# trainingOptions

Options for training deep learning neural network

## Description

returns training options for the optimizer specified by
`options`

= trainingOptions(`solverName`

)`solverName`

. To train a neural network, use the
training options as an input argument to the `trainnet`

function.

returns training options with additional options specified by one or more
name-value arguments.`options`

= trainingOptions(`solverName`

,`Name=Value`

)

## 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' CheckpointFrequency: 1 CheckpointFrequencyUnit: 'epoch' SequenceLength: 'longest' PreprocessingEnvironment: 'serial' L2Regularization: 1.0000e-04 GradientThresholdMethod: 'l2norm' GradientThreshold: Inf Verbose: 1 VerboseFrequency: 50 ValidationData: [] ValidationFrequency: 50 ValidationPatience: Inf ObjectiveMetricName: 'loss' CheckpointPath: '' ExecutionEnvironment: 'auto' OutputFcn: [] Metrics: [] Plots: 'training-progress' SequencePaddingValue: 0 SequencePaddingDirection: 'right' InputDataFormats: "auto" TargetDataFormats: "auto" ResetInputNormalization: 1 BatchNormalizationStatistics: 'auto' OutputNetwork: 'auto' Acceleration: "auto"

### Monitor Deep Learning Training Progress

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

When you train networks for deep learning, plotting various metrics during training enables you to 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 `trainnet`

function. If you are training a network using a custom training loop, use a `trainingProgressMonitor`

object instead 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, the `trainnet`

function 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 `trainnet`

validates the network. The figure plots the loss and any metrics specified by the `Metrics`

name-value option. By default, the software uses a linear scale for the plots. To specify a logarithmic scale for the y-axis, select the log scale button in the axes toolbar.

During training, you can stop training and return the current state of the network by clicking the stop button in the top-right corner. After you click the stop button, it can take a while for training to complete. Once training is complete, `trainnet`

returns the trained network.

Specify the `OutputNetwork`

training option as `"best-validation"`

to get finalized values that correspond to the iteration with the best validation metric value, where the optimized metric is specified by the `ObjectiveMetricName`

training options. Specify the `OutputNetwork`

training option as `"last-iteration"`

to get finalized metrics that correspond to the last training iteration.

On the right of the pane, 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 as Image** in the training window. You can save the plot as a PNG, JPEG, TIFF, or PDF file. You can also save the individual plots using the axes toolbar.

**Plot Training Progress During Training**

Train a network and plot the training progress during training.

Load the training and test data from the MAT files `DigitsDataTrain.mat`

and `DigitsDataTest`

`.mat`

, respectively. The training and test data sets each contain 5000 images.

load DigitsDataTrain.mat load DigitsDataTest.mat

Create a `dlnetwork`

object.

net = dlnetwork;

Specify the layers of the classification branch and add them to the network.

layers = [ imageInputLayer([28 28 1]) convolution2dLayer(3,8,Padding="same") batchNormalizationLayer reluLayer maxPooling2dLayer(2,Stride=2) convolution2dLayer(3,16,Padding="same") batchNormalizationLayer reluLayer maxPooling2dLayer(2,Stride=2) convolution2dLayer(3,32,Padding="same") batchNormalizationLayer reluLayer fullyConnectedLayer(10) softmaxLayer]; net = addLayers(net,layers);

Specify options for network training. To validate the network at regular intervals during training, specify validation data. Record the metric values for the accuracy an F-score. To plot training progress during training, set the `Plots`

training option to `"training-progress"`

.

options = trainingOptions("sgdm", ... MaxEpochs=8, ... Metrics = ["accuracy","fscore"], ... ValidationData={XTest,labelsTest}, ... ValidationFrequency=30, ... Verbose=false, ... Plots="training-progress");

Train the network.

`net = trainnet(XTrain,labelsTrain,net,"crossentropy",options);`

### Stop Training Early Using Metrics

Use metrics for early stopping and to return the best network.

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.

```
net = dlnetwork;
layers = [
imageInputLayer([28 28 1])
convolution2dLayer(3,8,Padding="same")
batchNormalizationLayer
reluLayer
fullyConnectedLayer(10)
softmaxLayer];
net = addLayers(net,layers);
```

Specify the training options:

Use an SGDM solver for training.

Monitor training performance by specifying validation data and validation frequency.

Track the accuracy and recall during training. To return the network with the best recall value, specify

`"recall"`

as the objective metric and set the output network to`"best-validation"`

.Specify the validation patience as 5 so training stops if the recall has not decreased for five iterations.

Visualize network training progress plot.

Suppress the verbose output.

options = trainingOptions("sgdm", ... ValidationData={XValidation,YValidation}, ... ValidationFrequency=35, ... ValidationPatience=5, ... Metrics=["accuracy","recall"], ... ObjectiveMetricName="recall", ... OutputNetwork="best-validation", ... Plots="training-progress", ... Verbose=false);

Train the network.

