Conjugate gradient backpropagation with Fletcher-Reeves updates
net.trainFcn = 'traincgf'
[net,tr] = train(net,...)
traincgf is a network training function that updates weight and bias
values according to conjugate gradient backpropagation with Fletcher-Reeves updates.
net.trainFcn = 'traincgf' sets the network
[net,tr] = train(net,...) trains the network with
Training occurs according to
traincgf 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
Name of line search routine to use
Parameters related to line search methods (not all used for all methods):
Scale factor that determines sufficient reduction in
Scale factor that determines sufficiently large step size
Initial step size in interval location step
Parameter to avoid small reductions in performance, usually set to
Lower limit on change in step size
Upper limit on change in step size
Maximum step length
Minimum step length
Maximum step size
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
This example shows how to train a neural network using the
traincgf train function.
Here a neural network is trained to predict body fat percentages.
[x, t] = bodyfat_dataset; net = feedforwardnet(10, 'traincgf'); net = train(net, x, t); y = net(x);
All the conjugate gradient algorithms start out by searching in the steepest descent direction (negative of the gradient) on the first iteration.
A line search is then performed to determine the optimal distance to move along the current search direction:
Then the next search direction is determined so that it is conjugate to previous search directions. The general procedure for determining the new search direction is to combine the new steepest descent direction with the previous search direction:
The various versions of the conjugate gradient algorithm are distinguished by the manner in which the constant βk is computed. For the Fletcher-Reeves update the procedure is
This is the ratio of the norm squared of the current gradient to the norm squared of the previous gradient.
The conjugate gradient algorithms are usually much faster than variable learning rate
backpropagation, and are sometimes faster than
trainrp, although the results
vary from one problem to another. The conjugate gradient algorithms require only a little more
storage than the simpler algorithms. Therefore, these algorithms are good for networks with a
large number of weights.
Try the Neural Network Design
nnd12cg [HDB96] for an illustration of the performance of a conjugate
traincgf 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:
X = X + a*dX;
dX is the search direction. The parameter
selected to minimize the performance along the search direction. The line search function
searchFcn is used to locate the minimum point. The first search direction is
the negative of the gradient of performance. In succeeding iterations the search direction is
computed from the new gradient and the previous search direction, according to the
dX = -gX + dX_old*Z;
gX is the gradient. The parameter
Z can be
computed in several different ways. For the Fletcher-Reeves variation of conjugate gradient it
is computed according to
Z = normnew_sqr/norm_sqr;
norm_sqr is the norm square of the previous gradient and
normnew_sqr is the norm square of the current gradient. See page 78 of
Scales (Introduction to Non-Linear Optimization) for a more detailed
discussion of the algorithm.
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).
Scales, L.E., Introduction to Non-Linear Optimization, New York, Springer-Verlag, 1985