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Gradient descent backpropagation


net.trainFcn = 'traingd'
[net,tr] = train(net,...)


traingd is a network training function that updates weight and bias values according to gradient descent.

net.trainFcn = 'traingd' sets the network trainFcn property.

[net,tr] = train(net,...) trains the network with traingd.

Training occurs according to traingd training parameters, shown here with their default values:


Maximum number of epochs to train


Performance goal


Generate command-line output


Show training GUI


Learning rate


Maximum validation failures


Minimum performance gradient


Epochs between displays (NaN for no displays)


Maximum time to train in seconds

Network Use

You can create a standard network that uses traingd with feedforwardnet or cascadeforwardnet. To prepare a custom network to be trained with traingd,

  1. Set net.trainFcn to 'traingd'. This sets net.trainParam to traingd’s default parameters.

  2. Set net.trainParam properties to desired values.

In either case, calling train with the resulting network trains the network with traingd.

See help feedforwardnet and help cascadeforwardnet for examples.

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Gradient Descent Backpropagation

The batch steepest descent training function is traingd. The weights and biases are updated in the direction of the negative gradient of the performance function. If you want to train a network using batch steepest descent, you should set the network trainFcn to traingd, and then call the function train. There is only one training function associated with a given network.

There are seven training parameters associated with traingd:

  • epochs

  • show

  • goal

  • time

  • min_grad

  • max_fail

  • lr

The learning rate lr is multiplied times the negative of the gradient to determine the changes to the weights and biases. The larger the learning rate, the bigger the step. If the learning rate is made too large, the algorithm becomes unstable. If the learning rate is set too small, the algorithm takes a long time to converge. See page 12-8 of [HDB96] for a discussion of the choice of learning rate.

The training status is displayed for every show iterations of the algorithm. (If show is set to NaN, then the training status is never displayed.) The other parameters determine when the training stops. The training stops if the number of iterations exceeds epochs, if the performance function drops below goal, if the magnitude of the gradient is less than mingrad, or if the training time is longer than time seconds. max_fail, which is associated with the early stopping technique, is discussed in Improving Generalization.

The following code creates a training set of inputs p and targets t. For batch training, all the input vectors are placed in one matrix.

p = [-1 -1 2 2; 0 5 0 5];
t = [-1 -1 1 1];

Create the feedforward network.

net = feedforwardnet(3,'traingd');

In this simple example, turn off a feature that is introduced later.

net.divideFcn = '';

At this point, you might want to modify some of the default training parameters. = 50; = 0.05;
net.trainParam.epochs = 300;
net.trainParam.goal = 1e-5;

If you want to use the default training parameters, the preceding commands are not necessary.

Now you are ready to train the network.

[net,tr] = train(net,p,t);

The training record tr contains information about the progress of training.

Now you can simulate the trained network to obtain its response to the inputs in the training set.

a = net(p)
a =
   -1.0026   -0.9962   1.0010   0.9960

Try the Neural Network Design demonstration nnd12sd1 [HDB96] for an illustration of the performance of the batch gradient descent algorithm.


traingd can train any network as long as its weight, net input, and transfer functions have derivative functions.

Backpropagation is used to calculate derivatives of performance perf with respect to the weight and bias variables X. Each variable is adjusted according to gradient descent:

dX = lr * dperf/dX

Training stops when any of these conditions occurs:

  • The maximum number of epochs (repetitions) is reached.

  • The maximum amount of time is exceeded.

  • Performance is minimized to the goal.

  • The performance gradient falls below min_grad.

  • Validation performance has increased more than max_fail times since the last time it decreased (when using validation).

Introduced before R2006a