`net = trainnet(XTrain,YTrain,net,"crossentropy",options);`

## Input Arguments

`solverName`

— Solver for training neural network

`"sgdm"`

| `"rmsprop"`

| `"adam"`

| `"lbfgs"`

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

`"sgdm"`

— Stochastic gradient descent with momentum (SGDM). SGDM is a stochastic solver. For additional training options, see Stochastic Solver Options. For more information, see Stochastic Gradient Descent with Momentum.`"rmsprop"`

— Root mean square propagation (RMSProp). RMSProp is a stochastic solver. For additional training options, see Stochastic Solver Options. For more information, see Root Mean Square Propagation.`"adam"`

— Adaptive moment estimation (Adam). Adam is a stochastic solver. For additional training options, see Stochastic Solver Options. For more information, see Adaptive Moment Estimation.`"lbfgs"`

*(since R2023b)*— Limited-memory Broyden–Fletcher–Goldfarb–Shanno (L-BFGS). L-BFGS is a batch solver. Use the L-BFGS algorithm for small networks and data sets that you can process in a single batch. For additional training options, see L-BFGS Solver Options. For more information, see Limited-Memory BFGS.

The `trainBERTDocumentClassifier`

(Text Analytics Toolbox) function supports
the `"sgdm"`

, `"rmsprop"`

, and
`"adam"`

solvers only.

### 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: **`Plots="training-progress",Metrics="accuracy",Verbose=false`

specifies to disable the verbose output and display the training progress in
a plot that also includes the accuracy metric.

**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.

The contents of the plot depends on the solver that you use.

When the

`solverName`

argument is`"sgdm"`

,`"adam"`

, or`"rmsprop"`

, the plot shows the mini-batch loss, validation loss, training mini-batch and validation metrics specified by the`Metrics`

option, and additional information about the training progress.When the

`solverName`

argument is`"lbfgs"`

, the plot shows the training and validation loss, training and validation metrics specified by the`Metrics`

option, 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"`

.

To switch the y-axis scale to logarithmic, use the axes toolbar.

`Metrics`

— Metrics to track

`[]`

(default) | character vector | string array | function handle | `deep.DifferentiableFunction`

object* (since R2024a)*
| 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`

), a `deep.DifferentiableFunction`

object, 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"`

,`"auc"`

,`"fscore"`

,`"precision"`

,`"recall"`

, and`"rmse"`

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

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.

`deep.DifferentiableFunction`

object*(since R2024a)*— Function object with custom backward function. For more information, see Define Custom Deep Learning Operations.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}`

`ObjectiveMetricName`

— Name of objective metric

`"loss"`

(default) | string scalar | character vector

*Since R2024a*

Name of objective metric to use for early stopping and returning the best network, specified as a string scalar or character vector.

The metric name must be `"loss"`

or match the name of a
metric specified by the `Metrics`

name-value argument.
Metrics specified using function handles are not supported. To specify the
`ObjectiveMetricName`

value as the name of a
custom metric, the value of the `Maximize`

property of
the custom metric object must be nonempty. For more information, see Define Custom Deep Learning Metric Object.

For more information about specifying the objective metric for early stopping,
see `ValidationPatience`

. For more information about returning
the best network using the objective metric, see `OutputNetwork`

.

**Data Types: **`char`

| `string`

`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 type of solver.

For stochastic solvers (SGDM, Adam, and RMSProp), the table contains 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. |

For the L-BFGS solver, the table contains these variables:

Variable | Description |
---|---|

`Iteration` | Iteration number. |

`TimeElapsed` | Time elapsed in hours, minutes, and seconds. |

`TrainingLoss` | Training loss. |

`ValidationLoss` | Validation loss. If you do not specify validation data, then the software does not display this information. |

`GradientNorm` | Norm of the gradients. |

`StepNorm` | Norm of the steps. |

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.

**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.

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

To enable this property, set the `Verbose`

training option to
`1`

(`true`

).

**Data Types: **`single`

| `double`

| `int8`

| `int16`

| `int32`

| `int64`

| `uint8`

| `uint16`

| `uint32`

| `uint64`

`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 `trainnet`

function passes the output function the structure
`info`

.

For stochastic solvers (SGDM, Adam, and RMSProp), `info`

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"` . |

For the L-BFGS solver, `info`

contains these fields:

Field | Description |
---|---|

`Iteration` | Iteration number |

`TimeElapsed` | Time elapsed in hours, minutes, and seconds |

`TrainingLoss` | Training loss |

`ValidationLoss` | Validation loss. If you do not specify validation data, then the software does not display this information. |

`GradientNorm` | Norm of the gradients |

`StepNorm` | Norm of the steps |

`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 Custom Stopping Criteria for Deep Learning Training.

