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Gradient descent with momentum and adaptive learning rate backpropagation


net.trainFcn = 'traingdx'
[net,tr] = train(net,...)


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

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

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

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


Maximum number of epochs to train


Performance goal


Learning rate


Ratio to increase learning rate


Ratio to decrease learning rate


Maximum validation failures


Maximum performance increase


Momentum constant


Minimum performance gradient


Epochs between displays (NaN for no displays)


Generate command-line output


Show training GUI


Maximum time to train in seconds

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