forward

Compute deep learning network output for training

Syntax

[Y1,...,YN] = forward(net,X1,...,XM)

[Y1,...,YN,state] = forward(X1,...,XM)

[Y1,...,YN,state,pruningActivations] = forward(X1,...,XM)

___ = forward(___,Name=Value)

Description

Some deep learning layers behave differently during training and inference (prediction). For example, during training, dropout layers randomly set input elements to zero to help prevent overfitting, but during inference, dropout layers do not change the input.

To compute network outputs for training, use the forward function. To compute network outputs for inference, use the predict function.

[Y1,...,YN] = forward(net,X1,...,XM) returns the network outputs Y1, …, YN for training given the input data X1, …, XM and the neural network net.

[Y1,...,YN,state] = forward(X1,...,XM) also returns the updated network state.

[Y1,...,YN,state,pruningActivations] = forward(X1,...,XM) also returns a cell array of activations of the pruning layers. This syntax is applicable only if net is a TaylorPrunableNetwork object.

To prune a deep neural network, you require the Deep Learning Toolbox™ Model Compression Library support package. This support package is a free add-on that you can download using the Add-On Explorer. Alternatively, see Deep Learning Toolbox Model Compression Library.

___ = forward(___,Name=Value) specifies additional options using one or more name-value arguments.

Examples

Train Network Using Custom Training Loop

This example shows how to train a network that classifies handwritten digits with a custom learning rate schedule.

You can train most types of neural networks using the trainnet and trainingOptions functions. If the trainingOptions function does not provide the options you need (for example, a custom solver), then you can define your own custom training loop using dlarray and dlnetwork objects for automatic differentiation. For an example showing how to retrain a pretrained deep learning network using the trainnet function, see Retrain Neural Network to Classify New Images.

Training a deep neural network is an optimization task. By considering a neural network as a function $$f(X;\theta )$$, where $$X$$ is the network input, and $$\theta$$ is the set of learnable parameters, you can optimize $$\theta$$ so that it minimizes some loss value based on the training data. For example, optimize the learnable parameters $$\theta$$ such that for a given inputs $$X$$ with a corresponding targets $$T$$, they minimize the error between the predictions $$Y=f(X;\theta )$$ and $$T$$.

The loss function used depends on the type of task. For example:

• For classification tasks, you can minimize the cross entropy error between the predictions and targets.

• For regression tasks, you can minimize the mean squared error between the predictions and targets.

You can optimize the objective using gradient descent: minimize the loss $$L$$ by iteratively updating the learnable parameters $$\theta$$ by taking steps towards the minimum using the gradients of the loss with respect to the learnable parameters. Gradient descent algorithms typically update the learnable parameters by using a variant of an update step of the form $${\theta }_{t+1}={\theta }_t-\rho \nabla L$$, where $$t$$ is the iteration number, $$\rho$$ is the learning rate, and $$\nabla L$$ denotes the gradients (the derivatives of the loss with respect to the learnable parameters).

This example trains a network to classify handwritten digits with the stochastic gradient descent algorithm (without momentum).

Load Training Data

Load the digits data as an image datastore using the imageDatastore function and specify the folder containing the image data.

unzip("DigitsData.zip")

imds = imageDatastore("DigitsData", ...
    IncludeSubfolders=true, ...
    LabelSource="foldernames");

Partition the data into training and test sets. Set aside 10% of the data for testing using the splitEachLabel function.

[imdsTrain,imdsTest] = splitEachLabel(imds,0.9,"randomize");

The network used in this example requires input images of size 28-by-28-by-1. To automatically resize the training images, use an augmented image datastore. Specify additional augmentation operations to perform on the training images: randomly translate the images up to 5 pixels in the horizontal and vertical axes. Data augmentation helps prevent the network from overfitting and memorizing the exact details of the training images.

inputSize = [28 28 1];
pixelRange = [-5 5];

imageAugmenter = imageDataAugmenter( ...
    RandXTranslation=pixelRange, ...
    RandYTranslation=pixelRange);

augimdsTrain = augmentedImageDatastore(inputSize(1:2),imdsTrain,DataAugmentation=imageAugmenter);

To automatically resize the test images without performing further data augmentation, use an augmented image datastore without specifying any additional preprocessing operations.

augimdsTest = augmentedImageDatastore(inputSize(1:2),imdsTest);

Determine the number of classes in the training data.

classes = categories(imdsTrain.Labels);
numClasses = numel(classes);

Define Network

Define the network for image classification.