**Data Types: **`function_handle`

| `cell`

**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 data dimension.

The characters are:

`"S"`

— Spatial`"C"`

— Channel`"B"`

— Batch`"T"`

— Time`"U"`

— Unspecified

For example, consider an array containing a batch of sequences where the first, second,
and third dimensions correspond to channels, observations, and time steps, respectively. You
can specify that this array has the format `"CBT"`

(channel, batch,
time).

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 after the second dimension.

For a neural networks with multiple inputs `net`

, specify an array of
input data formats, where `InputDataFormats(i)`

corresponds to the
input `net.InputNames(i)`

.

For more information, see Deep Learning Data Formats.

**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.String array, character vector, or cell array of character vectors — The

`trainnet`

function uses the data formats you specify.

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

The characters are:

`"S"`

— Spatial`"C"`

— Channel`"B"`

— Batch`"T"`

— Time`"U"`

— Unspecified

For example, consider an array containing a batch of sequences where the first, second,
and third dimensions correspond to channels, observations, and time steps, respectively. You
can specify that this array has the format `"CBT"`

(channel, batch,
time).

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 after the second dimension.

For more information, see Deep Learning Data Formats.

**Data Types: **`char`

| `string`

| `cell`

**Stochastic Solver Options**

`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.

This option supports stochastic solvers only (when the `solverName`

argument is `"sgdm"`

, `"adam"`

, or
`"rmsprop"`

).

**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 than the number of training samples, then the software does not discard any data.

This option supports stochastic solvers only (when the `solverName`

argument is `"sgdm"`

, `"adam"`

, or
`"rmsprop"`

).

**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"`

.

This option supports stochastic solvers only (when the `solverName`

argument is `"sgdm"`

, `"adam"`

, or
`"rmsprop"`

).

`InitialLearnRate`

— Initial learning rate

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.

`solverName`

argument is `"sgdm"`

, `"adam"`

, or
`"rmsprop"`

).

When `solverName`

is
`"sgdm"`

, the default value is
`0.01`

. When
`solverName`

is
`"rmsprop"`

or
`"adam"`

, the default value is
`0.001`

.

**Data Types: **`single`

| `double`

| `int8`

| `int16`

| `int32`

| `int64`

| `uint8`

| `uint16`

| `uint32`

| `uint64`

`LearnRateSchedule`

— Option for dropping learning rate during training

`"none"`

(default) | `"piecewise"`

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

`"none"`

— Keep learning rate constant throughout training.`"piecewise"`

— Update the learning rate periodically by multiplying it by a drop factor. To specify the period, use the`LearnRateDropPeriod`

training option. To specify the drop factor, use the`LearnRateDropFactor`

training option.

`solverName`

argument is `"sgdm"`

, `"adam"`

, or
`"rmsprop"`

).

`LearnRateDropPeriod`

— Number of epochs for dropping the learning rate

`10`

(default) | positive integer

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.

`solverName`

argument is `"sgdm"`

, `"adam"`

, or
`"rmsprop"`

).

**Data Types: **`single`

| `double`

| `int8`

| `int16`

| `int32`

| `int64`

| `uint8`

| `uint16`

| `uint32`

| `uint64`

`LearnRateDropFactor`

— Factor for dropping the learning rate

`0.1`

(default) | scalar from `0`

to
`1`

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.

`solverName`

argument is `"sgdm"`

, `"adam"`

, or
`"rmsprop"`

).

**Data Types: **`single`

| `double`

| `int8`

| `int16`

| `int32`

| `int64`

| `uint8`

| `uint16`

| `uint32`

| `uint64`

`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.

This option supports the SGDM solver only (when the `solverName`

argument is
`"sgdm"`

).

For more information, see Stochastic Gradient Descent with Momentum.

**Data Types: **`single`

| `double`

| `int8`

| `int16`

| `int32`

| `int64`

| `uint8`

| `uint16`

| `uint32`

| `uint64`

`GradientDecayFactor`

— Decay rate of gradient moving average

`0.9`

(default) | nonnegative scalar less than `1`

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 `β`

in the Adaptive Moment Estimation section._{1}

This option supports the Adam solver only (when the `solverName`

argument is
`"adam"`

).

For more information, see Adaptive Moment Estimation.

**Data Types: **`single`

| `double`

| `int8`

| `int16`

| `int32`

| `int64`

| `uint8`

| `uint16`

| `uint32`

| `uint64`

`SquaredGradientDecayFactor`

— Decay rate of squared gradient moving average

nonnegative scalar less than `1`

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
`β`

in
[4]._{2}

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.

This option supports the Adam and RMSProp solvers only (when the `solverName`

argument is `"adam"`

or
`"rmsprop"`

).

