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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 trainFcn property.

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

Training occurs according to traincgf 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 traincgf with feedforwardnet or cascadeforwardnet.

To prepare a custom network to be trained with traincgf,

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

  2. Set net.trainParam properties to desired values.

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


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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);

Figure Neural Network Training (26-Feb-2022 11:03:19) contains an object of type uigridlayout.

y = net(x);

More About

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Conjugate Gradient Algorithms

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.

See [FlRe64] or [HDB96] for a discussion of the Fletcher-Reeves conjugate gradient algorithm.

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 demonstration nnd12cg [HDB96] for an illustration of the performance of a conjugate gradient algorithm.


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 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 Fletcher-Reeves variation of conjugate gradient it is computed according to

Z = normnew_sqr/norm_sqr;

where 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 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