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Conjugate gradient backpropagation with Powell-Beale restarts


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


traincgb is a network training function that updates weight and bias values according to the conjugate gradient backpropagation with Powell-Beale restarts.

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

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

Training occurs according to traincgb 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 traincgb with feedforwardnet or cascadeforwardnet.

To prepare a custom network to be trained with traincgb,

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

  2. Set net.trainParam properties to desired values.

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


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

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

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

y = net(x);

More About

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Powell-Beale Algorithm

For all conjugate gradient algorithms, the search direction is periodically reset to the negative of the gradient. The standard reset point occurs when the number of iterations is equal to the number of network parameters (weights and biases), but there are other reset methods that can improve the efficiency of training. One such reset method was proposed by Powell [Powe77], based on an earlier version proposed by Beale [Beal72]. This technique restarts if there is very little orthogonality left between the current gradient and the previous gradient. This is tested with the following inequality:


If this condition is satisfied, the search direction is reset to the negative of the gradient.

The traincgb routine has somewhat better performance than traincgp for some problems, although performance on any given problem is difficult to predict. The storage requirements for the Powell-Beale algorithm (six vectors) are slightly larger than for Polak-Ribiére (four vectors).


traincgb 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. The Powell-Beale variation of conjugate gradient is distinguished by two features. First, the algorithm uses a test to determine when to reset the search direction to the negative of the gradient. Second, the search direction is computed from the negative gradient, the previous search direction, and the last search direction before the previous reset. See Powell, Mathematical Programming, Vol. 12, 1977, pp. 241 to 254, 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).


Powell, M.J.D., “Restart procedures for the conjugate gradient method,” Mathematical Programming, Vol. 12, 1977, pp. 241–254

Version History

Introduced before R2006a