The default value is `0.999`

for the Adam
solver. The default value is `0.9`

for
the RMSProp solver.

For more information, see Adaptive Moment Estimation and Root Mean Square Propagation.

**Data Types: **`single`

| `double`

| `int8`

| `int16`

| `int32`

| `int64`

| `uint8`

| `uint16`

| `uint32`

| `uint64`

`Epsilon`

— Denominator offset

`1e-8`

(default) | positive scalar

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

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

This option supports the Adam and RMSProp solvers only (when the `solverName`

argument is `"adam"`

or
`"rmsprop"`

).

For more information, see Adaptive Moment Estimation and Root Mean Square Propagation.

**Data Types: **`single`

| `double`

| `int8`

| `int16`

| `int32`

| `int64`

| `uint8`

| `uint16`

| `uint32`

| `uint64`

**L-BFGS Solver Options**

`MaxIterations`

— Maximum number of iterations

`1000`

(default) | positive integer

*Since R2023b*

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

The L-BFGS solver is a full-batch solver, which means that it processes the entire training set in a single iteration.

This option supports the L-BFGS solver only (when the `solverName`

argument is
`"lbfgs"`

).

**Data Types: **`single`

| `double`

| `int8`

| `int16`

| `int32`

| `int64`

| `uint8`

| `uint16`

| `uint32`

| `uint64`

`LineSearchMethod`

— Method to find suitable learning rate

`"weak-wolfe"`

(default) | `"strong-wolfe"`

| `"backtracking"`

*Since R2023b*

Method to find suitable learning rate, specified as one of these values:

`"weak-wolfe"`

— Search for a learning rate that satisfies the weak Wolfe conditions. This method maintains a positive definite approximation of the inverse Hessian matrix.`"strong-wolfe"`

— Search for a learning rate that satisfies the strong Wolfe conditions. This method maintains a positive definite approximation of the inverse Hessian matrix.`"backtracking"`

— Search for a learning rate that satisfies sufficient decrease conditions. This method does not maintain a positive definite approximation of the inverse Hessian matrix.

This option supports the L-BFGS solver only (when the `solverName`

argument is
`"lbfgs"`

).

`HistorySize`

— Number of state updates to store

10 (default) | positive integer

*Since R2023b*

Number of state updates to store, specified as a positive integer. Values between 3 and 20 suit most tasks.

The L-BFGS algorithm uses a history of gradient calculations to approximate the Hessian matrix recursively. For more information, see Limited-Memory BFGS.

This option supports the L-BFGS solver only (when the `solverName`

argument is
`"lbfgs"`

).

**Data Types: **`single`

| `double`

| `int8`

| `int16`

| `int32`

| `int64`

| `uint8`

| `uint16`

| `uint32`

| `uint64`

`InitialInverseHessianFactor`

— Initial value that characterizes approximate inverse Hessian matrix

`1`

(default) | positive scalar

*Since R2023b*

Initial value that characterizes the approximate inverse Hessian matrix, specified as a positive scalar.

To save memory, the L-BFGS algorithm does not store and invert the dense Hessian matrix
*B*. Instead, the algorithm uses the approximation $${B}_{k-m}^{-1}\approx {\lambda}_{k}I$$, where *m* is the history size, the inverse Hessian
factor $${\lambda}_{k}$$ is a scalar, and *I* is the identity matrix. The
algorithm then stores the scalar inverse Hessian factor only. The algorithm updates the
inverse Hessian factor at each step.

The initial inverse hessian factor is the value of $${\lambda}_{0}$$.

For more information, see Limited-Memory BFGS.

This option supports the L-BFGS solver only (when the `solverName`

argument is
`"lbfgs"`

).

**Data Types: **`single`

| `double`

| `int8`

| `int16`

| `int32`

| `int64`

| `uint8`

| `uint16`

| `uint32`

| `uint64`

`MaxNumLineSearchIterations`

— Maximum number of line search iterations

`20`

(default) | positive integer

*Since R2023b*

Maximum number of line search iterations to determine the learning rate, specified as a positive integer.

This option supports the L-BFGS solver only (when the `solverName`

argument is
`"lbfgs"`

).

**Data Types: **`single`

| `double`

| `int8`

| `int16`

| `int32`

| `int64`

| `uint8`

| `uint16`

| `uint32`

| `uint64`

`GradientTolerance`

— Relative gradient tolerance

`1e-5`

(default) | positive scalar

*Since R2023b*

Relative gradient tolerance, specified as a positive scalar.

The software stops training when the relative gradient is less than or equal to `GradientTolerance`

.

This option supports the L-BFGS solver only (when the `solverName`

argument is
`"lbfgs"`

).

