TrainingOptionsLBFGS
Description
Use a TrainingOptionsLBFGS
object to set training options for the
limited-memory BFGS (L-BFGS) optimizer, including line search method and gradient and step
tolerances.
The L-BFGS algorithm [1] 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.
Creation
Create a TrainingOptionsLBFGS
object by using the trainingOptions
function and specifying "lbfgs"
as the first
input argument.
Properties
L-BFGS
MaxIterations
— Maximum number of iterations
1000
(default) | positive integer
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.
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"
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.
HistorySize
— Number of state updates to store
10
(default) | positive integer
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.
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
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 , where m is the history size, the inverse Hessian factor 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 .
For more information, see Limited-Memory BFGS.
Data Types: single
| double
| int8
| int16
| int32
| int64
| uint8
| uint16
| uint32
| uint64
MaxNumLineSearchIterations
— Maximum number of line search iterations
20
(default) | positive integer
Maximum number of line search iterations to determine the learning rate, specified as a positive integer.
Data Types: single
| double
| int8
| int16
| int32
| int64
| uint8
| uint16
| uint32
| uint64
GradientTolerance
— Relative gradient tolerance
1e-5
(default) | positive scalar
Relative gradient tolerance, specified as a positive scalar.
The software stops training when the relative gradient is less than or equal to GradientTolerance
.
Data Types: single
| double
| int8
| int16
| int32
| int64
| uint8
| uint16
| uint32
| uint64
StepTolerance
— Step size tolerance
1e-5
(default) | positive scalar
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
.
Data Types: single
| double
| int8
| int16
| int32
| int64
| uint8
| uint16
| uint32
| uint64
InitialStepSize
— Initial step size
[]
(default) | "auto"
| real finite scalar
Since R2024b
Initial step size, specified as one of these values:
[]
— Do not use an initial step size to determine the initial Hessian approximation."auto"
— Determine the initial step size automatically. The software uses an initial step size of , where W0 are the initial learnable parameters of the network.Positive real scalar — Use the specified value as the initial step size .
If InitialStepSize
is "auto"
or a positive real
scalar, then the software approximates the initial inverse Hessian using , where λ0 is the initial inverse
Hessian factor and denotes the gradients of the loss with respect to the initial learnable
parameters. For more information, see Limited-Memory BFGS.
Data Formats
InputDataFormats
— Description of input data dimensions
"auto"
(default) | string array | cell array of character vectors | character vector
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"
once each, at most. The software ignores singleton trailing
"U"
dimensions after the second dimension.
For a neural networks with multiple inputs net
, specify an array of
input data formats, where InputDataFormats(i)
corresponds to the
input net.InputNames(i)
.
For more information, see Deep Learning Data Formats.
Data Types: char
| string
| cell
TargetDataFormats
— Description of target data dimensions
"auto"
(default) | string array | cell array of character vectors | character vector
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 thetrainnet
function uses the format specified byInputDataFormats
. If the target data has a different number of dimensions to the input data, then thetrainnet
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"
once each, at most. The software ignores singleton trailing
"U"
dimensions after the second dimension.
For more information, see Deep Learning Data Formats.
Data Types: char
| string
| cell
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 plot shows the training and validation loss, training and validation metrics
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"
.
To switch the y-axis scale to logarithmic, use the axes toolbar.
For more information about the plot, see Monitor Deep Learning Training Progress.
