traingdm

Gradient descent with momentum backpropagation

Syntax

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

Description

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:

`net.trainParam.epochs`	`1000`	Maximum number of epochs to train
`net.trainParam.goal`	`0`	Performance goal
`net.trainParam.lr`	`0.01`	Learning rate
`net.trainParam.max_fail`	`6`	Maximum validation failures
`net.trainParam.mc`	`0.9`	Momentum constant
`net.trainParam.min_grad`	`1e-5`	Minimum performance gradient
`net.trainParam.show`	`25`	Epochs between showing progress
`net.trainParam.showCommandLine`	`false`	Generate command-line output
`net.trainParam.showWindow`	`true`	Show training GUI
`net.trainParam.time`	`inf`	Maximum time to train in seconds

Network Use

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

Set net.trainFcn to 'traingdm'. This sets net.trainParam to traingdm’s default parameters.
Set net.trainParam properties to desired values.

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

See help feedforwardnet and help cascadeforwardnet for examples.

More About

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Gradient Descent with Momentum

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.

Algorithms

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).

Documentation