Neural Network Toolbox

traingdx

Gradient descent with momentum and adaptive learning rate backpropagation

Syntax

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

info = traingdx(code)

Description

traingdx is a network training function that updates weight and bias values according to gradient descent momentum and an adaptive learning rate.

traingdx(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 empty matrix [] or 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.

    TR.lr   - Adaptive learning rate.

  Ac - Collective layer outputs for last epoch.

  El - Layer errors for last epoch.

Training occurs according to the traingdx'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.lr_inc 1.05 Ratio to increase learning rate

  net.trainParam.lr_dec 0.7 Ratio to decrease learning rate

  net.trainParam.max_fail 5 Maximum validation failures

  net.trainParam.max_perf_inc 1.04 Maximum performance increase

  net.trainParam.mc 0.9 Momentum constant.

  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 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 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.

traingdx(code) return 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 traingdx with newff, newcf, or newelm.

To prepare a custom network to be trained with traingdx:

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

See newff, newcf, and newelm for examples.

Algorithm

traingdx 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 with momentum,

• dX = mc*dXprev + lr*mc*dperf/dX
  

where dXprev is the previous change to the weight or bias.

For each epoch, if performance decreases toward the goal, then the learning rate is increased by the factor lr_inc. If performance increases by more than the factor max_perf_inc, the learning rate is adjusted by the factor lr_dec and the change, which increased the performance, is not made.

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 increase more than max_fail times since the last time it decreased (when using validation).

See Also

newff, newcf, traingd, traingdm, traingda, trainlm

traingdm

trainlm