Gradient descent with momentum backpropagation
net.trainFcn = 'traingdm'
[net,tr] = train(net,...)
traingdm is a network training function that updates weight and bias values according to gradient descent with momentum.
net.trainFcn = 'traingdm' sets the network trainFcn property.
[net,tr] = train(net,...) trains the network with traingdm.
Training occurs according to traingdm training parameters, shown here with their default values:
Maximum number of epochs to train
Maximum validation failures
Minimum performance gradient
Epochs between showing progress
Generate command-line output
Show training GUI
Maximum time to train in seconds
You can create a standard network that uses traingdm with feedforwardnet or cascadeforwardnet. To prepare a custom network to be trained with traingdm,
In either case, calling train with the resulting network trains the network with traingdm.
See help feedforwardnet and help cascadeforwardnet for examples.
In addition to traingd, there are three other variations of gradient descent.
Gradient descent with momentum, implemented by traingdm, allows a network to respond not only to the local gradient, but also to recent trends in the error surface. Acting like a lowpass filter, momentum allows the network to ignore small features in the error surface. Without momentum a network can get stuck in a shallow local minimum. With momentum a network can slide through such a minimum. See page 12–9 of [HDB96] for a discussion of momentum.
Gradient descent with momentum depends on two training parameters. The parameter lr indicates the learning rate, similar to the simple gradient descent. The parameter mc is the momentum constant that defines the amount of momentum. mc is set between 0 (no momentum) and values close to 1 (lots of momentum). A momentum constant of 1 results in a network that is completely insensitive to the local gradient and, therefore, does not learn properly.)
p = [-1 -1 2 2; 0 5 0 5]; t = [-1 -1 1 1]; net = feedforwardnet(3,'traingdm'); net.trainParam.lr = 0.05; net.trainParam.mc = 0.9; net = train(net,p,t); y = net(p)
Try the Neural Network Design demonstration nnd12mo [HDB96] for an illustration of the performance of the batch momentum algorithm.
traingdm 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*(1-mc)*dperf/dX
where dXprev is the previous change to the weight or bias.
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).