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Gradient descent with momentum and adaptive learning rate backpropagation


net.trainFcn = 'traingdx' sets the network trainFcn property.

[trainedNet,tr] = train(net,...) trains the network with traingdx.

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

Training occurs according to traingdx training parameters, shown here with their default values:

  • net.trainParam.epochs — Maximum number of epochs to train. The default value is 1000.

  • net.trainParam.goal — Performance goal. The default value is 0.

  • — Learning rate. The default value is 0.01.

  • net.trainParam.lr_inc — Ratio to increase learning rate. The default value is 1.05.

  • net.trainParam.lr_dec — Ratio to decrease learning rate. The default value is 0.7.

  • net.trainParam.max_fail — Maximum validation failures. The default value is 6.

  • net.trainParam.max_perf_inc — Maximum performance increase. The default value is 1.04.

  • — Momentum constant. The default value is 0.9.

  • net.trainParam.min_grad — Minimum performance gradient. The default value is 1e-5.

  • — Epochs between displays (NaN for no displays). The default value is 25.

  • net.trainParam.showCommandLine — Generate command-line output. The default value is false.

  • net.trainParam.showWindow — Show training GUI. The default value is true.

  • net.trainParam.time — Maximum time to train in seconds. The default value is inf.

Input Arguments

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Input network, specified as a network object. To create a network object, use for example, feedforwardnet or narxnet.

Output Arguments

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Trained network, returned as a network object.

Training record (epoch and perf), returned as a structure whose fields depend on the network training function (net.NET.trainFcn). It can include fields such as:

  • Training, data division, and performance functions and parameters

  • Data division indices for training, validation and test sets

  • Data division masks for training validation and test sets

  • Number of epochs (num_epochs) and the best epoch (best_epoch).

  • A list of training state names (states).

  • Fields for each state name recording its value throughout training

  • Performances of the best network (best_perf, best_vperf, best_tperf)

More About

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Network Use

You can create a standard network that uses traingdx with feedforwardnet or cascadeforwardnet. To prepare a custom network to be trained with traingdx,

  1. Set net.trainFcn to 'traingdx'. This sets net.trainParam to traingdx’s default parameters.

  2. Set net.trainParam properties to desired values.

In either case, calling train with the resulting network trains the network with traingdx.

See help feedforwardnet and help cascadeforwardnet for examples.


The function traingdx combines adaptive learning rate with momentum training. It is invoked in the same way as traingda, except that it has the momentum coefficient mc as an additional training parameter.

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 that increased the performance is not made.

Training stops when any of these conditions occurs:

  • The maximum number of epochs (repetitions) is reached.

  • The maximum amount of time is exceeded.

  • Performance is minimized to the goal.

  • The performance gradient falls below min_grad.

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

Introduced before R2006a