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Conjugate gradient backpropagation with Polak-Ribiére updates


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


traincgp is a network training function that updates weight and bias values according to conjugate gradient backpropagation with Polak-Ribiére updates.

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

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

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


Maximum number of epochs to train


Epochs between displays (NaN for no displays)


Generate command-line output


Show training GUI


Performance goal


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):


Divide into delta to determine tolerance for linear search.


Scale factor that determines sufficient reduction in perf


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 0.1 (see srch_cha)


Lower limit on change in step size

net.trainParam.up_lim 0.5

Upper limit on change in step size


Maximum step length


Minimum step length


Maximum step size

Network Use

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

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

  2. Set net.trainParam properties to desired values.

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


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This example shows how to train a neural network using the traincgp train function.

Here a neural network is trained to predict body fat percentages.

[x, t] = bodyfat_dataset;
net = feedforwardnet(10, 'traincgp');
net = train(net, x, t);

y = net(x);

More About

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Conjugate Gradient Backpropagation with Polak-Ribiére Updates

Another version of the conjugate gradient algorithm was proposed by Polak and Ribiére. As with the Fletcher-Reeves algorithm, traincgf, the search direction at each iteration is determined by


For the Polak-Ribiére update, the constant βk is computed by


This is the inner product of the previous change in the gradient with the current gradient divided by the norm squared of the previous gradient. See [FlRe64] or [HDB96] for a discussion of the Polak-Ribiére conjugate gradient algorithm.

The traincgp routine has performance similar to traincgf. It is difficult to predict which algorithm will perform best on a given problem. The storage requirements for Polak-Ribiére (four vectors) are slightly larger than for Fletcher-Reeves (three vectors).


traincgp 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 the following:

X = X + a*dX;

where dX is the search direction. The parameter a is 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 formula

dX = -gX + dX_old*Z;

where gX is the gradient. The parameter Z can be computed in several different ways. For the Polak-Ribiére variation of conjugate gradient, it is computed according to

Z = ((gX - gX_old)'*gX)/norm_sqr;

where norm_sqr is the norm square of the previous gradient, and gX_old is the gradient on the previous iteration. See page 78 of Scales (Introduction to Non-Linear Optimization, 1985) 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 goal.

  • The performance gradient falls below min_grad.

  • Validation performance (validation error) 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

Version History

Introduced before R2006a