sgdmupdate

Update parameters using stochastic gradient descent with momentum (SGDM)

Syntax

[dlnet,vel] = sgdmupdate(dlnet,grad,vel)

[params,vel] = sgdmupdate(params,grad,vel)

[___] = sgdmupdate(___learnRate,momentum)

Description

Update the network learnable parameters in a custom training loop using the stochastic gradient descent with momentum (SGDM) algorithm.

Note

This function applies the SGDM optimization algorithm to update network parameters in custom training loops that use networks defined as dlnetwork objects or model functions. If you want to train a network defined as a Layer array or as a LayerGraph, use the following functions:

• Create a TrainingOptionsSGDM object using the trainingOptions function.

• Use the TrainingOptionsSGDM object with the trainNetwork function.

[dlnet,vel] = sgdmupdate(dlnet,grad,vel) updates the learnable parameters of the network dlnet using the SGDM algorithm. Use this syntax in a training loop to iteratively update a network defined as a dlnetwork object.

[params,vel] = sgdmupdate(params,grad,vel) updates the learnable parameters in params using the SGDM algorithm. Use this syntax in a training loop to iteratively update the learnable parameters of a network defined using functions.

[___] = sgdmupdate(___learnRate,momentum) also specifies values to use for the global learning rate and momentum, in addition to the input arguments in previous syntaxes.

Examples

Update Learnable Parameters Using sgdmupdate

Perform a single SGDM update step with a global learning rate of 0.05 and momentum of 0.95.

Create the parameters and parameter gradients as numeric arrays.

params = rand(3,3,4);
grad = ones(3,3,4);

Initialize the parameter velocities for the first iteration.

vel = [];

Specify custom values for the global learning rate and momentum.

learnRate = 0.05;
momentum = 0.95;

Update the learnable parameters using sgdmupdate.

[params,vel] = sgdmupdate(params,grad,vel,learnRate,momentum);

Train Network Using sgdmupdate

Use sgdmupdate to train a network using the SGDM algorithm.

Load Training Data

Load the digits training data.

[XTrain,YTrain] = digitTrain4DArrayData;
classes = categories(YTrain);
numClasses = numel(classes);

Define 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], 'Name','input','Mean',mean(XTrain,4))
    convolution2dLayer(5,20,'Name','conv1')
    reluLayer('Name', 'relu1')
    convolution2dLayer(3,20,'Padding',1,'Name','conv2')
    reluLayer('Name','relu2')
    convolution2dLayer(3,20,'Padding',1,'Name','conv3')
    reluLayer('Name','relu3')
    fullyConnectedLayer(numClasses,'Name','fc')
    softmaxLayer('Name','softmax')];
lgraph = layerGraph(layers);

Create a dlnetwork object from the layer graph.

dlnet = dlnetwork(lgraph);

Define Model Gradients Function

Create the helper function modelGradients, listed at the end of the example. The function takes a dlnetwork object dlnet and a mini-batch of input data dlX with corresponding labels Y, and returns the loss and the gradients of the loss with respect to the learnable parameters in dlnet.

Specify Training Options

Specify the options to use during training.

miniBatchSize = 128;
numEpochs = 20;
numObservations = numel(YTrain);
numIterationsPerEpoch = floor(numObservations./miniBatchSize);

Train on a GPU, if one is available. Using a GPU requires Parallel Computing Toolbox™ and a CUDA® enabled NVIDIA® GPU with compute capability 3.0 or higher.

executionEnvironment = "auto";

Visualize the training progress in a plot.

plots = "training-progress";

Train Network

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 sgdmupdate function. At the end of each epoch, display the training progress.

Initialize the training progress plot.

if plots == "training-progress"
    figure
    lineLossTrain = animatedline('Color',[0.85 0.325 0.098]);
    ylim([0 inf])
    xlabel("Iteration")
    ylabel("Loss")
    grid on
end

Initialize the velocity parameter.

vel = [];

Train the network.

iteration = 0;
start = tic;

for epoch = 1:numEpochs
    % Shuffle data.
    idx = randperm(numel(YTrain));
    XTrain = XTrain(:,:,:,idx);
    YTrain = YTrain(idx);
    
    for i = 1:numIterationsPerEpoch
        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);
        
        Y = zeros(numClasses, miniBatchSize, 'single');
        for c = 1:numClasses
            Y(c,YTrain(idx)==classes(c)) = 1;
        end
        
        % Convert mini-batch of data to a dlarray.
        dlX = dlarray(single(X),'SSCB');
        
        % If training on a GPU, then convert data to a gpuArray.
        if (executionEnvironment == "auto" && canUseGPU) || executionEnvironment == "gpu"
            dlX = gpuArray(dlX);
        end
        