• For image input, specify an image input layer with input size matching the training data.

• Do not normalize the image input, set the Normalization option of the input layer to "none".

• Specify three convolution-batchnorm-ReLU blocks.

• Pad the input to the convolution layers such that the output has the same size by setting the Padding option to "same".

• For the first convolution layer specify 20 filters of size 5. For the remaining convolution layers specify 20 filters of size 3.

• For classification, specify a fully connected layer with size matching the number of classes

• To map the output to probabilities, include a softmax layer.

When training a network using a custom training loop, do not include an output layer.

layers = [
    imageInputLayer(inputSize,Normalization="none")
    convolution2dLayer(5,20,Padding="same")
    batchNormalizationLayer
    reluLayer
    convolution2dLayer(3,20,Padding="same")
    batchNormalizationLayer
    reluLayer
    convolution2dLayer(3,20,Padding="same")
    batchNormalizationLayer
    reluLayer
    fullyConnectedLayer(numClasses)
    softmaxLayer];

Create a dlnetwork object from the layer array.

net = dlnetwork(layers)

net = 
  dlnetwork with properties:

         Layers: [12×1 nnet.cnn.layer.Layer]
    Connections: [11×2 table]
     Learnables: [14×3 table]
          State: [6×3 table]
     InputNames: {'imageinput'}
    OutputNames: {'softmax'}
    Initialized: 1

  View summary with summary.

Define Model Loss Function

Training a deep neural network is an optimization task. By considering a neural network as a function $$f(X;\theta )$$, where $$X$$ is the network input, and $$\theta$$ is the set of learnable parameters, you can optimize $$\theta$$ so that it minimizes some loss value based on the training data. For example, optimize the learnable parameters $$\theta$$ such that for a given inputs $$X$$ with a corresponding targets $$T$$, they minimize the error between the predictions $$Y=f(X;\theta )$$ and $$T$$.

Define the modelLoss function. The modelLoss function takes a dlnetwork object net, a mini-batch of input data X with corresponding targets T and returns the loss, the gradients of the loss with respect to the learnable parameters in net, and the network state. To compute the gradients automatically, use the dlgradient function.

function [loss,gradients,state] = modelLoss(net,X,T)

% Forward data through network.
[Y,state] = forward(net,X);

% Calculate cross-entropy loss.
loss = crossentropy(Y,T);

% Calculate gradients of loss with respect to learnable parameters.
gradients = dlgradient(loss,net.Learnables);

end

Define SGD Function

Create the function sgdStep that takes the parameters and the gradients of the loss with respect to the parameters, and returns the updated parameters using the stochastic gradient descent algorithm, expressed as $${\theta }_{t+1}={\theta }_t-\rho \nabla L$$, where $$t$$ is the iteration number, $$\rho$$ is the learning rate, and $$\nabla L$$ denotes the gradients (the derivatives of the loss with respect to the learnable parameters).

function parameters = sgdStep(parameters,gradients,learnRate)

parameters = parameters - learnRate .* gradients;

end

Defining a custom update function is not a necessary step for custom training loops. Alternatively, you can use built in update functions like sgdmupdate, adamupdate, and rmspropupdate.

Specify Training Options

Train for fifteen epochs with a mini-batch size of 128 and a learning rate of 0.01.

numEpochs = 15;
miniBatchSize = 128;
learnRate = 0.01;

Train Model

Create a minibatchqueue object that processes and manages mini-batches of images during training. For each mini-batch:

• Use the custom mini-batch preprocessing function preprocessMiniBatch (defined at the end of this example) to convert the targets to one-hot encoded vectors.

• Format the image data with the dimension labels "SSCB" (spatial, spatial, channel, batch). By default, the minibatchqueue object converts the data to dlarray objects with underlying type single. Do not format the targets.

• Discard partial mini-batches.

