rmspropupdate
Update parameters using root mean squared propagation (RMSProp)
Syntax
Description
Update the network learnable parameters in a custom training loop using the root mean squared propagation (RMSProp) algorithm.
Note
This function applies the RMSProp optimization algorithm to update network parameters in
custom training loops. To train a neural network using the trainnet
function
using the RMSProp solver, use the trainingOptions
function and set the solver to
"rmsprop"
.
[
updates the learnable parameters of the network netUpdated
,averageSqGrad
] = rmspropupdate(net
,grad
,averageSqGrad
)net
using the RMSProp
algorithm. Use this syntax in a training loop to iteratively update a network defined as a
dlnetwork
object.
[
updates the learnable parameters in params
,averageSqGrad
] = rmspropupdate(params
,grad
,averageSqGrad
)params
using the RMSProp algorithm.
Use this syntax in a training loop to iteratively update the learnable parameters of a
network defined using functions.
[___] = rmspropupdate(___
also specifies values to use for the global learning rate, square gradient decay, and small
constant epsilon, in addition to the input arguments in previous syntaxes. learnRate
,sqGradDecay
,epsilon
)
Examples
Update Learnable Parameters Using rmspropupdate
Perform a single root mean squared propagation update step with a
global learning rate of 0.05
and squared gradient decay factor of
0.95
.
Create the parameters and parameter gradients as numeric arrays.
params = rand(3,3,4); grad = ones(3,3,4);
Initialize the average squared gradient for the first iteration.
averageSqGrad = [];
Specify custom values for the global learning rate and squared gradient decay factor.
learnRate = 0.05; sqGradDecay = 0.95;
Update the learnable parameters using rmspropupdate
.
[params,averageSqGrad] = rmspropupdate(params,grad,averageSqGrad,learnRate,sqGradDecay);
Train a Network Using rmspropupdate
Use rmspropupdate
to train a network using the root mean squared propagation (RMSProp) algorithm.
Load Training Data
Load the digits training data.
[XTrain,TTrain] = digitTrain4DArrayData; classes = categories(TTrain); numClasses = numel(classes);
Define the Network
Define the network architecture and specify the average image value using the Mean
option in the image input layer.
layers = [ imageInputLayer([28 28 1],'Mean',mean(XTrain,4)) convolution2dLayer(5,20) reluLayer convolution2dLayer(3,20,'Padding',1) reluLayer convolution2dLayer(3,20,'Padding',1) reluLayer fullyConnectedLayer(numClasses) softmaxLayer];
Create a dlnetwork
object from the layer array.
net = dlnetwork(layers);
Define Model Loss Function
Create the helper function modelLoss
, listed at the end of the example. The function takes a dlnetwork
object and a mini-batch of input data with corresponding labels, and returns the loss and the gradients of the loss with respect to the learnable parameters.
Specify Training Options
Specify the options to use during training.
miniBatchSize = 128; numEpochs = 20; numObservations = numel(TTrain); numIterationsPerEpoch = floor(numObservations./miniBatchSize);
Train Network
Initialize the squared average gradients.
averageSqGrad = [];
Calculate the total number of iterations for the training progress monitor.
numIterations = numEpochs * numIterationsPerEpoch;
Initialize the TrainingProgressMonitor
object. Because the timer starts when you create the monitor object, make sure that you create the object close to the training loop.
monitor = trainingProgressMonitor(Metrics="Loss",Info="Epoch",XLabel="Iteration");
Train the model using a custom training loop. For each epoch, shuffle the data and loop over mini-batches of data. Update the network parameters using the rmspropupdate
function. At the end of each iteration, display the training progress.
Train on a GPU, if one is available. Using a GPU requires Parallel Computing Toolbox™ and a supported GPU device. For information on supported devices, see GPU Computing Requirements (Parallel Computing Toolbox).
Train the network.
iteration = 0; epoch = 0; while epoch < numEpochs && ~monitor.Stop epoch = epoch + 1; % Shuffle data. idx = randperm(numel(TTrain)); XTrain = XTrain(:,:,:,idx); TTrain = TTrain(idx); i = 0; while i < numIterationsPerEpoch && ~monitor.Stop i = i + 1; iteration = iteration + 1; % Read mini-batch of data and convert the labels to dummy % variables. idx = (i-1)*miniBatchSize+1:i*miniBatchSize; X = XTrain(:,:,:,idx); T = zeros(numClasses,miniBatchSize,"single"); for c = 1:numClasses T(c,TTrain(idx)==classes(c)) = 1; end % Convert mini-batch of data to a dlarray. X = dlarray(single(X),"SSCB"); % If training on a GPU, then convert data to a gpuArray. if canUseGPU X = gpuArray(X); end % Evaluate the model loss and gradients using dlfeval and the % modelLoss function. [loss,gradients] = dlfeval(@modelLoss,net,X,T); % Update the network parameters using the RMSProp optimizer. [net,averageSqGrad] = rmspropupdate(net,gradients,averageSqGrad); % Update the training progress monitor. recordMetrics(monitor,iteration,Loss=loss); updateInfo(monitor,Epoch=epoch + " of " + numEpochs); monitor.Progress = 100 * iteration/numIterations; end end
Test the Network
Test the classification accuracy of the model by comparing the predictions on a test set with the true labels.
