net.trainFcn = 'trainrp'
[net,tr] = train(net,...)
trainrp is a network training function that
updates weight and bias values according to the resilient backpropagation
net.trainFcn = 'trainrp' sets the network
[net,tr] = train(net,...) trains the network
Training occurs according to
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
to desired values.
In either case, calling
train with the resulting
network trains the network with
Here is a problem consisting of inputs
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
cascadeforwardnet 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
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
deltamax. The 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
respect to the weight and bias variables
variable is adjusted according to the following:
dX = deltaX.*sign(gX);
where the elements of
deltaX are all initialized
gX is the gradient.
At each iteration the elements of
deltaX are modified.
If an element of
gX changes sign from one iteration
to the next, then the corresponding element of
delta_dec. If an element of
the same sign from one iteration to the next, then the corresponding
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,
Training stops when any of these conditions occurs:
The maximum number of
The maximum amount of
time is exceeded.
Performance is minimized to the
The performance gradient falls below
Validation performance has increased more than
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.