TrainingOptionsSGDM

Training options for stochastic gradient descent with momentum

Description

Training options for stochastic gradient descent with momentum, including learning rate information, L₂ regularization factor, and mini-batch size.

Creation

Create a TrainingOptionsSGDM object using trainingOptions and specifying "sgdm" as the first input argument.

Properties

SGDM

MaxEpochs — Maximum number of epochs

30 (default) | positive integer

Maximum number of epochs (full passes of the data) to use for training, specified as a positive integer.

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

MiniBatchSize — Size of mini-batch

128 (default) | positive integer

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 the software discards the training data that does not fit into the final complete mini-batch of each epoch. If the mini-batch size is smaller then the number of training samples, then the software does not discard any data.

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

Shuffle — Option for data shuffling

"once" (default) | "never" | "every-epoch"

Option for data shuffling, specified as one of these values:

• "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 neural network validation. If the mini-batch size does not evenly divide the number of training samples, then the software 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".

InitialLearnRate — Initial learning rate

0.01 (default) | positive scalar

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

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

LearnRateScheduleSettings — Settings for learning rate schedule

structure

This property is read-only.

Settings for the learning rate schedule, specified as a structure. LearnRateScheduleSettings has the field Method, which specifies the type of method for adjusting the learning rate. The possible methods are:

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

• 'piecewise' — The learning rate drops periodically during training.

If Method is 'piecewise', then LearnRateScheduleSettings contains two more fields:

• DropRateFactor — The multiplicative factor by which the learning rate drops during training

• DropPeriod — The number of epochs that passes between adjustments to the learning rate during training

Specify the settings for the learning schedule rate using trainingOptions.

Data Types: struct

Momentum — Contribution of previous step

0.9 (default) | scalar from 0 to 1

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.

For more information, see Stochastic Gradient Descent with Momentum.

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

Data Formats

InputDataFormats — Description of input data dimensions

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

Since R2023b

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 dimension of the data.

The characters are:

• "S" — Spatial

• "C" — Channel

• "B" — Batch

• "T" — Time

• "U" — Unspecified

For example, for an array containing a batch of sequences where the first, second, and third dimension correspond to channels, observations, and time steps, respectively, you can specify that it has the format "CBT".

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

For more information, see Deep Learning Data Formats.

This option supports the trainnet function only.

Data Types: char | string | cell

TargetDataFormats — Description of target data dimensions

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

Since R2023b

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

• "auto" — If the target data has the same number of dimensions as the input data, then the trainnet function uses the format specified by InputDataFormats. If the target data has a different number of dimensions to the input data, then the trainnet function uses the format expected by the loss function.

• Data formats, specified as a string array, character vector, or cell array of character vectors — The trainnet function uses the specified data formats.

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

The characters are:

• "S" — Spatial

• "C" — Channel

• "B" — Batch

• "T" — Time

• "U" — Unspecified

For example, for an array containing a batch of sequences where the first, second, and third dimension correspond to channels, observations, and time steps, respectively, you can specify that it has the format "CBT".

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

For more information, see Deep Learning Data Formats.

This option supports the trainnet function only.

Data Types: char | string | cell

Monitoring

Plots — Plots to display during neural network training

"none" (default) | "training-progress"

Plots to display during neural network training, specified as one of these values:

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

• "training-progress" — Plot training progress.

trainnet Function

The plot shows the mini-batch loss, validation loss, training mini-batch and validation metrics as specified by the Metrics property, and additional information about the training progress.

To programmatically open and close the training progress plot after training, use the show and close functions with the second output of the trainnet function. You can use the show function to view the training progress even if the Plots training option is specified as "none".

trainNetwork Function

The plot shows the mini-batch loss and accuracy, validation loss and accuracy, and additional information about the training progress. For more information about the trainNetwork training progress plot, see Monitor Deep Learning Training Progress.

Metrics — Metrics to track

[] (default) | character vector | string array | function handle | cell array | metric object

Since R2023b

Metrics to track, specified as a character vector or string scalar of a built-in metric name, a string array of names, a built-in or custom metric object, a function handle (@myMetric), or a cell array of names, metric objects, and function handles.

