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
[net,tr] = train(net,...) trains the network with
Training occurs according to
traingd training parameters, shown here
with their default values:
Maximum number of epochs to train
Generate command-line output
Show training GUI
Maximum validation failures
Minimum performance gradient
Epochs between displays (
Maximum time to train in seconds
You can create a standard network that uses
cascadeforwardnet. To prepare a custom
network to be trained with
net.trainParam properties to desired values.
In either case, calling
train with the resulting network trains the
help feedforwardnet and
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
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
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
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
mingrad, or if the training time is longer than
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
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.
net.trainParam.show = 50; net.trainParam.lr = 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
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
nnd12sd1 [HDB96] for an illustration of the performance of the batch gradient
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
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
The performance gradient falls below
Validation performance has increased more than
max_fail times since
the last time it decreased (when using validation).