Metrics
— Metrics to monitor
[]
(default) | character vector | string array | function handle | deep.DifferentiableFunction
object (since R2024a) | cell array | metric object
Metrics to monitor, specified as one of these values:
Built-in metric or loss function name — Specify metrics as a string scalar, character vector, or a cell array or string array of one or more of these names:
Metrics:
"accuracy"
— Accuracy (also known as top-1 accuracy)"auc"
— Area under ROC curve (AUC)"fscore"
— F-score (also known as F1-score)"precision"
— Precision"recall"
— Recall"rmse"
— Root mean squared error"mape"
— Mean absolute percentage error (MAPE) (since R2024b)
Loss functions:
"crossentropy"
— Cross-entropy loss for classification tasks. (since R2024b)"indexcrossentropy"
— Index cross-entropy loss for classification tasks. (since R2024b)"binary-crossentropy"
— Binary cross-entropy loss for binary and multilabel classification tasks. (since R2024b)"mae"
/"mean-absolute-error"
/"l1loss"
— Mean absolute error for regression tasks. (since R2024b)"mse"
/"mean-squared-error"
/"l2loss"
— Mean squared error for regression tasks. (since R2024b)"huber"
— Huber loss for regression tasks (since R2024b)
Note that setting the loss function as
"crossentropy"
and specifying"index-crossentropy"
as a metric or setting the loss function as"index-crossentropy"
and specifying"crossentropy"
as a metric is not supported.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)
, whereY
corresponds to the network predictions andT
corresponds to the target responses. For networks with multiple outputs, the syntax must bemetric = metricFunction(Y1,…,YN,T1,…TM)
, whereN
is the number of outputs andM
is the number of targets. For more information, see Define Custom Metric Function.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 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 thetrainingOptions
function.
If you specify a metric as a function handle, a deep.DifferentiableFunction
object, or a custom metric object and train the neural network using the
trainnet
function, then the layout of the targets that the software
passes to the metric depends on the data type of the targets, and the loss function that you
specify in the trainnet
function and the other metrics that you specify:
If the targets are numeric arrays, then the software passes the targets to the metric directly.
If the loss function is
"index-crossentropy"
and the targets are categorical arrays, then the software automatically converts the targets to numeric class indices and passes them to the metric.For other loss functions, if the targets are categorical arrays, then the software automatically converts the targets to one-hot encoded vectors and then passes them to the metric.
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
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
).
When this property is 1
(true
), the software displays this information:
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.
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
that 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
Validation
ValidationData
— Data to use for validation during training
[]
(default) | datastore | 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.
If ValidationData
is []
, then the software does not validate the neural network during training.
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.
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"
ifValidationData
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 theObjectiveMetricName
option. To use this option, you must specify theValidationData
training option."last-iteration"
– Return the neural network corresponding to the last training iteration.
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.
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 stepswhere and denote the updated mean and variance, respectively, and denote the mean and variance decay values, respectively, and denote the mean and variance of the layer input, respectively, and and 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 L2 norm of the gradient of a learnable parameter is larger thanGradientThreshold
, then scale the gradient so that the L2 norm equalsGradientThreshold
."global-l2norm"
— If the global L2 norm, L, is larger thanGradientThreshold
, then scale all gradients by a factor ofGradientThreshold/
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 thanGradientThreshold
, then scale the partial derivative to have magnitude equal toGradientThreshold
and retain the sign of the partial derivative.
For more information, see Gradient Clipping.
Sequence
SequenceLength
— Option to pad or truncate input sequences
"longest"
(default) | "shortest"
Option to pad or truncate the input sequences, specified as one of these options:
"longest"
— Pad sequences 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 to have the same length as the shortest sequence. This option ensures that the function does not add padding, at the cost of discarding data.
To learn more about the effects of padding and truncating the input sequences, see Sequence Padding and Truncation.
SequencePaddingDirection
— Direction of padding or truncation
"right"
(default) | "left"
Direction of padding or truncation, specified as one of these options:
"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 each sequence."left"
— Pad or truncate sequences on the left. The software truncates or adds padding to the start of each sequence 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
argument 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 effects of padding and truncating sequences, see Sequence Padding and Truncation.
SequencePaddingValue
— Value by which to pad input sequences
0
(default) | scalar
Value by which to pad the input sequences, specified as a scalar.
Do not pad sequences with NaN
, because doing so can
propagate errors through the neural network.
Data Types: single
| double
| int8
| int16
| int32
| int64
| uint8
| uint16
| uint32
| uint64
Hardware and Acceleration
ExecutionEnvironment
— Hardware resource
"auto"
(default) | "gpu"
| "cpu"
Hardware resource, specified as one of these values:
"auto"
— Use a GPU if one is available. Otherwise, use the CPU."gpu"
— Use the GPU. Using a GPU requires a Parallel Computing Toolbox™ license and a supported GPU device. For information about supported devices, see GPU Computing Requirements (Parallel Computing Toolbox). If Parallel Computing Toolbox or a suitable GPU is not available, then the software returns an error."cpu"
— Use the CPU.
