# trainingOptions

Options for training deep learning neural network

## Description

example

options = trainingOptions(solverName) returns training options for the optimizer specified by solverName. To train a network, use the training options as an input argument to the trainNetwork function.

example

options = trainingOptions(solverName,Name=Value) returns training options with additional options specified by one or more name-value arguments.

## Examples

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Create a set of options for training a network using stochastic gradient descent with momentum. Reduce the learning rate by a factor of 0.2 every 5 epochs. Set the maximum number of epochs for training to 20, and use a mini-batch with 64 observations at each iteration. Turn on the training progress plot.

options = trainingOptions("sgdm", ...
LearnRateSchedule="piecewise", ...
LearnRateDropFactor=0.2, ...
LearnRateDropPeriod=5, ...
MaxEpochs=20, ...
MiniBatchSize=64, ...
Plots="training-progress")
options =
TrainingOptionsSGDM with properties:

Momentum: 0.9000
InitialLearnRate: 0.0100
LearnRateSchedule: 'piecewise'
LearnRateDropFactor: 0.2000
LearnRateDropPeriod: 5
L2Regularization: 1.0000e-04
MaxEpochs: 20
MiniBatchSize: 64
Verbose: 1
VerboseFrequency: 50
ValidationData: []
ValidationFrequency: 50
ValidationPatience: Inf
Shuffle: 'once'
CheckpointPath: ''
CheckpointFrequency: 1
CheckpointFrequencyUnit: 'epoch'
ExecutionEnvironment: 'auto'
OutputFcn: []
Plots: 'training-progress'
SequenceLength: 'longest'
DispatchInBackground: 0
ResetInputNormalization: 1
BatchNormalizationStatistics: 'population'
OutputNetwork: 'last-iteration'

This example shows how to monitor the training process of deep learning networks.

When you train networks for deep learning, it is often useful to monitor the training progress. By plotting various metrics during training, you can learn how the training is progressing. For example, you can determine if and how quickly the network accuracy is improving, and whether the network is starting to overfit the training data.

This example shows how to monitor training progress for networks trained using the trainNetwork function. For networks trained using a custom training loop, use a trainingProgressMonitor object to plot metrics during training. For more information, see Monitor Custom Training Loop Progress.

When you set the Plots training option to "training-progress" in trainingOptions and start network training, trainNetwork creates a figure and displays training metrics at every iteration. Each iteration is an estimation of the gradient and an update of the network parameters. If you specify validation data in trainingOptions, then the figure shows validation metrics each time trainNetwork validates the network. The figure plots the following:

• Training accuracy — Classification accuracy on each individual mini-batch.

• Smoothed training accuracy — Smoothed training accuracy, obtained by applying a smoothing algorithm to the training accuracy. It is less noisy than the unsmoothed accuracy, making it easier to spot trends.

• Validation accuracy — Classification accuracy on the entire validation set (specified using trainingOptions).

• Training loss, smoothed training loss, and validation loss — The loss on each mini-batch, its smoothed version, and the loss on the validation set, respectively. If the final layer of your network is a classificationLayer, then the loss function is the cross entropy loss. For more information about loss functions for classification and regression problems, see Output Layers.

For regression networks, the figure plots the root mean square error (RMSE) instead of the accuracy.

The figure marks each training Epoch using a shaded background. An epoch is a full pass through the entire data set.

During training, you can stop training and return the current state of the network by clicking the stop button in the top-right corner. For example, you might want to stop training when the accuracy of the network reaches a plateau and it is clear that the accuracy is no longer improving. After you click the stop button, it can take a while for the training to complete. Once training is complete, trainNetwork returns the trained network.

When training finishes, view the Results showing the finalized validation accuracy and the reason that training finished. If the OutputNetwork training option is "last-iteration" (default), the finalized metrics correspond to the last training iteration. If the OutputNetwork training option is "best-validation-loss", the finalized metrics correspond to the iteration with the lowest validation loss. The iteration from which the final validation metrics are calculated is labeled Final in the plots.

If your network contains batch normalization layers, then the final validation metrics can be different to the validation metrics evaluated during training. This is because the mean and variance statistics used for batch normalization can be different after training completes. For example, if the BatchNormalizationStatisics training option is "population", then after training, the software finalizes the batch normalization statistics by passing through the training data once more and uses the resulting mean and variance. If the BatchNormalizationStatisics training option is "moving", then the software approximates the statistics during training using a running estimate and uses the latest values of the statistics.

