forward
Compute deep learning network output for training
Syntax
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(___)
returns the
N
outputs Y1
, …, YN
during
training for networks that have N
outputs using any of the previous
syntaxes.
[Y1,...,YK] = forward(___,'Outputs',
returns the outputs layerNames
)Y1
, …, YK
during training for the
specified layers using any of the previous syntaxes.
[___] = forward(___,'Acceleration',
also specifies performance optimization to use during training, in addition to the input
arguments in previous syntaxes. acceleration
)
[___,
also returns the updated network state.state
] = forward(___)
[___,
also returns a cell array of activations of the pruning layers. This syntax is applicable
only if state
,pruningActivations
] = forward(___)net
is a TaylorPrunableNetwork
object.
To prune a deep neural network, you require the Deep Learning Toolbox™ Model Quantization 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 Quantization Library.
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 , where is the network input, and is the set of learnable parameters, you can optimize so that it minimizes some loss value based on the training data. For example, optimize the learnable parameters such that for a given inputs with a corresponding targets , they minimize the error between the predictions and .
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 by iteratively updating the learnable parameters 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 , where is the iteration number, is the learning rate, and 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 , where is the network input, and is the set of learnable parameters, you can optimize so that it minimizes some loss value based on the training data. For example, optimize the learnable parameters such that for a given inputs with a corresponding targets , they minimize the error between the predictions and .
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 , where is the iteration number, is the learning rate, and 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, theminibatchqueue
object converts the data todlarray
objects with underlying typesingle
. 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 agpuArray
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
andmodelLoss
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:
Preprocess the images using the
preprocessMiniBatchPredictors
function.Extract the label data from the incoming cell array and concatenate into a categorical array along the second dimension.
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
— Network for custom training loops or custom pruning loops
dlnetwork
object | TaylorPrunableNetwork
object
This argument can represent either of these:
Network for custom training loops, specified as a
dlnetwork
object.Network for custom pruning loops, specified as a
TaylorPrunableNetwork
object.
To prune a deep neural network, you require the Deep Learning Toolbox Model Quantization 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 Quantization Library.
layerNames
— Layers to extract outputs from
string array | cell array of character vectors
Layers to extract outputs from, specified as a string array or a cell array of character vectors containing the layer names.
If
layerNames(i)
corresponds to a layer with a single output, thenlayerNames(i)
is the name of the layer.If
layerNames(i)
corresponds to a layer with multiple outputs, thenlayerNames(i)
is the layer name followed by the/
character and the name of the layer output:"layerName/outputName"
.
acceleration
— Performance optimization
'auto'
(default) | 'none'
Performance optimization, specified as one of the following:
'auto'
— Automatically apply a number of optimizations suitable for the input network and hardware resources.'none'
— Disable all acceleration.
The default option is 'auto'
.
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.
Output Arguments
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 adlarray
object.
Layer states contain information calculated during the layer operation to be retained for use in subsequent forward passes of the layer. For example, the cell state and hidden state of LSTM layers, or running statistics in batch normalization layers.
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 that layer.
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 either or both of the following conditions are met:
Any of the values of the network learnable parameters inside
net.Learnables.Value
aredlarray
objects with underlying data of typegpuArray
The input argument
X
is adlarray
with underlying data of typegpuArray
For more information, see Run MATLAB Functions on a GPU (Parallel Computing Toolbox).
Version History
Introduced in R2019bR2021a: 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);
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