• Built-in metric name — Specify metrics as a string scalar, character vector, or string array of built-in metric names. Supported values are "accuracy", "fscore", "recall", "precision", "rmse", and "auc".

• Built-in metric object — If you need more flexibility, you can use built-in metric objects. The software supports these built-in metric objects:

  • AccuracyMetric

  • AUCMetric

  • FScoreMetric

  • PrecisionMetric

  • RecallMetric

  • RMSEMetric

  When you create a built-in metric object, you can specify additional options such as the averaging type and whether the task is single-label or multilabel.

• Custom metric function handle — If the metric you need is not a built-in metric, then you can specify custom metrics using a function handle. The function must have the syntax metric = metricFunction(Y,T), where Y corresponds to the network predictions and T corresponds to the target responses. For networks with multiple outputs, the syntax must be metric = metricFunction(Y1,…,YN,T1,…TM), where N is the number of outputs and M is the number of targets. For more information, see Define Custom Metric Function.

  Note

  When you have validation data in mini-batches, the software computes the validation metric for each mini-batch and then returns the average of those values. For some metrics, this behavior can result in a different metric value than if you compute the metric using the whole validation set at once. In most cases, the values are similar. To use a custom metric that is not batch-averaged for the validation data, you must create a custom metric object. For more information, see Define Custom Deep Learning Metric Object.

• Custom metric object — If you need greater customization, then you can define your own custom metric object. For an example that shows how to create a custom metric, see Define Custom F-Beta Score Metric Object . For general information about creating custom metrics, see Define Custom Deep Learning Metric Object. Specify your custom metric as the Metrics option of the trainingOptions function.

This option supports the trainnet and trainBERTDocumentClassifier (Text Analytics Toolbox) functions only.

Example: Metrics=["accuracy","fscore"]

Example: Metrics=["accuracy",@myFunction,precisionObj]

Verbose — Flag to display training progress information

1 (true) (default) | 0 (false)

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

The content of the verbose output depends on the function that you use for training.

trainnet Function

When you use the trainnet function, the verbose output displays a table with these variables:

Variable	Description
Iteration	Iteration number
Epoch	Epoch number
TimeElapsed	Time elapsed in hours, minutes, and seconds
LearnRate	Learning rate
TrainingLoss	Training loss
ValidationLoss	Validation loss. If you do not specify validation data, then the software does not display this information.

If you specify additional metrics in the training options, then they also appear in the verbose output. For example, if you set the Metrics training option to "accuracy", then the information includes the TrainingAccuracy and ValidationAccuracy variables.

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

To specify validation data, use the ValidationData training option.

trainNetwork Function

When you use the trainNetwork function, the verbose output displays a table. The variables of the table depends on the type of neural network.

For classification neural networks, the table contains these variables:

Variable	Description
Epoch	Epoch number. An epoch corresponds to a full pass of the data.
Iteration	Iteration number. An iteration corresponds to a mini-batch.
Time Elapsed	Time elapsed in hours, minutes, and seconds.
Mini-batch Accuracy	Classification accuracy on the mini-batch.
Validation Accuracy	Classification accuracy on the validation data. If you do not specify validation data, then the software does not display this information.
Mini-batch Loss	Loss 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 Loss	Loss 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 software does not display this information.
Base Learning Rate	Base learning rate. The software multiplies the learn rate factors of the layers by this value.

For regression neural networks, the table contains these variables:

Variable	Description
Epoch	Epoch number. An epoch corresponds to a full pass of the data.
Iteration	Iteration number. An iteration corresponds to a mini-batch.
Time Elapsed	Time elapsed in hours, minutes, and seconds.
Mini-batch RMSE	Root-mean-squared-error (RMSE) on the mini-batch.
Validation RMSE	RMSE on the validation data. If you do not specify validation data, then the software does not display this information.
Mini-batch Loss	Loss on the mini-batch. If the output layer is a RegressionOutputLayer object, then the loss is the half-mean-squared-error.
Validation Loss	Loss 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 information.
Base Learning Rate	Base 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

VerboseFrequency — Frequency of verbose printing

50 (default) | positive integer

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 neural network during training, then the software also prints to the command window every time validation occurs.