On the right, view information about the training time and settings. To learn more about training options, see Set Up Parameters and Train Convolutional Neural Network.

To save the training progress plot, click Export Training Plot in the training window. You can save the plot as a PNG, JPEG, TIFF, or PDF file. You can also save the individual plots of loss, accuracy, and root mean squared error using the axes toolbar.

Plot Training Progress During Training

Train a network and plot the training progress during training.

Load the training data, which contains 5000 images of digits. Set aside 1000 of the images for network validation.

[XTrain,YTrain] = digitTrain4DArrayData;

idx = randperm(size(XTrain,4),1000);
XValidation = XTrain(:,:,:,idx);
XTrain(:,:,:,idx) = [];
YValidation = YTrain(idx);
YTrain(idx) = [];

Construct a network to classify the digit image data.

layers = [
imageInputLayer([28 28 1])
batchNormalizationLayer
reluLayer
maxPooling2dLayer(2,Stride=2)
batchNormalizationLayer
reluLayer
maxPooling2dLayer(2,Stride=2)
batchNormalizationLayer
reluLayer
fullyConnectedLayer(10)
softmaxLayer
classificationLayer];

Specify options for network training. To validate the network at regular intervals during training, specify validation data. Choose the ValidationFrequency value so that the network is validated about once per epoch. To plot training progress during training, set the Plots training option to "training-progress".

options = trainingOptions("sgdm", ...
MaxEpochs=8, ...
ValidationData={XValidation,YValidation}, ...
ValidationFrequency=30, ...
Verbose=false, ...
Plots="training-progress");

Train the network.

net = trainNetwork(XTrain,YTrain,layers,options);

## Input Arguments

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Solver for training network, specified as one of the following:

• 'sgdm' — Use the stochastic gradient descent with momentum (SGDM) optimizer. You can specify the momentum value using the Momentum training option.

• 'rmsprop'— Use the RMSProp optimizer. You can specify the decay rate of the squared gradient moving average using the SquaredGradientDecayFactor training option.

### 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.

Before R2021a, use commas to separate each name and value, and enclose Name in quotes.

Example: InitialLearnRate=0.03,L2Regularization=0.0005,LearnRateSchedule="piecewise" specifies the initial learning rate as 0.03 and theL2 regularization factor as 0.0005, and instructs the software to drop the learning rate every given number of epochs by multiplying with a certain factor.

Plots and Display

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Plots to display during network training, specified as one of the following:

• 'none' — Do not display plots during training.

• 'training-progress' — Plot training progress. The plot shows mini-batch loss and accuracy, validation loss and accuracy, and additional information on the training progress. The plot has a stop button in the top-right corner. Click the button to stop training and return the current state of the network. You can save the training plot as an image or PDF by clicking . For more information on the training progress plot, see Monitor Deep Learning Training Progress.

Indicator to display training progress information in the command window, specified as 1 (true) or 0 (false).

The verbose output displays the following information:

Classification Networks

FieldDescription
EpochEpoch number. An epoch corresponds to a full pass of the data.
IterationIteration number. An iteration corresponds to a mini-batch.
Time ElapsedTime elapsed in hours, minutes, and seconds.
Mini-batch AccuracyClassification accuracy on the mini-batch.
Validation AccuracyClassification accuracy on the validation data. If you do not specify validation data, then the function does not display this field.
Mini-batch LossLoss on the mini-batch. If the output layer is a ClassificationOutputLayer object, then the loss is the cross entropy loss for multi-class classification problems with mutually exclusive classes.
Validation LossLoss on the validation data. If the output layer is a ClassificationOutputLayer object, then the loss is the cross entropy loss for multi-class classification problems with mutually exclusive classes. If you do not specify validation data, then the function does not display this field.
Base Learning RateBase learning rate. The software multiplies the learn rate factors of the layers by this value.

Regression Networks

FieldDescription
EpochEpoch number. An epoch corresponds to a full pass of the data.
IterationIteration number. An iteration corresponds to a mini-batch.
Time ElapsedTime elapsed in hours, minutes, and seconds.
Mini-batch RMSERoot-mean-squared-error (RMSE) on the mini-batch.
Validation RMSERMSE on the validation data. If you do not specify validation data, then the software does not display this field.
Mini-batch LossLoss on the mini-batch. If the output layer is a RegressionOutputLayer object, then the loss is the half-mean-squared-error.
Validation LossLoss on the validation data. If the output layer is a RegressionOutputLayer object, then the loss is the half-mean-squared-error. If you do not specify validation data, then the software does not display this field.
Base Learning RateBase learning rate. The software multiplies the learn rate factors of the layers by this value.

