Neural Network Toolbox

trainlm

Levenberg-Marquardt backpropagation

Syntax

• [net,TR] = trainlm(net,Pd,Tl,Ai,Q,TS,VV,TV)
  info = trainlm(code)
  

Description

trainlm is a network training function that updates weight and bias values according to Levenberg-Marquardt optimization.

trainlm(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 validation 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.

    TR.mu -- Adaptive mu value.

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

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

  net.trainParam.goal 0 Performance goal

  net.trainParam.max_fail 5 Maximum validation failures

  net.trainParam.mem_reduc    1  Factor to use for memory/speed
                                    tradeoff

  net.trainParam.min_grad 1e-10 Minimum performance gradient

      net.trainParam.mu 0.001 Initial Mu

  net.trainParam.mu_dec 0.1 Mu decrease factor

  net.trainParam.mu_inc 10 Mu increase factor

  net.trainParam.mu_max 1e10 Maximum Mu

  net.trainParam.show 25 Epochs between showing progress

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

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

• VV.PD, TV.PD -- Validation/test delayed inputs

  VV.Tl, TV.Tl -- Validation/test layer targets

  VV.Ai, TV.Ai -- Validation/test initial input conditions

  VV.Q, TV.Q -- Validation/test batch size

  VV.TS, TV.TS -- Validation/test time steps

Validation vectors are 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. Test vectors are used as a further check that the network is generalizing well, but do not have any effect on training.

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

• 'pnames' -- Names of training parameters

  'pdefaults' -- Default training parameters

Network Use

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

To prepare a custom network to be trained with trainlm

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

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

See newff, newcf, and newelm for examples.

Algorithm

trainlm can train any network as long as its weight, net input, and transfer functions have derivative functions.

Backpropagation is used to calculate the Jacobian jX of performance perf with respect to the weight and bias variables X. Each variable is adjusted according to Levenberg-Marquardt,

• jj = jX * jX
  je = jX * E
  dX = -(jj+I*mu) \ je
  

where E is all errors and I is the identity matrix.

The adaptive value mu is increased by mu_inc until the change above results in a reduced performance value. The change is then made to the network and mu is decreased by mu_dec.

The parameter mem_reduc indicates how to use memory and speed to calculate the Jacobian jX. If mem_reduc is 1, then trainlm runs the fastest, but can require a lot of memory. Increasing mem_reduc to 2 cuts some of the memory required by a factor of two, but slows trainlm somewhat. Higher values continue to decrease the amount of memory needed and increase training times.

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.
• mu exceeds mu_max.
• Validation performance has increased more than max_fail times since the last time it decreased (when using validation).

See Also

• newff, newcf, traingd, traingdm, traingda, traingdx
  

traingdx

trainoss

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