Learnable Parameters.

### Forward Functions

Some layers behave differently during training and during prediction. For example, a dropout layer performs dropout only during training and has no effect during prediction. A layer uses one of two functions to perform a forward pass: `predict` or `forward`. If the forward pass is at prediction time, then the layer uses the `predict` function. If the forward pass is at training time, then the layer uses the `forward` function. If you do not require two different functions for prediction time and training time, then you can omit the `forward` function. When you do so, the layer uses `predict` at training time.

If the layer has state parameters, then the forward functions must also return the updated layer state parameters as numeric arrays.

If you define both a custom `forward` function and a custom `backward` function, then the forward function must return a `memory` output.

The `predict` function syntax depends on the type of layer.

• `Z = predict(layer,X)` forwards the input data `X` through the layer and outputs the result `Z`, where `layer` has a single input and a single output.

• `[Z,state] = predict(layer,X)` also outputs the updated state parameter `state`, where `layer` has a single state parameter.

You can adjust the syntaxes for layers with multiple inputs, multiple outputs, or multiple state parameters:

• For layers with multiple inputs, replace `X` with `X1,...,XN`, where `N` is the number of inputs. The `NumInputs` property must match `N`.

• For layers with multiple outputs, replace `Z` with `Z1,...,ZM`, where `M` is the number of outputs. The `NumOutputs` property must match `M`.

• For layers with multiple state parameters, replace `state` with `state1,...,stateK`, where `K` is the number of state parameters.

Tip

If the number of inputs to the layer can vary, then use `varargin` instead of `X1,…,XN`. In this case, `varargin` is a cell array of the inputs, where `varargin{i}` corresponds to `Xi`.

If the number of outputs can vary, then use `varargout` instead of `Z1,…,ZN`. In this case, `varargout` is a cell array of the outputs, where `varargout{j}` corresponds to `Zj`.

Tip

If the custom layer has a `dlnetwork` object for a learnable parameter, then in the `predict` function of the custom layer, use the `predict` function for the `dlnetwork`. When you do so, the `dlnetwork` object `predict` function uses the appropriate layer operations for prediction. If the `dlnetwork` has state parameters, then also return the network state.

The `forward` function syntax depends on the type of layer:

• `Z = forward(layer,X)` forwards the input data `X` through the layer and outputs the result `Z`, where `layer` has a single input and a single output.

• `[Z,state] = forward(layer,X)` also outputs the updated state parameter `state`, where `layer` has a single state parameter.

• `[__,memory] = forward(layer,X)` also returns a memory value for a custom `backward` function using any of the previous syntaxes. If the layer has both a custom `forward` function and a custom `backward` function, then the forward function must return a memory value.

You can adjust the syntaxes for layers with multiple inputs, multiple outputs, or multiple state parameters:

• For layers with multiple inputs, replace `X` with `X1,...,XN`, where `N` is the number of inputs. The `NumInputs` property must match `N`.

• For layers with multiple outputs, replace `Z` with `Z1,...,ZM`, where `M` is the number of outputs. The `NumOutputs` property must match `M`.

• For layers with multiple state parameters, replace `state` with `state1,...,stateK`, where `K` is the number of state parameters.

Tip

If the number of inputs to the layer can vary, then use `varargin` instead of `X1,…,XN`. In this case, `varargin` is a cell array of the inputs, where `varargin{i}` corresponds to `Xi`.

If the number of outputs can vary, then use `varargout` instead of `Z1,…,ZN`. In this case, `varargout` is a cell array of the outputs, where `varargout{j}` corresponds to `Zj`.

Tip

If the custom layer has a `dlnetwork` object for a learnable parameter, then in the `forward` function of the custom layer, use the `forward` function of the `dlnetwork` object. When you do so, the `dlnetwork` object `forward` function uses the appropriate layer operations for training.

The dimensions of the inputs depend on the type of data and the output of the connected layers.

Layer InputInput SizeObservation Dimension
Feature vectorsc-by-N, where c corresponds to the number of channels and N is the number of observations2
2-D imagesh-by-w-by-c-by-N, where h, w, and c correspond to the height, width, and number of channels of the images, respectively, and N is the number of observations4
3-D imagesh-by-w-by-d-by-c-by-N, where h, w, d, and c correspond to the height, width, depth, and number of channels of the 3-D images, respectively, and N is the number of observations5
Vector sequencesc-by-N-by-S, where c is the number of features of the sequences, N is the number of observations, and S is the sequence length2
2-D image sequencesh-by-w-by-c-by-N-by-S, where h, w, and c correspond to the height, width, and number of channels of the images, respectively, N is the number of observations, and S is the sequence length4
3-D image sequencesh-by-w-by-d-by-c-by-N-by-S, where h, w, d, and c correspond to the height, width, depth, and number of channels of the 3-D images, respectively, N is the number of observations, and S is the sequence length5

For layers that output sequences, the layers can output sequences of any length or output data with no time dimension. Note that when you train a network that outputs sequences using the `trainNetwork` function, the lengths of the input and output sequences must match.