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

Validation

ValidationData — Data to use for validation during training

[] (default) | datastore | table | cell array

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

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

If your neural 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 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 neural network validation.

The supported formats depend on the training function that you use.

trainnet Function

Specify the validation data as a datastore or the cell array {predictors,targets}, where predictors contains the validation predictors and targets contains the validation targets. Specify the validation predictors and targets using any of the formats supported by the trainnet function.

For more information, see the input arguments of the trainnet function.

trainNetwork Function

Specify the validation data as a datastore, table, or the cell array {predictors,targets}, where predictors contains the validation predictors and targets contains the validation targets. Specify the validation predictors and targets using any of the formats supported by the trainNetwork function.

For more information, see the input arguments of the trainNetwork function.

trainBERTDocumentClassifier Function (Text Analytics Toolbox)

Specify the validation data as one of these values:

• Cell array {documents,targets}, where documents contains the input documents, and targets contains the document labels

• Table, where the first variable contains the input documents and the second variable contains the document labels.

For more information, see the input arguments of the trainBERTDocumentClassifier (Text Analytics Toolbox) function.

ValidationFrequency — Frequency of neural network validation

50 (default) | positive integer

Frequency of neural 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

ValidationPatience — Patience of validation stopping

Inf (default) | positive integer

Patience of validation stopping of neural 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 neural network training stops. If ValidationPatience is Inf, then the values of the validation loss do not cause training to stop early.

The returned neural network depends on the OutputNetwork training option. To return the neural 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

OutputNetwork — Neural network to return when training completes

"last-iteration" (default) | "best-validation-loss"

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

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

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

Regularization and Normalization

L2Regularization — Factor for L₂ regularization

0.0001 (default) | nonnegative scalar

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 neural 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

ResetInputNormalization — Option to reset input layer normalization

1 (true) (default) | 0 (false)

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

BatchNormalizationStatistics — Mode to evaluate statistics in batch normalization layers

"auto" (default) | "population" | "moving"

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

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

  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, $$\widehat{\mu }$$ and $$\widehat{{\sigma }^2}$$ 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.

• "auto" — Use the "moving" option for the trainnet function and the "population" option for the trainNetwork function.

Gradient Clipping

GradientThreshold — Gradient threshold

Inf (default) | positive scalar

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.

For more information, see Gradient Clipping.

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

GradientThresholdMethod — Gradient threshold method

"l2norm" (default) | "global-l2norm" | "absolute-value"

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.

For more information, see Gradient Clipping.

Sequence

SequenceLength — Option to pad or truncate sequences

"longest" (default) | "shortest" | positive integer

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 neural 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.

  • This option supports the trainNetwork function only.

To learn more about the effect of padding, truncating, and splitting the input sequences, see Sequence Padding, Truncation, and Splitting.

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

SequencePaddingDirection — Direction of padding or truncation

"right" (default) | "left"

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 neural 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".

To learn more about the effect of padding, truncating, and splitting the input sequences, see Sequence Padding, Truncation, and Splitting.

SequencePaddingValue — Value to pad sequences

0 (default) | scalar

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

Do not pad sequences with NaN, because doing so can propagate errors throughout the neural network.

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

Hardware

ExecutionEnvironment — Hardware resource for training neural network

"auto" (default) | "cpu" | "gpu" | "multi-gpu" | "parallel" | "parallel-auto" | "parallel-cpu" | "parallel-gpu"

Hardware resource for training neural network, specified as one of these values:

Execution Environment	Hardware Resources Used
"auto"	Use a local GPU if one is available. Otherwise, use the local CPU.
"cpu"	Use the local CPU.
"gpu"	Use the local 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. 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 and excess workers become idle. If the pool does not have GPUs, then training takes place on all available CPU workers instead.
"parallel-auto"	Use a local or remote parallel pool. 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 and excess workers become idle. If the pool does not have GPUs, then training takes place on all available CPU workers instead. This option supports the trainnet function only.
"parallel-cpu"	Use CPU resources in a local or remote parallel pool. If there is no current parallel pool, the software starts one using the default cluster profile. If the pool has access to GPUs, the GPUs will not be used. This option supports the trainnet function only.
"parallel-gpu"	Use GPUs in a local or remote parallel pool. Excess workers become idle. If there is no current parallel pool, the software starts one using the default cluster profile. This option supports the trainnet function only.