**Data Types: **`single`

| `double`

| `int8`

| `int16`

| `int32`

| `int64`

| `uint8`

| `uint16`

| `uint32`

| `uint64`

`StepTolerance`

— Step size tolerance

`1e-5`

(default) | positive scalar

*Since R2023b*

Step size tolerance, specified as a positive scalar.

The software stops training when the step that the algorithm takes is less than or equal to
`StepTolerance`

.

This option supports the L-BFGS solver only (when the `solverName`

argument is
`"lbfgs"`

).

**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 | `minibatchqueue`

object* (since R2024a)*

Data to use for validation during training, specified as `[]`

, a
datastore, a table, a cell array, or a `minibatchqueue`

object that
contains the validation predictors and targets.

During training, the software uses the validation data to calculate the validation loss and
metric values. To specify the validation frequency, use the `ValidationFrequency`

training option. You can also use the validation data to
stop training automatically when the validation objective metric stops improving. By
default, the objective metric is set to the loss. 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 loss can be lower than the training loss.

The software shuffles the validation data according to the `Shuffle`

training option. If
`Shuffle`

is `"every-epoch"`

, then the software
shuffles the validation data 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, `minibatchqueue`

object, 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.

`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 objective
metric on the validation set can be worse than or equal to the previous best value
before neural network training stops. If `ValidationPatience`

is
`Inf`

, then the values of the validation metric do not cause
training to stop early. The software aims to maximize or minimize the metric, as
specified by the `Maximize`

property of the metric. When the
objective metric is `"loss"`

, the software aims to minimize the loss
value.

The returned neural network depends on the `OutputNetwork`

training option. To return the neural network with the
best validation metric value, set the `OutputNetwork`

training option to
`"best-validation"`

.

*Before R2024a: The software computes the validation patience
using the validation loss value.*

**Data Types: **`single`

| `double`

| `int8`

| `int16`

| `int32`

| `int64`

| `uint8`

| `uint16`

| `uint32`

| `uint64`

`OutputNetwork`

— Neural network to return when training completes

`"auto"`

(default) | `"last-iteration"`

| `"best-validation"`

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

`"auto"`

– Use`"best-validation"`

if`ValidationData`

is specified. Otherwise, use`"last-iteration"`

.`"best-validation"`

– Return the neural network corresponding to the training iteration with the best validation metric value, where the metric to optimize is specified by the`ObjectiveMetricName`

option. To use this option, you must specify the`ValidationData`

training option.`"last-iteration"`

– Return the neural network corresponding to the last training iteration.

**Regularization and Normalization**

`L2Regularization`

— Factor for L_{2} regularization

`0.0001`

(default) | nonnegative scalar

Factor for L_{2} regularization (weight decay), specified as a
nonnegative scalar. For more information, see L2 Regularization.

**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.

**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 L_{2}norm of the gradient of a learnable parameter is larger than`GradientThreshold`

, then scale the gradient so that the L_{2}norm equals`GradientThreshold`

.`"global-l2norm"`

— If the global L_{2}norm,*L*, is larger than`GradientThreshold`

, then scale all gradients by a factor of`GradientThreshold/`

*L*. The global L_{2}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"`

Option to pad, truncate, or split input sequences, specified as one of these values:

`"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.

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

**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 and truncating sequences, see Sequence Padding and Truncation.

`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 and Acceleration**

`ExecutionEnvironment`

— Hardware resource for training neural network

`"auto"`

(default) | `"cpu"`

| `"gpu"`

| `"multi-gpu"`

| `"parallel-auto"`

| `"parallel-cpu"`

| `"parallel-gpu"`

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

`"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-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.*(since R2024a)**Before R2024a: Use*`"parallel"`

instead.`"parallel-cpu"`

– Use CPU resources in a local or remote parallel pool, ignoring any GPUs. If there is no current parallel pool, the software starts one using the default cluster profile.*(since R2023b)*`"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.*(since R2023b)*

The `"gpu"`

, `"multi-gpu"`

,
`"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.

The `"multi-gpu"`

,
`"parallel-auto"`

,
`"parallel-cpu"`

, and
`"parallel-gpu"`

options support
stochastic solvers only (when the `solverName`

argument is
`"sgdm"`

,
`"adam"`

, or
`"rmsprop"`

).

`PreprocessingEnvironment`

— Environment for fetching and preprocessing data

`"serial"`

(default) | `"background"`

| `"parallel"`

*Since R2024a*

Environment for fetching and preprocessing data from a datastore during training, specified as one of these values:

`"serial"`

– Fetch and preprocess data in serial.`"background"`

– Fetch and preprocess data using the background pool.`"parallel"`

– Fetch and preprocess data using parallel workers. The software opens a 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. This option is not supported when training in parallel (when the`ExecutionEnvironment`

option is`"parallel-auto"`

,`"parallel-cpu"`

,`"parallel-gpu"`

, or`"multi-gpu"`

).