        % Evaluate the model gradients and loss using dlfeval and the
        % modelGradients helper function.
        [gradients,loss] = dlfeval(@modelGradients,dlnet,dlX,Y);
        
        % Update the network parameters using the SGDM optimizer.
        [dlnet,vel] = sgdmupdate(dlnet,gradients,vel);
        
        % Display the training progress.
        if plots == "training-progress"
            D = duration(0,0,toc(start),'Format','hh:mm:ss');
            addpoints(lineLossTrain,iteration,double(gather(extractdata(loss))))
            title("Epoch: " + epoch + ", Elapsed: " + string(D))
            drawnow
        end
    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, YTest] = digitTest4DArrayData;

Convert the data to a dlarray with the dimension format 'SSCB'. For GPU prediction, also convert the data to a gpuArray.

dlXTest = dlarray(XTest,'SSCB');
if (executionEnvironment == "auto" && canUseGPU) || executionEnvironment == "gpu"
    dlXTest = gpuArray(dlXTest);
end

To classify images using a dlnetwork object, use the predict function and find the classes with the highest scores.

dlYPred = predict(dlnet,dlXTest);
[~,idx] = max(extractdata(dlYPred),[],1);
YPred = classes(idx);

Evaluate the classification accuracy.

accuracy = mean(YPred==YTest)

accuracy = 0.9916

Model Gradients Function

The modelGradients helper function takes a dlnetwork object dlnet and a mini-batch of input data dlX with corresponding labels Y, and returns the loss and the gradients of the loss with respect to the learnable parameters in dlnet. To compute the gradients automatically, use the dlgradient function.

function [gradients,loss] = modelGradients(dlnet,dlX,Y)

    dlYPred = forward(dlnet,dlX);
    
    loss = crossentropy(dlYPred,Y);
    
    gradients = dlgradient(loss,dlnet.Learnables);

end

Input Arguments

dlnet — Network

dlnetwork object

Network, specified as a dlnetwork object.

The function updates the dlnet.Learnables property of the dlnetwork object. dlnet.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 a dlarray.

The input argument grad must be a table of the same form as dlnet.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 a dlarray.

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.

Data Types: single | double | struct | table | cell

grad — Gradients of the 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 sgdmupdate.

Input	Learnable Parameters	Gradients
dlnet	Table dlnet.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 dlnet.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.

vel — Parameter velocities

[] | dlarray | numeric array | cell array | structure | table

Parameter velocities, specified as an empty array, a dlarray, a numeric array, a cell array, a structure, or a table.

The exact form of vel depends on the input network or learnable parameters. The following table shows the required format for vel for possible inputs to sgdmpdate.

Input	Learnable Parameters	Velocities
dlnet	Table dlnet.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 dlnet.Learnables. vel must have a Value variable consisting of cell arrays that contain the velocity 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. vel must have a Value variable consisting of cell arrays that contain the velocity of each learnable parameter.

If you specify vel as an empty array, the function assumes no previous velocities and runs in the same way as for the first update in a series of iterations. To update the learnable parameters iteratively, use the vel output of a previous call to sgdmupdate as the vel input.

learnRate — Global learning rate

0.01 (default) | positive scalar

Learning rate, specified as a positive scalar. The default value of learnRate is 0.01.

If you specify the network parameters as a dlnetwork object, the learning rate for each parameter is the global learning rate multiplied by the corresponding learning rate factor property defined in the network layers.

momentum — Momentum

0.9 (default) | positive scalar between 0 and 1

Momentum, specified as a positive scalar between 0 and 1. The default value of momentum is 0.9.

Output Arguments

dlnet — Updated network

dlnetwork object

Network, returned as a dlnetwork object.

The function updates the dlnet.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.

vel — Updated parameter velocities

dlarray | numeric array | cell array | structure | table

Updated parameter velocities, returned as a dlarray, a numeric array, a cell array, a structure, or a table.

More About

Stochastic Gradient Descent with Momentum

The function uses the stochastic gradient descent with momentum algorithm to update the learnable parameters. For more information, see the definition of the stochastic gradient descent with momentum algorithm under Stochastic Gradient Descent on the trainingOptions reference page.

Extended Capabilities

GPU Arrays

Accelerate code by running on a graphics processing unit (GPU) using Parallel Computing Toolbox™.

Usage notes and limitations:

• When at least one of the following input arguments is a gpuArray or a dlarray with underlying data of type gpuArray, this function runs on the GPU.

  • grad

  • params

For more information, see Run MATLAB Functions on a GPU (Parallel Computing Toolbox).