When training stops, the verbose output displays the reason for stopping.

To specify validation data, use the ValidationData training option.

Data Types: single | double | int8 | int16 | int32 | int64 | uint8 | uint16 | uint32 | uint64 | logical

Frequency of verbose printing, which is the number of iterations between printing to the command window, specified as a positive integer. This option only has an effect when the Verbose training option is 1 (true).

If you validate the network during training, then trainNetwork also prints to the command window every time validation occurs.

Data Types: single | double | int8 | int16 | int32 | int64 | uint8 | uint16 | uint32 | uint64

Mini-Batch Options

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Maximum number of epochs to use for training, specified as a positive integer.

An iteration is one step taken in the gradient descent algorithm towards minimizing the loss function using a mini-batch. An epoch is the full pass of the training algorithm over the entire training set.

Data Types: single | double | int8 | int16 | int32 | int64 | uint8 | uint16 | uint32 | uint64

Size of the mini-batch to use for each training iteration, specified as a positive integer. A mini-batch is a subset of the training set that is used to evaluate the gradient of the loss function and update the weights.

If the mini-batch size does not evenly divide the number of training samples, then trainNetwork discards the training data that does not fit into the final complete mini-batch of each epoch.

Data Types: single | double | int8 | int16 | int32 | int64 | uint8 | uint16 | uint32 | uint64

Option for data shuffling, specified as one of the following:

• 'once' — Shuffle the training and validation data once before training.

• 'never' — Do not shuffle the data.

• 'every-epoch' — Shuffle the training data before each training epoch, and shuffle the validation data before each network validation. If the mini-batch size does not evenly divide the number of training samples, then trainNetwork discards the training data that does not fit into the final complete mini-batch of each epoch. To avoid discarding the same data every epoch, set the Shuffle training option to 'every-epoch'.

Validation

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Data to use for validation during training, specified as [], a datastore, a table, or a cell array containing the validation predictors and responses.

You can specify validation predictors and responses using the same formats supported by the trainNetwork function. You can specify the validation data as a datastore, table, or the cell array {predictors,responses}, where predictors contains the validation predictors and responses contains the validation responses.

For more information, see the images, sequences, and features input arguments of the trainNetwork function.

During training, trainNetwork calculates the validation accuracy and validation loss on the validation data. To specify the validation frequency, use the ValidationFrequency training option. You can also use the validation data to stop training automatically when the validation loss stops decreasing. To turn on automatic validation stopping, use the ValidationPatience training option.

If your network has layers that behave differently during prediction than during training (for example, dropout layers), then the validation accuracy can be higher than the training (mini-batch) accuracy.

The validation data is shuffled according to the Shuffle training option. If Shuffle is 'every-epoch', then the validation data is shuffled before each network validation.

If ValidationData is [], then the software does not validate the network during training.

Frequency of network validation in number of iterations, specified as a positive integer.

The ValidationFrequency value is the number of iterations between evaluations of validation metrics. To specify validation data, use the ValidationData training option.

Data Types: single | double | int8 | int16 | int32 | int64 | uint8 | uint16 | uint32 | uint64

Patience of validation stopping of network training, specified as a positive integer or Inf.

ValidationPatience specifies the number of times that the loss on the validation set can be larger than or equal to the previously smallest loss before network training stops. If ValidationPatience is Inf, then the values of the validation loss do not cause training to stop early.

The returned network depends on the OutputNetwork training option. To return the network with the lowest validation loss, set the OutputNetwork training option to "best-validation-loss".

Data Types: single | double | int8 | int16 | int32 | int64 | uint8 | uint16 | uint32 | uint64

Network to return when training completes, specified as one of the following:

• 'last-iteration' – Return the network corresponding to the last training iteration.

• 'best-validation-loss' – Return the network corresponding to the training iteration with the lowest validation loss. To use this option, you must specify the ValidationData training option.

Solver Options

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Initial learning rate used for training, specified as a positive scalar.

The default value is 0.01 for the 'sgdm' solver and 0.001 for the 'rmsprop' and 'adam' solvers.

If the learning rate is too low, then training can take a long time. If the learning rate is too high, then training might reach a suboptimal result or diverge.