To use the `"background"`

or `"parallel"`

options, the input datastore must be subsettable or partitionable. Custom datastores must implement the `matlab.io.datastore.Subsettable`

class.

The `"background"`

and `"parallel"`

options are not
supported when the `Shuffle`

option is `"never"`

.

Use the `"background"`

or `"parallel"`

options when your mini-batches require significant preprocessing. For more information about the preprocessing environment, see Use Datastore for Parallel Training and Background Preprocessing.

`solverName`

argument is `"sgdm"`

, `"adam"`

, or
`"rmsprop"`

).

*Before R2024a: To preprocess data
in parallel, set the
DispatchInBackground training
option to 1
(true).*

`Acceleration`

— Performance optimization

`"auto"`

(default) | `"none"`

*Since R2024a*

Performance optimization, specified as one of these values:

`"auto"`

– Automatically apply a number of optimizations suitable for the input network and hardware resources.`"none"`

– Disable all optimizations.

**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.

**Data Types: **`char`

| `string`

`CheckpointFrequency`

— Frequency of saving checkpoint neural networks

positive integer

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

If `solverName`

is `"lbfgs"`

or `CheckpointFrequencyUnit`

is
`"iteration"`

, then the software
saves checkpoint neural networks every
`CheckpointFrequency`

iterations.
Otherwise, the software saves checkpoint neural networks
every `CheckpointFrequency`

epochs.

When `solverName`

is
`"sgdm"`

,
`"adam"`

, or
`"rmsprop"`

, the default value is
`1`

. When
`solverName`

is
`"lbfgs"`

, default value is
`30`

.

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.

`solverName`

argument is `"sgdm"`

, `"adam"`

, or
`"rmsprop"`

).

## Output Arguments

`options`

— Training options

`TrainingOptionsSGDM`

| `TrainingOptionsRMSProp`

| `TrainingOptionsADAM`

| `TrainingOptionsLBFGS`

Training options, returned as a `TrainingOptionsSGDM`

, `TrainingOptionsRMSProp`

, `TrainingOptionsADAM`

, or `TrainingOptionsLBFGS`

object. To train a neural
network, use the training options as an input argument to the
`trainnet`

function.

If `solverName`

is `"sgdm"`

,
`"rmsprop"`

, `"adam"`

,
or `"lbfgs"`

, then the training options are
returned as a `TrainingOptionsSGDM`

,
`TrainingOptionsRMSProp`

,
`TrainingOptionsADAM`

, or
`TrainingOptionsLBFGS`

object,
respectively.

## Tips

For most deep learning tasks, you can use a pretrained neural network and adapt it to your own data. For an example showing how to use transfer learning to retrain a convolutional neural network to classify a new set of images, see Retrain Neural Network to Classify New Images. Alternatively, you can create and train neural networks from scratch using the

`trainnet`

and`trainingOptions`

functions.If the

`trainingOptions`

function does not provide the training options that you need for your task, then you can create a custom training loop using automatic differentiation. To learn more, see Train Network Using Custom Training Loop.If the

`trainnet`

function does not provide the loss function that you need for your task, then you can specify a custom loss function to the`trainnet`

as a function handle. For loss functions that require more inputs than the predictions and targets (for example, loss functions that require access to the neural network or additional inputs), train the model using a custom training loop. To learn more, see Train Network Using Custom Training Loop.If Deep Learning Toolbox™ does not provide the layers you need for your task, then you can create a custom layer. To learn more, see Define Custom Deep Learning Layers. For models that cannot be specified as networks of layers, you can define the model as a function. To learn more, see Train Network Using Model Function.

For more information about which training method to use for which task, see Train Deep Learning Model in MATLAB.

## Algorithms

### 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.

### 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.

### Root Mean Square Propagation

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. Root mean square propagation (RMSProp) is one such algorithm. It keeps a moving average of the element-wise squares of the parameter gradients,

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

*β _{2}* is the squared gradient
decay factor 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-β*, that is, 10, 100, and 1000 parameter updates, respectively. The RMSProp algorithm uses this moving average to normalize the updates of each parameter individually,

_{2})$${\theta}_{\ell +1}={\theta}_{\ell}-\frac{\alpha \nabla E\left({\theta}_{\ell}\right)}{\sqrt{{v}_{\ell}}+\u03f5}$$

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.

