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Scaled conjugate gradient backpropagation


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


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

trainscg is a network training function that updates weight and bias values according to the scaled conjugate gradient method.

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

  • net.trainParam.epochs — Maximum number of epochs to train. The default value is 1000.

  • — Epochs between displays (NaN for no displays). The default value is 25.

  • net.trainParam.showCommandLine — Generate command-line output. The default value is false.

  • net.trainParam.showWindow — Show training GUI. The default value is true.

  • net.trainParam.goal — Performance goal. The default value is 0.

  • net.trainParam.time — Maximum time to train in seconds. The default value is inf.

  • net.trainParam.min_grad — Minimum performance gradient. The default value is 1e-6.

  • net.trainParam.max_fail — Maximum validation failures. The default value is 6.

  • — Marquardt adjustment parameter. The default value is 0.005.

  • net.trainParam.sigma — Determine change in weight for second derivative approximation. The default value is 5.0e-5.

  • net.trainParam.lambda — Parameter for regulating the indefiniteness of the Hessian. The default value is 5.0e-7.


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This example shows how to solve a problem consisting of inputs p and targets t by using 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.

net = feedforwardnet(2,'trainscg');

Here the network is trained and tested.

net = train(net,p,t);
a = net(p)

See help feedforwardnet and help cascadeforwardnet for other examples.

Input Arguments

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Input network, specified as a network object. To create a network object, use for example, feedforwardnet or narxnet.

Output Arguments

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Trained network, returned as a network object.

Training record (epoch and perf), returned as a structure whose fields depend on the network training function (net.NET.trainFcn). It can include fields such as:

  • Training, data division, and performance functions and parameters

  • Data division indices for training, validation and test sets

  • Data division masks for training validation and test sets

  • Number of epochs (num_epochs) and the best epoch (best_epoch).

  • A list of training state names (states).

  • Fields for each state name recording its value throughout training

  • Performances of the best network (best_perf, best_vperf, best_tperf)

More About

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Network Use

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

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

  2. Set net.trainParam properties to desired values.

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


trainscg 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.

The scaled conjugate gradient algorithm is based on conjugate directions, as in traincgp, traincgf, and traincgb, but this algorithm does not perform a line search at each iteration. See Moller (Neural Networks, Vol. 6, 1993, pp. 525–533) for a more detailed discussion of the scaled conjugate gradient 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).


[1] Moller. Neural Networks, Vol. 6, 1993, pp. 525–533

Version History

Introduced before R2006a