Data Types: single | double | int8 | int16 | int32 | int64 | uint8 | uint16 | uint32 | uint64

Option for dropping the learning rate during training, specified as of the following:

• 'none' — The learning rate remains constant throughout training.

• 'piecewise' — The software updates the learning rate every certain number of epochs by multiplying with a certain factor. Use the LearnRateDropFactor training option to specify the value of this factor. Use the LearnRateDropPeriod training option to specify the number of epochs between multiplications.

Number of epochs for dropping the learning rate, specified as a positive integer. This option is valid only when the LearnRateSchedule training option is 'piecewise'.

The software multiplies the global learning rate with the drop factor every time the specified number of epochs passes. Specify the drop factor using the LearnRateDropFactor training option.

Data Types: single | double | int8 | int16 | int32 | int64 | uint8 | uint16 | uint32 | uint64

Factor for dropping the learning rate, specified as a scalar from 0 to 1. This option is valid only when the LearnRateSchedule training option is 'piecewise'.

LearnRateDropFactor is a multiplicative factor to apply to the learning rate every time a certain number of epochs passes. Specify the number of epochs using the LearnRateDropPeriod training option.

Data Types: single | double | int8 | int16 | int32 | int64 | uint8 | uint16 | uint32 | uint64

Factor for L2 regularization (weight decay), specified as a nonnegative scalar. For more information, see L2 Regularization.

You can specify a multiplier for the L2 regularization for network layers with learnable parameters. For more information, see Set Up Parameters in Convolutional and Fully Connected Layers.

Data Types: single | double | int8 | int16 | int32 | int64 | uint8 | uint16 | uint32 | uint64

Contribution of the parameter update step of the previous iteration to the current iteration of stochastic gradient descent with momentum, specified as a scalar from 0 to 1.

A value of 0 means no contribution from the previous step, whereas a value of 1 means maximal contribution from the previous step. The default value works well for most tasks.

To specify the Momentum training option, solverName must be 'sgdm'.

Data Types: single | double | int8 | int16 | int32 | int64 | uint8 | uint16 | uint32 | uint64

Decay rate of gradient moving average for the Adam solver, specified as a nonnegative scalar less than 1. The gradient decay rate is denoted by β1 in the Adam section.

The default value works well for most tasks.

Data Types: single | double | int8 | int16 | int32 | int64 | uint8 | uint16 | uint32 | uint64

Decay rate of squared gradient moving average for the Adam and RMSProp solvers, specified as a nonnegative scalar less than 1. The squared gradient decay rate is denoted by β2 in [4].

To specify the SquaredGradientDecayFactor training option, solverName must be 'adam' or 'rmsprop'.

Typical values of the decay rate are 0.9, 0.99, and 0.999, corresponding to averaging lengths of 10, 100, and 1000 parameter updates, respectively.

The default value is 0.999 for the Adam solver. The default value is 0.9 for the RMSProp solver.

Data Types: single | double | int8 | int16 | int32 | int64 | uint8 | uint16 | uint32 | uint64

Denominator offset for Adam and RMSProp solvers, specified as a positive scalar.

The solver adds the offset to the denominator in the network parameter updates to avoid division by zero. The default value works well for most tasks.

To specify the Epsilon training option, solverName must be 'adam' or 'rmsprop'.

Data Types: single | double | int8 | int16 | int32 | int64 | uint8 | uint16 | uint32 | uint64

Option to reset input layer normalization, specified as one of the following:

• 1 (true) — Reset the input layer normalization statistics and recalculate them at training time.

• 0 (false) — Calculate normalization statistics at training time when they are empty.

Data Types: single | double | int8 | int16 | int32 | int64 | uint8 | uint16 | uint32 | uint64 | logical

Mode to evaluate the statistics in batch normalization layers, specified as one of the following:

• 'population' – Use the population statistics. After training, the software finalizes the statistics by passing through the training data once more and uses the resulting mean and variance.

