Neural Network Toolbox

traingd

Gradient descent backpropagation

Syntax

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

info = traingd(code)

Description

traingd is a network training function that updates weight and bias values according to gradient descent.

traingd(net,Pd,Tl,Ai,Q,TS,VV) 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 an empty matrix [] or a structure of validation vectors.

  TV - 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 traingd's training parameters shown here with their default values:

• net.trainParam.epochs 10 Maximum number of epochs to train

  net.trainParam.goal 0 Performance goal

  net.trainParam.lr 0.01 Learning rate

  net.trainParam.max_fail 5 Maximum validation failures

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

  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 an 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 validation 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.

traingd(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 traingd with newff, newcf, or newelm.

To prepare a custom network to be trained with traingd:

1. Set net.trainFcn to 'traingd'. This will set net.trainParam to traingd'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 traingd.

See newff, newcf, and newelm for examples.

Algorithm

traingd 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 gradient descent:

• dX = lr * dperf/dX
  

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

traincgp

traingda