trainbfg (Neural Network Toolbox)

Neural Network Toolbox

trainbfg

BFGS quasi-Newton backpropagation

Syntax

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

info = trainbfg(code)

Description

trainbfg is a network training function that updates weight and bias values according to the BFGS quasi-Newton method.

trainbfg(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 trainbfg'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.

trainbfg(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 trainbfg network training function is to be used.

Create and Test a Network

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

To prepare a custom network to be trained with trainbfg:

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

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

Algorithm

trainbfg 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 according to the following formula:

```
dX = -H\gX;
```

where gX is the gradient and H is an approximate Hessian matrix. See page 119 of Gill, Murray, and Wright (see reference below) for a more detailed discussion of the BFGS quasi-Newton method.

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, traincgp, trainoss.

References

Gill, P. E.,W. Murray, and M. H. Wright, Practical Optimization, New York: Academic Press, 1981.

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