• 'moving' – Approximate the statistics during training using a running estimate given by update steps

$\begin{array}{l}{\mu }^{*}={\lambda }_{\mu }\stackrel{^}{\mu }+\left(1-{\lambda }_{\mu }\right)\mu \\ {\sigma }^{2}{}^{*}={\lambda }_{{\sigma }^{2}}\stackrel{^}{{\sigma }^{2}}\text{​}\text{+}\text{​}\text{(1-}{\lambda }_{{\sigma }^{2}}\right)\text{​}{\sigma }^{2}\end{array}$

where ${\mu }^{*}$ and ${\sigma }^{2}{}^{*}$ denote the updated mean and variance, respectively, ${\lambda }_{\mu }$ and ${\lambda }_{{\sigma }^{2}}$ denote the mean and variance decay values, respectively, $\stackrel{^}{\mu }$ and $\stackrel{^}{{\sigma }^{2}}$ denote the mean and variance of the layer input, respectively, and $\mu$ and ${\sigma }^{2}$ denote the latest values of the moving mean and variance values, respectively. After training, the software uses the most recent value of the moving mean and variance statistics. This option supports CPU and single GPU training only.

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Gradient threshold, specified as Inf or a positive scalar. If the gradient exceeds the value of GradientThreshold, then the gradient is clipped according to the GradientThresholdMethod training option.

Data Types: single | double | int8 | int16 | int32 | int64 | uint8 | uint16 | uint32 | uint64

Gradient threshold method used to clip gradient values that exceed the gradient threshold, specified as one of the following:

• 'l2norm' — If the L2 norm of the gradient of a learnable parameter is larger than GradientThreshold, then scale the gradient so that the L2 norm equals GradientThreshold.

• 'global-l2norm' — If the global L2 norm, L, is larger than GradientThreshold, then scale all gradients by a factor of GradientThreshold/L. The global L2 norm considers all learnable parameters.

• 'absolute-value' — If the absolute value of an individual partial derivative in the gradient of a learnable parameter is larger than GradientThreshold, then scale the partial derivative to have magnitude equal to GradientThreshold and retain the sign of the partial derivative.

Sequence Options

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Option to pad, truncate, or split input sequences, specified as one of the following:

• "longest" — Pad sequences in each mini-batch to have the same length as the longest sequence. This option does not discard any data, though padding can introduce noise to the network.

• "shortest" — Truncate sequences in each mini-batch to have the same length as the shortest sequence. This option ensures that no padding is added, at the cost of discarding data.

• Positive integer — For each mini-batch, pad the sequences to the length of the longest sequence in the mini-batch, and then split the sequences into smaller sequences of the specified length. If splitting occurs, then the software creates extra mini-batches. If the specified sequence length does not evenly divide the sequence lengths of the data, then the mini-batches containing the ends those sequences have length shorter than the specified sequence length. Use this option if the full sequences do not fit in memory. Alternatively, try reducing the number of sequences per mini-batch by setting the MiniBatchSize option to a lower value.

Data Types: single | double | int8 | int16 | int32 | int64 | uint8 | uint16 | uint32 | uint64 | char | string

Direction of padding or truncation, specified as one of the following:

• "right" — Pad or truncate sequences on the right. The sequences start at the same time step and the software truncates or adds padding to the end of the sequences.

• "left" — Pad or truncate sequences on the left. The software truncates or adds padding to the start of the sequences so that the sequences end at the same time step.

Because recurrent layers process sequence data one time step at a time, when the recurrent layer OutputMode property is 'last', any padding in the final time steps can negatively influence the layer output. To pad or truncate sequence data on the left, set the SequencePaddingDirection option to "left".

For sequence-to-sequence networks (when the OutputMode property is 'sequence' for each recurrent layer), any padding in the first time steps can negatively influence the predictions for the earlier time steps. To pad or truncate sequence data on the right, set the SequencePaddingDirection option to "right".

Value by which to pad input sequences, specified as a scalar.

The option is valid only when SequenceLength is "longest" or a positive integer. Do not pad sequences with NaN, because doing so can propagate errors throughout the network.

Data Types: single | double | int8 | int16 | int32 | int64 | uint8 | uint16 | uint32 | uint64

Hardware Options

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Hardware resource for training network, specified as one of the following:

• 'auto' — Use a GPU if one is available. Otherwise, use the CPU.

• 'cpu' — Use the CPU.

• 'gpu' — Use the GPU.

• 'multi-gpu' — Use multiple GPUs on one machine, using a local parallel pool based on your default cluster profile. If there is no current parallel pool, the software starts a parallel pool with pool size equal to the number of available GPUs.

• 'parallel' — Use a local or remote parallel pool based on your default cluster profile. If there is no current parallel pool, the software starts one using the default cluster profile. If the pool has access to GPUs, then only workers with a unique GPU perform training computation. If the pool does not have GPUs, then training takes place on all available CPU workers instead.

