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
[net,tr] = train(net,...) trains the network with
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
cascadeforwardnet. To prepare a custom
network to be trained with
'traingdm'. This sets
traingdm’s default parameters.
net.trainParamproperties to desired values.
In either case, calling
train with the resulting network trains the
help feedforwardnet and
Gradient Descent with Momentum
In addition to
traingd, there are three other variations of gradient
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
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
nnd12mo [HDB96] for an illustration of the performance of the batch momentum
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
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
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
Performance is minimized to the
The performance gradient falls below
Validation performance has increased more than
max_failtimes since the last time it decreased (when using validation).