The "gpu", "multi-gpu", "parallel", "parallel-auto", "parallel-cpu", and "parallel-gpu" 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.

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

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

When you train a network using the trainNetwork function, the "multi-gpu" and "parallel" options do not support neural networks containing custom layers with state parameters or built-in layers that are stateful at training time. For example:

• recurrent layers such as LSTMLayer, BiLSTMLayer, or GRULayer objects when the SequenceLength training option is a positive integer

• BatchNormalizationLayer objects when the BatchNormalizationStatistics training option is set to "moving"

WorkerLoad — Parallel worker load division

scalar from 0 to 1 | positive integer | numeric vector

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 neural network training computation. If you train the neural 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 neural network training computation. If you train the neural 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 — Neural 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 neural 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.

This option supports stochastic solvers only (when the solverName argument is "sgdm", "adam", or "rmsprop").

This option supports the trainNetwork function only.

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

DispatchInBackground — Flag to enable background dispatch

0 (false) (default) | 1 (true)

Flag to enable background dispatch, specified as 0 (false) or 1 (true).

Background dispatch uses parallel workers to fetch and preprocess data from a datastore during training. Use this option when your mini-batches require significant preprocessing. For more information on when to use background dispatch, see Use Datastore for Parallel Training and Background Dispatching.

When DispatchInBackground is set to true, the software opens a local parallel pool using the default profile, if a local pool is not currently open. Non-local parallel pools are not supported.

Using this option requires Parallel Computing Toolbox. The input datastore must be subsettable or partitionable. To use this option, custom datastores must implement the matlab.io.datastore.Subsettable class.

This option supports stochastic solvers only (when the solverName argument is "sgdm", "adam", or "rmsprop").

This option does not support the trainnet function when training in parallel.

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

Checkpoints

CheckpointPath — Path for saving checkpoint neural networks

"" (default) | string scalar | character vector

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

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

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

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

For more information about saving neural network checkpoints, see Save Checkpoint Networks and Resume Training.

Data Types: char | string

CheckpointFrequency — Frequency of saving checkpoint neural networks

1 (default) | positive integer

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

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

If CheckpointFrequencyUnit is "iteration", then the software saves checkpoint neural 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

CheckpointFrequencyUnit — Checkpoint frequency unit

"epoch" (default) | "iteration"

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

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

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

This option only has an effect when CheckpointPath is nonempty.

OutputFcn — Output functions

function handle | cell array of function handles

Output functions to call during training, specified as a function handle or cell array of function handles. The software calls the functions once before the start of training, after each iteration, and once when training is complete.

The functions must have the syntax stopFlag = f(info), where info is a structure containing information about the training progress, and stopFlag is a scalar that indicates to stop training early. If stopFlag is 1 (true), then the software stops training. Otherwise, the software continues training.

The fields of the structure info depend on the training function that you use.

trainnet Function

The trainnet function passes the output function the structure info that contains these fields:

Field	Description
Epoch	Epoch number
Iteration	Iteration number
TimeElapsed	Time since start of training
LearnRate	Iteration learn rate
TrainingLoss	Iteration training loss
ValidationLoss	Validation loss, if specified and evaluated at iteration.
State	Iteration training state, specified as "start", "iteration", or "done".

If you specify additional metrics in the training options, then they also appear in the training information. For example, if you set the Metrics training option to "accuracy", then the information includes the TrainingAccuracy and ValidationAccuracy fields.