For more information on when to use the different execution environments, see Scale Up Deep Learning in Parallel, on GPUs, and in the Cloud.

'gpu', 'multi-gpu', and 'parallel' options require 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). If you choose one of these options and Parallel Computing Toolbox or a suitable GPU is not available, then the software returns an error.

To see an improvement in performance when training in parallel, try scaling up the MiniBatchSize and InitialLearnRate training options by the number of GPUs.

The 'multi-gpu' and 'parallel' options do not support networks containing custom layers with state parameters or built-in layers that are stateful at training time. For example:

Parallel worker load division between GPUs or CPUs, specified as one of the following:

• Scalar from 0 to 1 — Fraction of workers on each machine to use for network training computation. If you train the network using data in a mini-batch datastore with background dispatch enabled, then the remaining workers fetch and preprocess data in the background.

• Positive integer — Number of workers on each machine to use for network training computation. If you train the network using data in a mini-batch datastore with background dispatch enabled, then the remaining workers fetch and preprocess data in the background.

• Numeric vector — Network training load for each worker in the parallel pool. For a vector W, worker i gets a fraction W(i)/sum(W) of the work (number of examples per mini-batch). If you train a network using data in a mini-batch datastore with background dispatch enabled, then you can assign a worker load of 0 to use that worker for fetching data in the background. The specified vector must contain one value per worker in the parallel pool.

If the parallel pool has access to GPUs, then workers without a unique GPU are never used for training computation. The default for pools with GPUs is to use all workers with a unique GPU for training computation, and the remaining workers for background dispatch. If the pool does not have access to GPUs and CPUs are used for training, then the default is to use one worker per machine for background data dispatch.

Data Types: single | double | int8 | int16 | int32 | int64 | uint8 | uint16 | uint32 | uint64

Flag to enable background dispatch (asynchronous prefetch queuing) to read training data from datastores, specified as 0 (false) or 1 (true). Background dispatch requires Parallel Computing Toolbox.

DispatchInBackground is only supported for datastores that are partitionable. For more information, see Use Datastore for Parallel Training and Background Dispatching.

Data Types: single | double | int8 | int16 | int32 | int64 | uint8 | uint16 | uint32 | uint64

Checkpoints

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Path for saving the checkpoint networks, specified as a character vector or string scalar.

• If you do not specify a path (that is, you use the default ""), then the software does not save any checkpoint networks.

• If you specify a path, then trainNetwork saves checkpoint networks to this path and assigns a unique name to each network. You can then load any checkpoint network and resume training from that network.

If the folder does not exist, then you must first create it before specifying the path for saving the checkpoint networks. If the path you specify does not exist, then trainingOptions returns an error.

The CheckpointFrequency and CheckpointFrequencyUnit options specify the frequency of saving checkpoint networks.

Data Types: char | string

Frequency of saving checkpoint networks, specified as a positive integer.

If CheckpointFrequencyUnit is 'epoch', then the software saves checkpoint networks every CheckpointFrequency epochs.

If CheckpointFrequencyUnit is 'iteration', then the software saves checkpoint networks every CheckpointFrequency iterations.

This option only has an effect when CheckpointPath is nonempty.

Data Types: single | double | int8 | int16 | int32 | int64 | uint8 | uint16 | uint32 | uint64

Checkpoint frequency unit, specified as 'epoch' or 'iteration'.

If CheckpointFrequencyUnit is 'epoch', then the software saves checkpoint networks every CheckpointFrequency epochs.

If CheckpointFrequencyUnit is 'iteration', then the software saves checkpoint networks every CheckpointFrequency iterations.

This option only has an effect when CheckpointPath is nonempty.

Output functions to call during training, specified as a function handle or cell array of function handles. trainNetwork calls the specified functions once before the start of training, after each iteration, and once after training has finished. trainNetwork passes a structure containing information in the following fields:

FieldDescription
EpochCurrent epoch number
IterationCurrent iteration number
TimeSinceStartTime in seconds since the start of training
TrainingLossCurrent mini-batch loss
ValidationLossLoss on the validation data
BaseLearnRateCurrent base learning rate
TrainingAccuracy Accuracy on the current mini-batch (classification networks)
TrainingRMSERMSE on the current mini-batch (regression networks)
ValidationAccuracyAccuracy on the validation data (classification networks)
ValidationRMSERMSE on the validation data (regression networks)
StateCurrent training state, with a possible value of "start", "iteration", or "done".