[XTest,TTest] = digitTest4DArrayData;
Convert the data to a dlarray
with dimension format "SSCB"
. For GPU prediction, also convert the data to a gpuArray
.
XTest = dlarray(XTest,"SSCB"); if canUseGPU XTest = gpuArray(XTest); end
To classify images using a dlnetwork
object, use the predict
function and find the classes with the highest scores.
YTest = predict(net,XTest); [~,idx] = max(extractdata(YTest),[],1); YTest = classes(idx);
Evaluate the classification accuracy.
accuracy = mean(YTest==TTest)
accuracy = 0.9926
Model Loss Function
The helper function modelLoss
takes a dlnetwork
object net
and a mini-batch of input data X
with corresponding labels T
, and returns the loss and the gradients of the loss with respect to the learnable parameters in net
. To compute the gradients automatically, use the dlgradient
function.
function [loss,gradients] = modelLoss(net,X,T) Y = forward(net,X); loss = crossentropy(Y,T); gradients = dlgradient(loss,net.Learnables); end
Input Arguments
net
— Network
dlnetwork
object
Network, specified as a dlnetwork
object.
The function updates the Learnables
property of the
dlnetwork
object. net.Learnables
is a table with
three variables:
Layer
— Layer name, specified as a string scalar.Parameter
— Parameter name, specified as a string scalar.Value
— Value of parameter, specified as a cell array containing adlarray
.
The input argument grad
must be a table of the same
form as net.Learnables
.
params
— Network learnable parameters
dlarray
| numeric array | cell array | structure | table
Network learnable parameters, specified as a dlarray
, a numeric
array, a cell array, a structure, or a table.
If you specify params
as a table, it must contain the following
three variables.
Layer
— Layer name, specified as a string scalar.Parameter
— Parameter name, specified as a string scalar.Value
— Value of parameter, specified as a cell array containing adlarray
.
You can specify params
as a container of learnable parameters for
your network using a cell array, structure, or table, or nested cell arrays or
structures. The learnable parameters inside the cell array, structure, or table must be
dlarray
or numeric values of data type double
or
single
.
The input argument grad
must be provided with exactly the same
data type, ordering, and fields (for structures) or variables (for tables) as
params
.
The learnables can be complex-valued. (since R2024a) Ensure that the corresponding operations support complex-valued learnables.
Before R2024a: The learnables must not be complex-valued. If your model involves complex learnables, then convert the learnables to real values before calculating the gradients.
grad
— Gradients of loss
dlarray
| numeric array | cell array | structure | table
Gradients of the loss, specified as a dlarray
, a numeric array, a
cell array, a structure, or a table.
The exact form of grad
depends on the input network or learnable
parameters. The following table shows the required format for grad
for possible inputs to rmspropupdate
.
Input | Learnable Parameters | Gradients |
---|---|---|
net | Table net.Learnables containing
Layer , Parameter , and
Value variables. The Value variable
consists of cell arrays that contain each learnable parameter as a
dlarray . | Table with the same data type, variables, and ordering as
net.Learnables . grad must have a
Value variable consisting of cell arrays that contain the
gradient of each learnable parameter. |
params | dlarray | dlarray with the same data type and ordering as
params
|
Numeric array | Numeric array with the same data type and ordering as
params
| |
Cell array | Cell array with the same data types, structure, and ordering as
params | |
Structure | Structure with the same data types, fields, and ordering as
params | |
Table with Layer , Parameter , and
Value variables. The Value variable must
consist of cell arrays that contain each learnable parameter as a
dlarray . | Table with the same data types, variables, and ordering as
params . grad must have a
Value variable consisting of cell arrays that contain the
gradient of each learnable parameter. |
You can obtain grad
from a call to dlfeval
that
evaluates a function that contains a call to dlgradient
.
For more information, see Use Automatic Differentiation In Deep Learning Toolbox.
The gradients can be complex-valued. (since R2024a) Using complex valued gradients can lead to complex-valued learnable parameters. Ensure that the corresponding operations support complex-valued learnables.
Before R2024a: The gradients must not be complex-valued. If your model involves complex numbers, then convert all outputs to real values before calculating the gradients.
averageSqGrad
— Moving average of squared parameter gradients
[]
| dlarray
| numeric array | cell array | structure | table
Moving average of squared parameter gradients, specified as an empty array, a
dlarray
, a numeric array, a cell array, a structure, or a table.
The exact form of averageSqGrad
depends on the input network or
learnable parameters. The following table shows the required format for
averageSqGrad
for possible inputs to
rmspropupdate
.