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

For an example showing how to use output functions, see Customize Output During Deep Learning Network Training.

trainNetwork Function

The trainNetwork function passes the output function the structure info that contains these fields:

Field	Description
Epoch	Current epoch number
Iteration	Current iteration number
TimeSinceStart	Time in seconds since the start of training
TrainingLoss	Current mini-batch loss
ValidationLoss	Loss on the validation data
BaseLearnRate	Current base learning rate
TrainingAccuracy	Accuracy on the current mini-batch (classification neural networks)
TrainingRMSE	RMSE on the current mini-batch (regression neural networks)
ValidationAccuracy	Accuracy on the validation data (classification neural networks)
ValidationRMSE	RMSE on the validation data (regression neural networks)
State	Current training state, with a possible value of "start", "iteration", or "done".

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

For an example showing how to use output functions, see Customize Output During Deep Learning Network Training.

Data Types: function_handle | cell

Examples

Specify Training Options

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
                       MaxEpochs: 20
               LearnRateSchedule: 'piecewise'
             LearnRateDropFactor: 0.2000
             LearnRateDropPeriod: 5
                   MiniBatchSize: 64
                         Shuffle: 'once'
                      WorkerLoad: []
             CheckpointFrequency: 1
         CheckpointFrequencyUnit: 'epoch'
                  SequenceLength: 'longest'
            DispatchInBackground: 0
                L2Regularization: 1.0000e-04
         GradientThresholdMethod: 'l2norm'
               GradientThreshold: Inf
                         Verbose: 1
                VerboseFrequency: 50
                  ValidationData: []
             ValidationFrequency: 50
              ValidationPatience: Inf
                  CheckpointPath: ''
            ExecutionEnvironment: 'auto'
                       OutputFcn: []
                         Metrics: []
                           Plots: 'training-progress'
            SequencePaddingValue: 0
        SequencePaddingDirection: 'right'
                InputDataFormats: "auto"
               TargetDataFormats: "auto"
         ResetInputNormalization: 1
    BatchNormalizationStatistics: 'auto'
                   OutputNetwork: 'last-iteration'

Algorithms

Stochastic Gradient Descent

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.

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 the learning rate α and the momentum value $$\gamma$$ determine the contribution of the previous gradient step to the current iteration.

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.

Gradient Clipping

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.

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.

Version History

Introduced in R2016a

R2023b: Specify input and target data formats

Specify the input and target data formats using the InputDataFormats and TargetDataFormats options, respectively.

This option supports the trainnet function only.

R2023b: Train neural network in parallel using only CPU or only GPU resources

Train a neural network in parallel using specific hardware resources by specifying the ExecutionEnvironment as "parallel-cpu" or "parallel-gpu".

This option supports the trainnet function only.

R2023b: BatchNormalizationStatistics default is "auto"

Starting in R2023b, the BatchNormalizationStatistics training option default value is "auto".

This change does not affect the behavior of the function. If you have code that checks the BatchNormalizationStatistics property, then update your code to account for the "auto" option.

R2022b: trainNetwork pads mini-batches to length of longest sequence before splitting when you specify SequenceLength training option as an integer

Starting in R2022b, when you train a neural network with sequence data using the trainNetwork function and the SequenceLength option is an integer, the software pads sequences to the length of the longest sequence in each mini-batch and then splits the sequences into mini-batches with the specified sequence length. If SequenceLength does not evenly divide the sequence length of the mini-batch, then the last split mini-batch has a length shorter than SequenceLength. This behavior prevents the neural network training on time steps that contain only padding values.

In previous releases, the software pads mini-batches of sequences to have a length matching the nearest multiple of SequenceLength that is greater than or equal to the mini-batch length and then splits the data. To reproduce this behavior, use a custom training loop and implement this behavior when you preprocess mini-batches of data.

R2018b: ValidationPatience training option default is Inf

Starting in R2018b, the default value of the ValidationPatience training option is Inf, which means that automatic stopping via validation is turned off. This behavior prevents the training from stopping before sufficiently learning from the data.

In previous versions, the default value is 5. To reproduce this behavior, set the ValidationPatience option to 5.