• Train on a GPU if one is available. By default, the minibatchqueue object converts each output to a gpuArray if a GPU is available. Using a GPU requires Parallel Computing Toolbox™ and a supported GPU device. For information on supported devices, see GPU Computing Requirements (Parallel Computing Toolbox).

mbq = minibatchqueue(augimdsTrain,...
    MiniBatchSize=miniBatchSize,...
    MiniBatchFcn=@preprocessMiniBatch,...
    MiniBatchFormat=["SSCB" ""], ...
    PartialMiniBatch="discard");

Calculate the total number of iterations for the training progress monitor.

numObservationsTrain = numel(imdsTrain.Files);
numIterationsPerEpoch = floor(numObservationsTrain / miniBatchSize);
numIterations = numEpochs * numIterationsPerEpoch;

Initialize the TrainingProgressMonitor object. Because the timer starts when you create the monitor object, make sure that you create the object close to the training loop.

monitor = trainingProgressMonitor( ...
    Metrics="Loss", ...
    Info="Epoch", ...
    XLabel="Iteration");

Train the network using a custom training loop. For each epoch, shuffle the data and loop over mini-batches of data. For each mini-batch:

• Evaluate the model loss, gradients, and state using the dlfeval and modelLoss functions and update the network state.

• Update the network parameters using the dlupdate function with the custom update function.

• Update the loss and epoch values in the training progress monitor.

• Stop if the Stop property of the monitor is true. The Stop property value of the TrainingProgressMonitor object changes to true when you click the Stop button.

epoch = 0;
iteration = 0;

% Loop over epochs.
while epoch < numEpochs && ~monitor.Stop
    
    epoch = epoch + 1;

    % Shuffle data.
    shuffle(mbq);
    
    % Loop over mini-batches.
    while hasdata(mbq) && ~monitor.Stop

        iteration = iteration + 1;
        
        % Read mini-batch of data.
        [X,T] = next(mbq);
        
        % Evaluate the model gradients, state, and loss using dlfeval and the
        % modelLoss function and update the network state.
        [loss,gradients,state] = dlfeval(@modelLoss,net,X,T);
        net.State = state;
        
        % Update the network parameters using SGD.
        updateFcn = @(parameters,gradients) sgdStep(parameters,gradients,learnRate);
        net = dlupdate(updateFcn,net,gradients);
        
        % Update the training progress monitor.
        recordMetrics(monitor,iteration,Loss=loss);
        updateInfo(monitor,Epoch=epoch);
        monitor.Progress = 100 * iteration/numIterations;
    end
end

Test Model

Test the neural network using the testnet function. For single-label classification, evaluate the accuracy. The accuracy is the percentage of correct predictions. By default, the testnet function uses a GPU if one is available. To select the execution environment manually, use the ExecutionEnvironment argument of the testnet function.

accuracy = testnet(net,augimdsTest,"accuracy")

accuracy = 
96.3000

Visualize the predictions in a confusion chart. Make predictions using the minibatchpredict function, and convert the classification scores to labels using the scores2label function. By default, the minibatchpredict function uses a GPU if one is available. To select the execution environment manually, use the ExecutionEnvironment argument of the minibatchpredict function.

scores = minibatchpredict(net,augimdsTest);
YTest = scores2label(scores,classes);

Visualize the predictions in a confusion chart.

TTest = imdsTest.Labels;
figure
confusionchart(TTest,YTest)

Large values on the diagonal indicate accurate predictions for the corresponding class. Large values on the off-diagonal indicate strong confusion between the corresponding classes.

Supporting Functions

Mini Batch Preprocessing Function

The preprocessMiniBatch function preprocesses a mini-batch of predictors and labels using the following steps:

1. Preprocess the images using the preprocessMiniBatchPredictors function.

2. Extract the label data from the incoming cell array and concatenate into a categorical array along the second dimension.

3. One-hot encode the categorical labels into numeric arrays. Encoding into the first dimension produces an encoded array that matches the shape of the network output.

function [X,T] = preprocessMiniBatch(dataX,dataT)

% Preprocess predictors.
X = preprocessMiniBatchPredictors(dataX);

% Extract label data from cell and concatenate.
T = cat(2,dataT{:});

% One-hot encode labels.
T = onehotencode(T,1);

end

Mini-Batch Predictors Preprocessing Function

The preprocessMiniBatchPredictors function preprocesses a mini-batch of predictors by extracting the image data from the input cell array and concatenate into a numeric array. For grayscale input, concatenating over the fourth dimension adds a third dimension to each image, to use as a singleton channel dimension.

function X = preprocessMiniBatchPredictors(dataX)

% Concatenate.
X = cat(4,dataX{:});

end

Input Arguments

net — Neural network

dlnetwork object | TaylorPrunableNetwork object

Neural network, specified as one of these values:

• dlnetwork object — Neural network for custom training loop.