### Adaptive Moment Estimation

Adaptive moment estimation (Adam) [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,

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

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

The *β _{1}* and

*β*decay rates are the gradient decay and squared gradient decay factors, respectively. Adam uses the moving averages to update the network parameters as

_{2}$${\theta}_{\ell +1}={\theta}_{\ell}-\frac{\alpha {m}_{l}}{\sqrt{{v}_{l}}+\u03f5}$$

The value *α* is the learning rate. If gradients over
many iterations are similar, then using a moving average of the gradient enables the
parameter updates to pick up momentum in a certain direction. If the gradients contain
mostly noise, then the moving average of the gradient becomes smaller, and so the parameter
updates become smaller too. The full Adam update also includes a mechanism to correct a bias
the appears in the beginning of training. For more information, see [4].

### Limited-Memory BFGS

The L-BFGS algorithm [5] is a quasi-Newton method that approximates the Broyden-Fletcher-Goldfarb-Shanno (BFGS) algorithm. Use the L-BFGS algorithm for small networks and data sets that you can process in a single batch.

The algorithm updates learnable parameters *W* at iteration
*k+1* using the update step given by

$${W}_{k+1}={W}_{k}-{\eta}_{k}{B}_{k}^{-1}\nabla J({W}_{k}),$$

where *W _{k}* denotes the weights at iteration

*k*, $${\eta}_{k}$$ is the learning rate at iteration

*k*,

*B*is an approximation of the Hessian matrix at iteration

_{k}*k*, and $$\nabla J({W}_{k})$$ denotes the gradients of the loss with respect to the learnable parameters at iteration

*k*.

The L-BFGS algorithm computes the matrix-vector product $${B}_{k}^{-1}\nabla J({W}_{k})$$ directly. The algorithm does not require computing the inverse of
*B _{k}*.

To save memory, the L-BFGS algorithm does not store and invert the dense Hessian matrix
*B*. Instead, the algorithm uses the approximation $${B}_{k-m}^{-1}\approx {\lambda}_{k}I$$, where *m* is the history size, the inverse Hessian
factor $${\lambda}_{k}$$ is a scalar, and *I* is the identity matrix. The
algorithm then stores the scalar inverse Hessian factor only. The algorithm updates the
inverse Hessian factor at each step.

To compute the matrix-vector product $${B}_{k}^{-1}\nabla J({W}_{k})$$ directly, the L-BFGS algorithm uses this recursive algorithm:

Set $$r={B}_{k-m}^{-1}\nabla J({W}_{k})$$, where

*m*is the history size.For $$i=m,\text{\hspace{0.17em}}\dots ,\text{\hspace{0.17em}}1$$:

Let $$\beta =\frac{1}{{s}_{k-i}^{\top}{y}_{k-i}}{y}_{k-i}^{\top}r$$, where $${s}_{k-i}$$ and $${y}_{k-i}$$ are the step and gradient differences for iteration $$k-i$$, respectively.

Set $$r=r+\text{}{s}_{k-i}\text{}\left({a}_{k-i}-\beta \right)$$, where $$a$$ is derived from $$s$$, $$y$$, and the gradients of the loss with respect to the loss function. For more information, see [5].

Return $${B}_{k}^{-1}\nabla J({W}_{k})=r$$.

### 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.

### L_{2} 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.

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).

[5] Liu, Dong C.,
and Jorge Nocedal. "On the limited memory BFGS method for large scale optimization."
*Mathematical programming* 45, no. 1 (August 1989): 503-528. https://doi.org/10.1007/BF01589116.

## Version History

**Introduced in R2016a**

### R2024a: Specify validation data using `minibatchqueue`

object

Specify validation data as a `minibatchqueue`

object using the `ValidationData`

argument.

### R2024a: Automatic performance optimization

Accelerate training with automatic performance optimization. When you train a network
using the `trainnet`

function, automatic performance optimization is
enabled by default. You can disable performance optimization by setting the
`Acceleration`

option to `"none"`

using the
`trainingOptions`

function.

### R2024a: Specify metrics as `deep.DifferentiableFunction`

object

Specify the metrics as `deep.DifferentiableFunction`

object.

### R2024a: Setting `SequenceLength`

to an integer is not
recommended

Setting `SequenceLength`

to an integer is not
recommended, set `SequenceLength`

to
`"longest"`

or `"shortest"`

instead.

For `trainNetwork`

workflows (not recommended), you can
set `SequenceLength`

to an integer. If
`SequenceLength`

is an integer, then for each
mini-batch, the software pads 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 and updates the network recurrent state between
these 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.

### R2024a: `DispatchInBackground`

training option is not recommended

The `DispatchInBackground`

training option is not recommended. Use the
`PreprocessingEnvironment`

option instead.

The `PreprocessingEnvironment`

option provides the same functionality and also allows you to use the `backgroundPool`

for preprocessing when you set `PreprocessingEnvironment`

to `"background"`

.