If a field is not calculated or relevant for a certain call to the output functions, then that field contains an empty array.

You can use output functions to display or plot progress information, or to stop training. To stop training early, make your output function return 1 (true). If any output function returns 1 (true), then training finishes and trainNetwork returns the latest network. For an example showing how to use output functions, see Customize Output During Deep Learning Network Training.

Data Types: function_handle | cell

## Output Arguments

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Training options, returned as a TrainingOptionsSGDM, TrainingOptionsRMSProp, or TrainingOptionsADAM object. To train a neural network, use the training options as an input argument to the trainNetwork function.

If solverName is 'sgdm', 'rmsprop', or 'adam', then the training options are returned as a TrainingOptionsSGDM, TrainingOptionsRMSProp, or TrainingOptionsADAM object, respectively.

You can edit training option properties of TrainingOptionsSGDM, TrainingOptionsADAM, and TrainingOptionsRMSProp objects directly. For example, to change the mini-batch size after using the trainingOptions function, you can edit the MiniBatchSize property directly:

options = trainingOptions('sgdm');
options.MiniBatchSize = 64;

## Algorithms

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### Initial Weights and Biases

For convolutional and fully connected layers, the initialization for the weights and biases are given by the WeightsInitializer and BiasInitializer properties of the layers, respectively. For examples showing how to change the initialization for the weights and biases, see Specify Initial Weights and Biases in Convolutional Layer and Specify Initial Weights and Biases in Fully Connected Layer.

The standard gradient descent algorithm updates the network parameters (weights and biases) to minimize the loss function by taking small steps at each iteration in the direction of the negative gradient of the loss,

${\theta }_{\ell +1}={\theta }_{\ell }-\alpha \nabla E\left({\theta }_{\ell }\right),$

where $\ell$is the iteration number, $\alpha >0$ is the learning rate, $\theta$ is the parameter vector, and $E\left(\theta \right)$ is the loss function. In the standard gradient descent algorithm, the gradient of the loss function, $\nabla E\left(\theta \right)$, is evaluated using the entire training set, and the standard gradient descent algorithm uses the entire data set at once.

By contrast, at each iteration the stochastic gradient descent algorithm evaluates the gradient and updates the parameters using a subset of the training data. A different subset, called a mini-batch, is used at each iteration. The full pass of the training algorithm over the entire training set using mini-batches is one epoch. Stochastic gradient descent is stochastic because the parameter updates computed using a mini-batch is a noisy estimate of the parameter update that would result from using the full data set. You can specify the mini-batch size and the maximum number of epochs by using the MiniBatchSize and MaxEpochs training options, respectively.

### Stochastic Gradient Descent with Momentum

The stochastic gradient descent algorithm can oscillate along the path of steepest descent towards the optimum. Adding a momentum term to the parameter update is one way to reduce this oscillation [2]. The stochastic gradient descent with momentum (SGDM) update is

${\theta }_{\ell +1}={\theta }_{\ell }-\alpha \nabla E\left({\theta }_{\ell }\right)+\gamma \left({\theta }_{\ell }-{\theta }_{\ell -1}\right),$

where $\gamma$ determines the contribution of the previous gradient step to the current iteration. You can specify this value using the Momentum training option. To train a neural network using the stochastic gradient descent with momentum algorithm, specify 'sgdm' as the first input argument to trainingOptions. To specify the initial value of the learning rate α, use the InitialLearnRate training option. You can also specify different learning rates for different layers and parameters. For more information, see Set Up Parameters in Convolutional and Fully Connected Layers.

### RMSProp

Stochastic gradient descent with momentum uses a single learning rate for all the parameters. Other optimization algorithms seek to improve network training by using learning rates that differ by parameter and can automatically adapt to the loss function being optimized. RMSProp (root mean square propagation) is one such algorithm. It keeps a moving average of the element-wise squares of the parameter gradients,

${v}_{\ell }={\beta }_{2}{v}_{\ell -1}+\left(1-{\beta }_{2}\right){\left[\nabla E\left({\theta }_{\ell }\right)\right]}^{2}$

β2 is the decay rate of the moving average. Common values of the decay rate are 0.9, 0.99, and 0.999. The corresponding averaging lengths of the squared gradients equal 1/(1-β2), that is, 10, 100, and 1000 parameter updates, respectively. You can specify β2 by using the SquaredGradientDecayFactor training options. The RMSProp algorithm uses this moving average to normalize the updates of each parameter individually,

${\theta }_{\ell +1}={\theta }_{\ell }-\frac{\alpha \nabla E\left({\theta }_{\ell }\right)}{\sqrt{{v}_{\ell }}+ϵ}$

where the division is performed element-wise. Using RMSProp effectively decreases the learning rates of parameters with large gradients and increases the learning rates of parameters with small gradients. ɛ is a small constant added to avoid division by zero. You can specify ɛ by using the Epsilon training option, but the default value usually works well. To use RMSProp to train a neural network, specify 'rmsprop' as the first input to trainingOptions.

