traingd (Neural Network Toolbox)

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traingd

See Also

Gradient descent backpropagation

Syntax

[net,tr] = traingd(net,Pd,Tl,Ai,Q,TS,VV)

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.

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.

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 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 are used to stop training early if the network performance on the validation vectors fails to improve or remain the same for max_fail epochs in a row.

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 occurs:

1.: The maximum number of epochs (repetitions) is reached.

2.: The maximum amount of time has been exceeded.

3.: Performance has been minimized to the goal.

4.: The performance gradient falls below mingrad.

5.: Validation performance has increased more than max_fail times since the last time it decreased (when using validation).