This table shows how to update your code:

Not recommended | Recommended |
---|---|

`trainingOptions(solverName,DispatchInBackground=false)` (default) | `trainingOptions(solverName,PreprocessingEnvironment="serial")`
(default) |

`trainingOptions(solverName,DispatchInBackground=true)` | `trainingOptions(solverName,PreprocessingEnvironment="parallel")` |

There are no plans to remove the `DispatchInBackground`

option.

### R2024a: `OutputNetwork`

default is `"auto"`

Starting in R2024a, the `OutputNetwork`

training option default value is
`"auto"`

. If you have specified validation data, then the software
returns the network corresponding to the best validation metric value. If you have not
specified validation data, then the software returns the network corresponding to the last
training iteration. If you have validation data and want to replicate the previous default,
then set `OutputNetwork`

to `"last-iteration"`

.

This change applies when using the training options with `trainnet`

only. If you are using the training options with the `trainNetwork`

function, then there is no behavior change and by default the software returns the network
corresponding to the last training iteration.

### R2024a: `OutputNetwork`

value `"best-validation-loss"`

is not recommended

Specifying `OutputNetwork`

as `"best-validation-loss"`

is
not recommended. If you have code that set `OutputNetwork`

to
`"best-validation-loss"`

, then use `"best-validation"`

instead. The software returns the network corresponding to the best validation metric value
as specified by the `ObjectiveMetricName`

option. By default, the `ObjectiveMetricName`

value is set to
`"loss"`

. This behavior applies when using the training options with
the `trainnet`

function only.

When using the training options with the `trainNetwork`

function, if
you specify `OutputNetwork`

as `"best-validation"`

, then
software always returns the network with the best validation loss value.

### R2024a: `ExecutionEnvironment`

value `"parallel"`

is not recommended

Starting in R2024a, specifying the `ExecutionEnvironment`

option as `"parallel"`

is not recommended. Use `"parallel-auto"`

instead.

`"parallel-auto"`

has these advantages over `"parallel"`

:

The name of the option more accurately describes the execution environment, as the software trains in parallel automatically using whatever hardware is available.

The name of the option is consistent with the serial equivalent

`"auto"`

.

There are no plans to remove the `"parallel"`

option. `"parallel-auto"`

supports the `trainnet`

function only. If you are using the training options with the `trainNetwork`

function, then continue to use `"parallel"`

### R2024a: `WorkerLoad`

training option is not recommended

Starting in R2024a, specifying the `WorkerLoad`

training option is not recommended. Use `spmd`

(Parallel Computing Toolbox) or the `CUDA_VISIBLE_DEVICES`

environment variable instead.

There are no plans to remove support for `WorkerLoad`

for training networks using the `trainNetwork`

function. `WorkerLoad`

is not supported for training networks using the `trainnet`

function.

This table shows some typical usages of `WorkerLoad`

and how to update your code to use `spmd`

or the `CUDA_VISIBLE_DEVICES`

environment variable instead.

Not Recommended | Recommended |
---|---|

options = trainingOptions(solver, ... ExecutionEnvironment="multi-gpu", ... WorkerLoad=[1 1 0 1]); | % Alternative 1 pool = parpool(3); spmd if spmdIndex == 3 gpuDevice(spmdIndex + 1); else gpuDevice(spmdIndex); end end options = trainingOptions(solver, ... ExecutionEnvironment="multi-gpu"); % Alternative 2 % Set this environment variable immediately after your start MATLAB. setenv("CUDA_VISIBLE_DEVICES","0,1,3"); options = trainingOptions(solver, ... ExecutionEnvironment="multi-gpu"); |

options = trainingOptions(solver, ... ExecutionEnvironment="parallel", ... WorkerLoad=[1 1 0 1]); | pool = parpool(3); spmd if spmdIndex == 3 gpuDevice(spmdIndex + 1); else gpuDevice(spmdIndex); end end options = trainingOptions(solver, ... ExecutionEnvironment="parallel-auto"); |

If you were previously using the `WorkerLoad`

option to reserve a worker
to preprocess your data, consider also preprocessing you data in the background by
specifying the `PreprocessingEnvironment`

option as
`"background"`

.

### R2023b: Train neural network using L-BFGS solver

Train a neural network using the L-BFGS solver by specifying `solverName`

as `"lbfgs"`

. Use the L-BFGS algorithm for small networks and data sets that
you can process in a single batch. To customize the L-BFGS solver, use the L-BFGS Solver Options
properties.

This option supports the `trainnet`

function only.

### 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`

.

### R2018b: Different file name for checkpoint networks

Starting in R2018b, when saving checkpoint networks, the software assigns
file names beginning with `net_checkpoint_`

. In previous
versions, the software assigns file names beginning with
`convnet_checkpoint_`

.

If you have code that saves and loads checkpoint networks, then update your code to load files with the new name.

## See Also

`trainnet`

| `dlnetwork`

| `analyzeNetwork`

| Deep Network
Designer

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