Input | Learnable Parameters | Average Squared Gradients |
---|---|---|
net | Table net.Learnables containing
Layer , Parameter , and
Value variables. The Value variable
consists of cell arrays that contain each learnable parameter as a
dlarray . | Table with the same data type, variables, and ordering as
net.Learnables . averageSqGrad must have
a Value variable consisting of cell arrays that contain the
average squared gradient of each learnable parameter. |
params | dlarray | dlarray with the same data type and ordering as
params
|
Numeric array | Numeric array with the same data type and ordering as
params
| |
Cell array | Cell array with the same data types, structure, and ordering as
params | |
Structure | Structure with the same data types, fields, and ordering as
params | |
Table with Layer , Parameter , and
Value variables. The Value variable must
consist of cell arrays that contain each learnable parameter as a
dlarray . | Table with the same data types, variables, and ordering as
params . averageSqGrad must have a
Value variable consisting of cell arrays that contain the
average squared gradient of each learnable parameter. |
If you specify averageSqGrad
as an empty array, the function
assumes no previous gradients and runs in the same way as for the first update in a
series of iterations. To update the learnable parameters iteratively, use the
averageSqGrad
output of a previous call to
rmspropupdate
as the averageSqGrad
input.
The gradients can be complex-valued. (since R2024a) Using complex valued gradients can lead to complex-valued learnable parameters. Ensure that the corresponding operations support complex-valued learnables.
Before R2024a: The gradients must not be complex-valued. If your model involves complex numbers, then convert all outputs to real values before calculating the gradients.
learnRate
— Global learning rate
0.001
(default) | positive scalar
Global learning rate, specified as a positive scalar. The default value of
learnRate
is 0.001
.
If you specify the network parameters as a dlnetwork
, the
learning rate for each parameter is the global learning rate multiplied by the
corresponding learning rate factor property defined in the network layers.
sqGradDecay
— Squared gradient decay factor
0.9
(default) | positive scalar between 0
and 1
.
Squared gradient decay factor, specified as a positive scalar between
0
and 1
. The default value of
sqGradDecay
is 0.9
.
epsilon
— Small constant
1e-8
(default) | positive scalar
Small constant for preventing divide-by-zero errors, specified as a positive scalar.
The default value of epsilon
is 1e-8
.
Output Arguments
netUpdated
— Updated network
dlnetwork
object
Updated network, returned as a dlnetwork
object.
The function updates the Learnables
property of the
dlnetwork
object.
params
— Updated network learnable parameters
dlarray
| numeric array | cell array | structure | table
Updated network learnable parameters, returned as a dlarray
, a
numeric array, a cell array, a structure, or a table with a Value
variable containing the updated learnable parameters of the network.
The learnables can be complex-valued. (since R2024a) Ensure that the corresponding operations support complex-valued learnables.
Before R2024a: The learnables must not be complex-valued. If your model involves complex learnables, then convert the learnables to real values before calculating the gradients.
averageSqGrad
— Updated moving average of squared parameter gradients
dlarray
| numeric array | cell array | structure | table
Updated moving average of squared parameter gradients, returned as a
dlarray
, a numeric array, a cell array, a structure, or a table.
The gradients can be complex-valued. (since R2024a) Using complex valued gradients can lead to complex-valued learnable parameters. Ensure that the corresponding operations support complex-valued learnables.
Before R2024a: The gradients must not be complex-valued. If your model involves complex numbers, then convert all outputs to real values before calculating the gradients.
Algorithms
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,
β2 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-β2), that is, 10, 100, and 1000 parameter updates, respectively. The RMSProp algorithm uses this moving average to normalize the updates of each parameter individually,
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.
Extended Capabilities
GPU Arrays
Accelerate code by running on a graphics processing unit (GPU) using Parallel Computing Toolbox™.
The rmspropupdate
function
supports GPU array input with these usage notes and limitations:
When at least one of the following input arguments is a
gpuArray
or adlarray
with underlying data of typegpuArray
, this function runs on the GPU.grad
averageSqGrad
params
For more information, see Run MATLAB Functions on a GPU (Parallel Computing Toolbox).
Version History
Introduced in R2019bR2024a: Complex-valued learnable parameters and gradients
The learnable parameters, gradients, and moving average of squared gradients can be complex-valued. When the updated learnable parameters are complex-valued, ensure that the corresponding operations support complex-valued parameters.
R2020a: rmspropupdate
squared gradient decay factor default is 0.9
Starting in R2020a, the default value of the squared gradient decay factor in rmspropupdate
is
0.9
. In previous versions, the default value was
0.999
. To reproduce the previous default behavior, use one of the
following
syntaxes:
[net,averageSqGrad] = rmspropupdate(net,grad,averageSqGrad,0.001,0.999) [params,averageSqGrad] = rmspropupdate(params,grad,averageSqGrad,0.001,0.999)
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