The outputs of the custom layer forward functions must not be complex. If the `predict` or `forward` functions of your custom layer involve complex numbers, convert all outputs to real values before returning them. Using complex numbers in the `predict` or `forward` functions of your custom layer can lead to complex learnable parameters. If you are using automatic differentiation (in other words, you are not writing a backward function for your custom layer) then convert all learnable parameters to real values at the beginning of the function computation. Doing so ensures that the outputs of automatically generated backward functions are not complex.

### Reset State Function

When `DAGNetwork` or `SeriesNetwork` objects contain layers with state parameters, you can make predictions and update the layer states using the `predictAndUpdateState` and `classifyAndUpdateState` functions. You can reset the network state using the `resetState` function.

The `resetState` function for `DAGNetwork`, `SeriesNetwork`, and `dlnetwork` objects, by default, has no effect on custom layers with state parameters. To define the layer behavior for the `resetState` function for network objects, define the optional layer `resetState` function in the layer definition that resets the state parameters.

The `resetState` function must have the syntax ```layer = resetState(layer)```, where the returned layer has the reset state properties.

The `resetState` function must not set any layer properties except for learnable and state properties. If the function sets other layers properties, then the layer can behave unexpectedly. (since R2023a)

### Backward Function

The layer backward function computes the derivatives of the loss with respect to the input data and then outputs (backward propagates) results to the previous layer. If the layer has learnable parameters (for example, layer weights), then `backward` also computes the derivatives of the learnable parameters. When you use the `trainNetwork` function, the layer automatically updates the learnable parameters using these derivatives during the backward pass.

Defining the backward function is optional. If you do not specify a backward function, and the layer forward functions support `dlarray` objects, then the software automatically determines the backward function using automatic differentiation. For a list of functions that support `dlarray` objects, see List of Functions with dlarray Support. Define a custom backward function when you want to:

• Use a specific algorithm to compute the derivatives.

• Use operations in the forward functions that do not support `dlarray` objects.

Custom layers with learnable `dlnetwork` objects do not support custom backward functions.

To define a custom backward function, create a function named `backward`.

The `backward` function syntax depends on the type of layer.

• `dLdX = backward(layer,X,Z,dLdZ,memory)` returns the derivatives `dLdX` of the loss with respect to the layer input, where `layer` has a single input and a single output. `Z` corresponds to the forward function output and `dLdZ` corresponds to the derivative of the loss with respect to `Z`. The function input `memory` corresponds to the memory output of the forward function.

• `[dLdX,dLdW] = backward(layer,X,Z,dLdZ,memory)` also returns the derivative `dLdW` of the loss with respect to the learnable parameter, where `layer` has a single learnable parameter.

• `[dLdX,dLdSin] = backward(layer,X,Z,dLdZ,dLdSout,memory)` also returns the derivative `dLdSin` of the loss with respect to the state input, where `layer` has a single state parameter and `dLdSout` corresponds to the derivative of the loss with respect to the layer state output.

• `[dLdX,dLdW,dLdSin] = backward(layer,X,Z,dLdZ,dLdSout,memory)` also returns the derivative `dLdW` of the loss with respect to the learnable parameter and returns the derivative `dLdSin` of the loss with respect to the layer state input, where `layer` has a single state parameter and single learnable parameter.

You can adjust the syntaxes for layers with multiple inputs, multiple outputs, multiple learnable parameters, or multiple state parameters:

• For layers with multiple inputs, replace `X` and `dLdX` with `X1,...,XN` and `dLdX1,...,dLdXN`, respectively, where `N` is the number of inputs.

• For layers with multiple outputs, replace `Z` and `dLdZ` with `Z1,...,ZM` and `dLdZ1,...,dLdZM`, respectively, where `M` is the number of outputs.

• For layers with multiple learnable parameters, replace `dLdW` with `dLdW1,...,dLdWP`, where `P` is the number of learnable parameters.

• For layers with multiple state parameters, replace `dLdSin` and `dLdSout` with `dLdSin1,...,dLdSinK` and `dLdSout1,...,dLdSoutK`, respectively, where `K` is the number of state parameters.

To reduce memory usage by preventing unused variables being saved between the forward and backward pass, replace the corresponding input arguments with `~`.

Tip

If the number of inputs to `backward` can vary, then use `varargin` instead of the input arguments after `layer`. In this case, `varargin` is a cell array of the inputs, where the first `N` elements correspond to the `N` layer inputs, the next `M` elements correspond to the `M` layer outputs, the next `M` elements correspond to the derivatives of the loss with respect to the `M` layer outputs, the next `K` elements correspond to the `K` derivatives of the loss with respect to the `K` state outputs, and the last element corresponds to `memory`.

If the number of outputs can vary, then use `varargout` instead of the output arguments. In this case, `varargout` is a cell array of the outputs, where the first `N` elements correspond to the `N` the derivatives of the loss with respect to the `N` layer inputs, the next `P` elements correspond to the derivatives of the loss with respect to the `P` learnable parameters, and the next `K` elements correspond to the derivatives of the loss with respect to the `K` state inputs.