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
30
(default) | positive integer
Frequency of saving checkpoint neural networks in iterations, specified as a positive integer.
This option only has an effect when CheckpointPath
is nonempty.
Data Types: single
| double
| int8
| int16
| int32
| int64
| uint8
| uint16
| uint32
| uint64
Examples
Create Training Options for the L-BFGS Optimizer
Create a set of options for training a neural network using the L-BFGS optimizer:
Determine the learn rate using the
"strong-wolfe"
line search method.Stop training when the relative gradient is less than or equal to
1e-5
.Turn on the training progress plot.
options = trainingOptions("lbfgs", ... LineSearchMethod="strong-wolfe", ... GradientTolerance=1e-5, ... Plots="training-progress")
options = TrainingOptionsLBFGS with properties: MaxIterations: 1000 HistorySize: 10 InitialInverseHessianFactor: 1 InitialStepSize: [] LineSearchMethod: 'strong-wolfe' MaxNumLineSearchIterations: 20 GradientTolerance: 1.0000e-05 StepTolerance: 1.0000e-05 SequenceLength: 'longest' CheckpointFrequency: 30 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"
Algorithms
Limited-Memory BFGS
The L-BFGS algorithm [1] 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
where Wk denotes the weights at iteration k, is the learning rate at iteration k, Bk is an approximation of the Hessian matrix at iteration k, and denotes the gradients of the loss with respect to the learnable parameters at iteration k.
The L-BFGS algorithm computes the matrix-vector product directly. The algorithm does not require computing the inverse of Bk.
To save memory, the L-BFGS algorithm does not store and invert the dense Hessian matrix B. Instead, the algorithm uses the approximation , where m is the history size, the inverse Hessian factor 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 directly, the L-BFGS algorithm uses this recursive algorithm:
Set , where m is the history size.
For :
Let , where and are the step and gradient differences for iteration , respectively.
Set , where is derived from , , and the gradients of the loss with respect to the loss function. For more information, see [1].
Return .
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 [2]. 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 ofGradientThresholdMethod
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 ofGradientThresholdMethod
is a value-based gradient clipping method.
L2 Regularization
Adding a regularization term for the weights to the loss function is one way to reduce overfitting [3], [4]. The regularization term is also called weight decay. The loss function with the regularization term takes the form
where is the weight vector, is the regularization factor (coefficient), and the regularization function is
Note that the biases are not regularized [4]. You can specify the regularization factor 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] 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.
[2] 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.
[3] Bishop, C. M. Pattern Recognition and Machine Learning. Springer, New York, NY, 2006.
[4] Murphy, K. P. Machine Learning: A Probabilistic Perspective. The MIT Press, Cambridge, Massachusetts, 2012.
Version History
Introduced in R2023bR2024b: Monitor and plot more metrics during training
Use new and updated metric objects during training and testing.
MAPEMetric
— Mean absolute percentage error (MAPE)AccuracyMetric
with newNumTopKClasses
option — Top-k accuracyFScoreMetric
with newBeta
option — Fβ-score
You can also directly specify these new built-in metric and loss names:
"mape"
— Mean absolute percentage error (MAPE)"crossentropy"
— Cross-entropy loss"index-crossentropy"
— Index cross-entropy loss"binary-crossentropy"
— Binary cross-entropy loss"mse"
/"mean-squared-error"
/"l2loss"
— Mean squared error"mae"
/"mean-absolute-error"
/"l1loss"
— Mean absolute error"huber"
— Huber loss
R2024b: Specify initial step size for L-BFGS solver
Specify the initial step size for the L-BFGS solver using the InitialStepSize
argument.
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: 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.
See Also
trainingOptions
| trainnet
| dlnetwork
| analyzeNetwork
| Deep Network Designer
Topics
- Train Neural Network with Tabular Data
- Solve PDE Using Physics-Informed Neural Network
- Create Simple Deep Learning Neural Network for Classification
- Retrain Neural Network to Classify New Images
- Resume Training from Checkpoint Network
- Deep Learning with Big Data on CPUs, GPUs, in Parallel, and on the Cloud
- Define Custom Training Loops, Loss Functions, and Networks
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