trainscg (Neural Network Toolbox)

Neural Network Toolbox

trainscg

Scaled conjugate gradient backpropagation

Syntax

[net,TR,Ac,El] = trainscg(net,Pd,Tl,Ai,Q,TS,VV,TV)

info = trainscg(code)

Description

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

trainscg(net,Pd,Tl,Ai,Q,TS,VV,TV) takes these inputs,

net -- Neural network.

Pd -- Delayed input vectors.

Tl -- Layer target vectors.

Ai -- Initial input delay conditions.

Q -- Batch size.

TS -- Time steps.

VV -- Either empty matrix [] or structure of validation vectors.

TV -- Either empty matrix [] or structure of test vectors.

and returns,

net -- Trained network.

TR -- Training record of various values over each epoch:
- TR.epoch -- Epoch number.
  TR.perf -- Training performance.
  TR.vperf -- Validation performance.
  TR.tperf -- Test performance.
Ac -- Collective layer outputs for last epoch.

El -- Layer errors for last epoch.

Training occurs according to the trainscg's training parameters shown here with their default values:

net.trainParam.epochs     100 Maximum number of epochs to train

net.trainParam.show        25 Epochs between showing progress

net.trainParam.goal         0 Performance goal

net.trainParam.time       inf Maximum time to train in seconds

net.trainParam.min_grad 1e-6 Minimum performance gradient

net.trainParam.max_fail     5 Maximum validation failures

net.trainParam.sigma   5.0e-5  Determines change in weight for                                   second derivative approximation.

net.trainParam.lambda 5.0e-7  Parameter for regulating the                                   indefiniteness of the Hessian.

Dimensions for these variables are

Pd -- No x Ni x TS cell array, each element P{i,j,ts} is a Dij x Q matrix.

Tl -- Nl x TS cell array, each element P{i,ts} is a Vi x Q matrix.

Ai -- Nl x LD cell array, each element Ai{i,k} is an Si x Q matrix.

where

Ni = net.numInputs

Nl = net.numLayers

LD = net.numLayerDelays

Ri = net.inputs{i}.size

Si = net.layers{i}.size

Vi = net.targets{i}.size

Dij = Ri * length(net.inputWeights{i,j}.delays)

If VV is not [], it must be a structure of validation vectors,

VV.PD -- Validation delayed inputs.

VV.Tl -- Validation layer targets.

VV.Ai -- Validation initial input conditions.

VV.Q -- Validation batch size.

VV.TS -- Validation time steps.

which is used to stop training early if the network performance on the validation vectors fails to improve or remains the same for max_fail epochs in a row.

If TV is not [], it must be a structure of validation vectors,

TV.PD -- Validation delayed inputs

TV.Tl -- Validation layer targets

TV.Ai -- Validation initial input conditions

TV.Q -- Validation batch size

TV.TS -- Validation time steps

which is used to test the generalization capability of the trained network.

trainscg(code) returns useful information for each code string:

'pnames' -- Names of training parameters

'pdefaults' -- Default training parameters

Examples

Here is a problem consisting of inputs p and targets t that we would like to solve with a network.

```
p = [0 1 2 3 4 5];
t = [0 0 0 1 1 1];
```

Here a two-layer feed-forward network is created. The network's input ranges from [0 to 10]. The first layer has two tansig neurons, and the second layer has one logsig neuron. The trainscg network training function is used.

Create and Test a Network

net = newff([0 5],[2 1],{'tansig','logsig'},'trainscg');
a = sim(net,p)

Train and Retest the Network
net.trainParam.epochs = 50;
net.trainParam.show = 10;
net.trainParam.goal = 0.1;
net = train(net,p,t);
a = sim(net,p)

See newff, newcf, and newelm for other examples.

Network Use

You can create a standard network that uses trainscg with newff, newcf, or newelm.

To prepare a custom network to be trained with trainscg

Set net.trainFcn to 'trainscg'. This will set net.trainParam to trainscg's default parameters.
Set net.trainParam properties to desired values.

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

Algorithm

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) for a more detailed discussion of the scaled conjugate gradient algorithm.

Training stops when any of these conditions occur:

The maximum number of epochs (repetitions) is reached.
The maximum amount of time has been exceeded.
Performance has been minimized to the goal.
The performance gradient falls below mingrad.
Validation performance has increased more than max_fail times since the last time it decreased (when using validation).

See Also

newff, newcf, traingdm, traingda, traingdx, trainlm, trainrp, traincgf, traincgb, trainbfg, traincgp, trainoss

References

Moller, M. F., "A scaled conjugate gradient algorithm for fast supervised learning," Neural Networks, vol. 6, pp. 525-533, 1993.

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