traincgp (Neural Network Toolbox)

Neural Network Toolbox

traincgp

Conjugate gradient backpropagation with Polak-Ribiere updates

Syntax

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

info = traincgp(code)

Description

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

traincgp(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 traincgp'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.searchFcn       Name of line search routine to use
'srchcha'

Parameters related to line search methods (not all used for all methods):

net.trainParam.scal_tol 20
- Divide into delta to determine tolerance for linear search.
net.trainParam.alpha 0.001
- Scale factor which determines sufficient reduction in perf.
net.trainParam.beta 0.1
- Scale factor which determines sufficiently large step size.
net.trainParam.delta 0.01
- Initial step size in interval location step.
net.trainParam.gama 0.1
- Parameter to avoid small reductions in performance. Usually set to 0.1. (See use in srch_cha.)
net.trainParam.low_lim 0.1 Lower limit on change in step size.

net.trainParam.up_lim 0.5 Upper limit on change in step size.

net.trainParam.maxstep 100 Maximum step length.

net.trainParam.minstep 1.0e-6 Minimum step length.

net.trainParam.bmax 26 Maximum step size.

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.

traincgp(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 traincgp network training function is to be used.

Create and Test a Network

net = newff([0 5],[2 1],{'tansig','logsig'},'traincgp');
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 traincgp with newff, newcf, or newelm.

To prepare a custom network to be trained with traincgp

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

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

Algorithm

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-Ribiere 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) for a more detailed discussion of the 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, trainscg, trainoss, trainbfg

References

Scales, L. E., Introduction to Non-Linear Optimization, New York: Springer-Verlag, 1985.

traincgf traingd