• TaylorPrunableNetwork object — Neural network for custom pruning loop.

To prune a deep neural network, you require the Deep Learning Toolbox Model Compression Library support package. This support package is a free add-on that you can download using the Add-On Explorer. Alternatively, see Deep Learning Toolbox Model Compression Library.

X1,...,XM — Input data

formatted dlarray objects | unformatted dlarray objects | numeric arrays

Input data, each specified as one of these values:

• Formatted dlarray object

• Unformatted dlarray object (since R2025a)

• Numeric array (since R2025a)

The input Xi corresponds to the network input net.InputNames(i).

To train a neural network using a custom training loop using automatic differentiation, the input data must be formatted or unformatted dlarray objects.

Tip

Neural networks expect input data with a specific layout. For example, vector-sequence classification networks typically expect vector-sequence representations to be t-by-c arrays, where t and c are the number of time steps and channels of sequences, respectively. Neural networks typically have an input layer that specifies the expected layout of the data.

Most datastores and functions output data in the layout that the network expects. If your data is in a different layout to what the network expects, then indicate that your data has a different layout by using the InputDataFormats option or by specifying input data as a formatted dlarray object. It is usually easiest to adjust the InputDataFormats training option than to preprocess the input data.

For more information, see Deep Learning Data Formats.

To create a neural network that receives unformatted data, use an inputLayer object and do not specify a format. To input unformatted data into a network directly, do not specify the InputDataFormats argument. (since R2025a)

Before R2025a: For neural networks that do not have input layers, you must specify a format using the InputDataFormats argument or use formatted dlarray objects as input.

Name-Value Arguments

Specify optional pairs of arguments as Name1=Value1,...,NameN=ValueN, where Name is the argument name and Value is the corresponding value. Name-value arguments must appear after other arguments, but the order of the pairs does not matter.

Example: forward(net,X,Outputs=["relu1" "relu2"]) specifies to extract outputs from the layers with the names "relu1" and "relu2".

Outputs — Neural network outputs

string array | cell array of character vectors

Neural network outputs, specified as a string array or a cell array of character vectors of layer names or layer output paths. Specify the output using one of these forms:

• "layerName", where layerName is the name of a layer with a single output.

• "layerName/outputName", where layerName is the name of a layer and outputName is the name of the layer output. Use this option for layers with multiple outputs.

To use the outputs of layers inside a networkLayer object, first expand the nested network using the expandLayers function.

If you do not specify the layers to extract outputs from, then, by default, the software uses the outputs specified by net.Outputs.

Acceleration — Performance optimization

"auto" (default) | "none"

Performance optimization, specified as one of these values:

• "auto" – Automatically apply a number of optimizations suitable for the input network and hardware resources.

• "none" – Disable all optimizations.

Using the "auto" acceleration option can offer performance benefits, but at the expense of an increased initial run time. Subsequent calls with compatible parameters are faster. Use performance optimization when you plan to call the function multiple times using different input data with the same size and shape.

InputDataFormats — Description of input data dimensions

"auto" (default) | string array | cell array of character vectors | character vector

Since R2025a

Description of the input data dimensions, specified as a string array, character vector, or cell array of character vectors.

If InputDataFormats is "auto", then the software uses the formats expected by the network input. Otherwise, the software uses the specified formats for the corresponding network input.

A data format is a string of characters, where each character describes the type of the corresponding data dimension.

The characters are:

• "S" — Spatial

• "C" — Channel

• "B" — Batch

• "T" — Time

• "U" — Unspecified

For example, consider an array that represents a batch of sequences where the first, second, and third dimensions correspond to channels, observations, and time steps, respectively. You can describe the data as having the format "CBT" (channel, batch, time).

You can specify multiple dimensions labeled "S" or "U". You can use the labels "C", "B", and "T" once each, at most. The software ignores singleton trailing "U" dimensions after the second dimension.

For a neural networks with multiple inputs net, specify an array of input data formats, where InputDataFormats(i) corresponds to the input net.InputNames(i).

For more information, see Deep Learning Data Formats.

