net.trainFcn = 'trainrp'
[net,tr] = train(net,...)
trainrp is a network training function that updates weight and bias
values according to the resilient backpropagation algorithm (Rprop).
net.trainFcn = 'trainrp' sets the network
[net,tr] = train(net,...) trains the network with
Training occurs according to
trainrp training parameters, shown here
with their default values:
Maximum number of epochs to train
Epochs between displays (
Generate command-line output
Show training GUI
Maximum time to train in seconds
Minimum performance gradient
Maximum validation failures
Increment to weight change
Decrement to weight change
Initial weight change
Maximum weight change
You can create a standard network that uses
To prepare a custom network to be trained with
net.trainParam properties to desired
In either case, calling
train with the resulting network trains the
Here is a problem consisting of inputs
p and targets
t to be solved with a network.
p = [0 1 2 3 4 5]; t = [0 0 0 1 1 1];
A two-layer feed-forward network with two hidden neurons and this training function is created.
Create and test a network.
net = feedforwardnet(2,'trainrp');
Here the network is trained and retested.
net.trainParam.epochs = 50; net.trainParam.show = 10; net.trainParam.goal = 0.1; net = train(net,p,t); a = net(p)
help feedforwardnet and
for other examples.
Multilayer networks typically use sigmoid transfer functions in the hidden layers. These functions are often called “squashing” functions, because they compress an infinite input range into a finite output range. Sigmoid functions are characterized by the fact that their slopes must approach zero as the input gets large. This causes a problem when you use steepest descent to train a multilayer network with sigmoid functions, because the gradient can have a very small magnitude and, therefore, cause small changes in the weights and biases, even though the weights and biases are far from their optimal values.
The purpose of the resilient backpropagation (Rprop) training algorithm is to eliminate
these harmful effects of the magnitudes of the partial derivatives. Only the sign of the
derivative can determine the direction of the weight update; the magnitude of the derivative
has no effect on the weight update. The size of the weight change is determined by a separate
update value. The update value for each weight and bias is increased by a factor
delt_inc whenever the derivative of the performance function with respect
to that weight has the same sign for two successive iterations. The update value is decreased
by a factor
delt_dec whenever the derivative with respect to that weight
changes sign from the previous iteration. If the derivative is zero, the update value remains
the same. Whenever the weights are oscillating, the weight change is reduced. If the weight
continues to change in the same direction for several iterations, the magnitude of the weight
change increases. A complete description of the Rprop algorithm is given in [RiBr93].
The following code recreates the previous network and trains it using the Rprop algorithm.
The training parameters for
first eight parameters have been previously discussed. The last two are the initial step size and the maximum step size, respectively. The performance of Rprop is not very sensitive to
the settings of the training parameters. For the example below, the training parameters are
left at the default values:
p = [-1 -1 2 2;0 5 0 5]; t = [-1 -1 1 1]; net = feedforwardnet(3,'trainrp'); net = train(net,p,t); y = net(p)
rprop is generally much faster than the standard steepest descent
algorithm. It also has the nice property that it requires only a modest increase in memory
requirements. You do need to store the update values for each weight and bias, which is
equivalent to storage of the gradient.
trainrp 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 the following:
dX = deltaX.*sign(gX);
where the elements of
deltaX are all initialized to
gX is the gradient. At each iteration the
deltaX are modified. If an element of
changes sign from one iteration to the next, then the corresponding element of
deltaX is decreased by
delta_dec. If an element of
gX maintains the same sign from one iteration to the next, then the
corresponding element of
deltaX is increased by
See Riedmiller, M., and H. Braun, “A direct adaptive method for faster backpropagation
learning: The RPROP algorithm,” Proceedings of the IEEE International
Conference on Neural Networks,1993, pp. 586–591.
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).
Riedmiller, M., and H. Braun, “A direct adaptive method for faster backpropagation learning: The RPROP algorithm,” Proceedings of the IEEE International Conference on Neural Networks,1993, pp. 586–591.