The values of `X` and `Z` are the same as in the forward functions. The dimensions of `dLdZ` are the same as the dimensions of `Z`.

The dimensions and data type of `dLdX` are the same as the dimensions and data type of `X`. The dimensions and data types of `dLdW` are the same as the dimensions and data types of `W`.

To calculate the derivatives of the loss, you can use the chain rule:

`$\frac{\partial L}{\partial {X}^{\left(i\right)}}=\sum _{j}\frac{\partial L}{\partial {Z}_{j}}\frac{\partial {Z}_{j}}{\partial {X}^{\left(i\right)}}$`

`$\frac{\partial L}{\partial {W}_{i}}=\sum _{j}\frac{\partial L}{\partial {Z}_{j}}\frac{\partial {Z}_{j}}{\partial {W}_{i}}$`

When you use the `trainNetwork` function, the layer automatically updates the learnable parameters using the derivatives `dLdW` during the backward pass.

For an example showing how to define a custom backward function, see Specify Custom Layer Backward Function.

The outputs of the custom layer backward function must not be complex. If your backward function involves complex numbers, then convert all outputs of the backward function to real values before returning them.

#### 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 Computing Requirements (Parallel Computing Toolbox). For more information on working with GPUs in MATLAB, see GPU Computing in MATLAB (Parallel Computing Toolbox).

#### Code Generation Compatibility

To create a custom layer that supports code generation:

• The layer must specify the pragma `%#codegen` in the layer definition.

• The inputs of `predict` must be:

• Consistent in dimension. Each input must have the same number of dimensions.

• Consistent in batch size. Each input must have the same batch size.

• The outputs of `predict` must be consistent in dimension and batch size with the layer inputs.

• Nonscalar properties must have type single, double, or character array.

• Scalar properties must have type numeric, logical, or string.

Code generation supports intermediate layers with 2-D image or feature input only. Code generation does not support layers with state properties (properties with attribute `State`).

For an example showing how to create a custom layer that supports code generation, see Define Custom Deep Learning Layer for Code Generation.

#### Network Composition

To create a custom layer that itself defines a layer graph, you can declare a `dlnetwork` object as a learnable parameter in the ```properties (Learnable)``` section of the layer definition. This method is known as network composition. You can use network composition to:

• Create a single custom layer that represents a block of learnable layers, for example, a residual block.

• Create a network with control flow, for example, a network with a section that can dynamically change depending on the input data.

• Create a network with loops, for example, a network with sections that feed the output back into itself.

For nested networks that have both learnable and state parameters, for example, networks with batch normalization or LSTM layers, declare the network in the ```properties (Learnable, State)``` section of the layer definition.

### 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 Computing Requirements (Parallel Computing Toolbox). For more information on working with GPUs in MATLAB, see GPU Computing in MATLAB (Parallel Computing Toolbox).

### Check Validity of Layer

If you create a custom deep learning layer, then you can use the `checkLayer` function to check that the layer is valid. The function checks layers for validity, GPU compatibility, correctly defined gradients, and code generation compatibility. To check that a layer is valid, run the following command:

`checkLayer(layer,validInputSize)`
`layer` is an instance of the layer and `validInputSize` is a vector or cell array specifying the valid input sizes to the layer. To check with multiple observations, use the `ObservationDimension` option. To run the check for code generation compatibility, set the `CheckCodegenCompatibility` option to `1` (true). For large input sizes, the gradient checks take longer to run. To speed up the check, specify a smaller valid input size.

#### Check Validity of Custom Layer Using `checkLayer`

Check the layer validity of the custom layer `preluLayer`.

The custom layer `preluLayer`, attached to this is example as a supporting file, applies the PReLU operation to the input data. To access this layer, open this example as a live script.

Create an instance of the layer.

`layer = preluLayer;`

Because the layer has a custom initialize function, initialize the layer using a `networkDataFormat` object that specifies the expected input size and format of a single observation of typical input to the layer.

Specify a valid input size of `[24 24 20]`, where the dimensions correspond to the height, width, and number of channels of the previous layer output.

```validInputSize = [24 24 20]; layout = networkDataLayout(validInputSize,"SSC"); layer = initialize(layer,layout);```

Check the layer validity using `checkLayer`. Specify the valid input size as the size as the size as used to initialize the layer. When you pass data through the network, the layer expects 4-D array inputs, where the first three dimensions correspond to the height, width, and number of channels of the previous layer output, and the fourth dimension corresponds to the observations.

Specify the typical size of the input of an observation and set the `ObservationDimension` option to 4.

`checkLayer(layer,validInputSize,ObservationDimension=4)`
```Skipping GPU tests. No compatible GPU device found. Skipping code generation compatibility tests. To check validity of the layer for code generation, specify the 'CheckCodegenCompatibility' and 'ObservationDimension' options. Running nnet.checklayer.TestLayerWithoutBackward .......... ........ Done nnet.checklayer.TestLayerWithoutBackward __________ Test Summary: 18 Passed, 0 Failed, 0 Incomplete, 10 Skipped. Time elapsed: 0.22352 seconds. ```

The function does not detect any issues with the layer.