Adam (derived from adaptive moment estimation) [4] uses a parameter update that is similar to RMSProp, but with an added momentum term. It keeps an element-wise moving average of both the parameter gradients and their squared values,

${m}_{\ell }={\beta }_{1}{m}_{\ell -1}+\left(1-{\beta }_{1}\right)\nabla E\left({\theta }_{\ell }\right)$

${v}_{\ell }={\beta }_{2}{v}_{\ell -1}+\left(1-{\beta }_{2}\right){\left[\nabla E\left({\theta }_{\ell }\right)\right]}^{2}$

You can specify the β1 and β2 decay rates using the GradientDecayFactor and SquaredGradientDecayFactor training options, respectively. Adam uses the moving averages to update the network parameters as

${\theta }_{\ell +1}={\theta }_{\ell }-\frac{\alpha {m}_{l}}{\sqrt{{v}_{l}}+ϵ}$

Specify the learning rate α for all optimization algorithms using theInitialLearnRate training option. The effect of the learning rate is different for the different optimization algorithms, so the optimal learning rates are also different in general. You can also specify learning rates that differ by layers and by parameter. For more information, see Set Up Parameters in Convolutional and Fully Connected Layers.

If the gradients increase in magnitude exponentially, then the training is unstable and can diverge within a few iterations. This "gradient explosion" is indicated by a training loss that goes to NaN or Inf. Gradient clipping helps prevent gradient explosion by stabilizing the training at higher learning rates and in the presence of outliers [3]. Gradient clipping enables networks to be trained faster, and does not usually impact the accuracy of the learned task.

There are two types of gradient clipping.

• Norm-based gradient clipping rescales the gradient based on a threshold, and does not change the direction of the gradient. The 'l2norm' and 'global-l2norm' values of GradientThresholdMethod are norm-based gradient clipping methods.

• Value-based gradient clipping clips any partial derivative greater than the threshold, which can result in the gradient arbitrarily changing direction. Value-based gradient clipping can have unpredictable behavior, but sufficiently small changes do not cause the network to diverge. The 'absolute-value' value of GradientThresholdMethod is a value-based gradient clipping method.

### L2 Regularization

Adding a regularization term for the weights to the loss function $E\left(\theta \right)$ is one way to reduce overfitting [1], [2]. The regularization term is also called weight decay. The loss function with the regularization term takes the form

${E}_{R}\left(\theta \right)=E\left(\theta \right)+\lambda \Omega \left(w\right),$

where $w$ is the weight vector, $\lambda$ is the regularization factor (coefficient), and the regularization function $\Omega \left(w\right)$ is

$\Omega \left(w\right)=\frac{1}{2}{w}^{T}w.$

Note that the biases are not regularized [2]. You can specify the regularization factor $\lambda$ by using the L2Regularization training option. You can also specify different regularization factors for different layers and parameters. For more information, see Set Up Parameters in Convolutional and Fully Connected Layers.

The loss function that the software uses for network training includes the regularization term. However, the loss value displayed in the command window and training progress plot during training is the loss on the data only and does not include the regularization term.

## References

[1] Bishop, C. M. Pattern Recognition and Machine Learning. Springer, New York, NY, 2006.

[2] Murphy, K. P. Machine Learning: A Probabilistic Perspective. The MIT Press, Cambridge, Massachusetts, 2012.

[3] Pascanu, R., T. Mikolov, and Y. Bengio. "On the difficulty of training recurrent neural networks". Proceedings of the 30th International Conference on Machine Learning. Vol. 28(3), 2013, pp. 1310–1318.

[4] Kingma, Diederik, and Jimmy Ba. "Adam: A method for stochastic optimization." arXiv preprint arXiv:1412.6980 (2014).

## Version History

Introduced in R2016a

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