To create a neural network that receives unformatted data, use an inputLayer object and do not specify a format. To input unformatted data into a network directly, do not specify the InputDataFormats argument. (since R2025a)

Before R2025a: For neural networks that do not have input layers, you must specify a format using the InputDataFormats argument or use formatted dlarray objects as input.

Data Types: char | string | cell

OutputDataFormats — Description of output data dimensions

"auto" (default) | string array | cell array of character vectors | character vector

Since R2025a

Description of the output data dimensions, specified as one of these values:

• "auto" — If the output data has the same number of dimensions as the input data, then the forward function uses the format specified by InputDataFormats. If the output data has a different number of dimensions than the input data, then the forward function automatically permutes the dimensions of the output data so that they are consistent with the network input layers or the InputDataFormats value.

• String, character vector, or cell array of character vectors — The forward function uses the specified data formats.

A data format is a string of characters, where each character describes the type of the corresponding data dimension.

The characters are:

• "S" — Spatial

• "C" — Channel

• "B" — Batch

• "T" — Time

• "U" — Unspecified

For example, consider an array that represents a batch of sequences where the first, second, and third dimensions correspond to channels, observations, and time steps, respectively. You can describe the data as having the format "CBT" (channel, batch, time).

You can specify multiple dimensions labeled "S" or "U". You can use the labels "C", "B", and "T" once each, at most. The software ignores singleton trailing "U" dimensions after the second dimension.

For more information, see Deep Learning Data Formats.

Data Types: char | string | cell

Output Arguments

Y1,...,YN — Output data

numeric array | dlarray object

Output data of network with multiple outputs, returned as a one of these values:

• Formatted dlarray object

• Unformatted dlarray object (since R2025a)

• Numeric array (since R2025a)

The data type matches the data type of the input data.

The order of the outputs Y1, …, YN match the order of the outputs specified by the Outputs argument.

For a classification neural network, the elements of the output correspond to the scores for each class. The order of the scores matches the order of the categories in the training data. For example, if you train the neural network using the categorical labels TTrain, then the order of the scores matches the order of the categories given by categories(TTrain).

state — Updated network state

table

Updated network state, returned as a table.

The network state is a table with three columns:

• Layer – Layer name, specified as a string scalar.

• Parameter – State parameter name, specified as a string scalar.

• Value – Value of state parameter, specified as a dlarray object.

Layer states retain information calculated during the layer operation for use in subsequent forward passes of the layer. For example, LSTM layers contain cell states and hidden states, and batch normalization layers calculate running statistics.

For recurrent layers, such as LSTM layers, with the HasStateInputs property set to 1 (true), the state table does not contain entries for the states of the layer.

Update the state of a dlnetwork using the State property.

pruningActivations — Activations of the pruning layers

cell array containing dlarray objects

Cell array of activations of the pruning layers, if the input network is a TaylorPrunableNetwork object.

Extended Capabilities

GPU Arrays

Accelerate code by running on a graphics processing unit (GPU) using Parallel Computing Toolbox™.

The forward function supports GPU array input with these usage notes and limitations:

• This function runs on the GPU if you meet at least one of these conditions:

  • Any of the values of the network learnable parameters inside net.Learnables.Value are dlarray objects with underlying data of type gpuArray.

  • The input argument X is a dlarray with underlying data of type gpuArray.

For more information, see Run MATLAB Functions on a GPU (Parallel Computing Toolbox).

Version History

Introduced in R2019b

R2025a: Specify numeric arrays and unformatted dlarray objects

Optionally, specify the input and output data formats using the InputDataFormats and OutputDataFormats options, respectively. If you specify unformatted data as input to the neural network and do not specify the InputDataFormats argument, then the function passes the unformatted data to the network directly.

To create a neural network that receives unformatted data, use an inputLayer object and do not specify a format.

R2021a: forward returns state values as dlarray objects

For dlnetwork objects, the state output argument returned by the forward function is a table containing the state parameter names and values for each layer in the network.

Starting in R2021a, the state values are dlarray objects. This change enables better support when using AcceleratedFunction objects. To accelerate deep learning functions that have frequently changing input values, for example, an input containing the network state, the frequently changing values must be specified as dlarray objects.

In previous versions, the state values are numeric arrays.

In most cases, you will not need to update your code. If you have code that requires the state values to be numeric arrays, then to reproduce the previous behavior, extract the data from the state values manually using the extractdata function with the dlupdate function.

state = dlupdate(@extractdata,net.State);