learngdm :: Functions (Neural Network Toolbox™)

learngdm

Purpose

Gradient descent with momentum weight and bias learning function

Syntax

[dW,LS] = learngdm(W,P,Z,N,A,T,E,gW,gA,D,LP,LS)
[db,LS] = learngdm(b,ones(1,Q),Z,N,A,T,E,gW,gA,D,LP,LS)
info = learngdm(code)

Description

learngdm is the gradient descent with momentum weight and bias learning function.

learngdm(W,P,Z,N,A,T,E,gW,gA,D,LP,LS) takes several inputs,

W
S x R weight matrix (or S x 1 bias vector)

P
R x Q input vectors (or ones(1,Q))

Z
S x Q weighted input vectors

N
S x Q net input vectors

A
S x Q output vectors

T
S x Q layer target vectors

E
S x Q layer error vectors

gW
S x R gradient with respect to performance

gA
S x Q output gradient with respect to performance

D
S x S neuron distances

LP
Learning parameters, none, LP = []

LS
Learning state, initially should be = []

`W`	`S` x `R` weight matrix (or `S` x `1` bias vector)
`P`	`R` x `Q` input vectors (or ones(`1`,`Q`))
`Z`	`S` x `Q` weighted input vectors
`N`	`S` x `Q` net input vectors
`A`	`S` x `Q` output vectors
`T`	`S` x `Q` layer target vectors
`E`	`S` x `Q` layer error vectors
`gW`	`S` x `R` gradient with respect to performance
`gA`	`S` x `Q` output gradient with respect to performance
`D`	`S` x `S` neuron distances
`LP`	Learning parameters, none, `LP = []`
`LS`	Learning state, initially should be = `[]`

and returns

dW
S x R weight (or bias) change matrix

LS
New learning state

`dW`	`S` x `R` weight (or bias) change matrix
`LS`	New learning state

Learning occurs according to learngdm's learning parameters, shown here with their default values.

LP.lr - 0.01
Learning rate

LP.mc - 0.9
Momentum constant

`LP.lr - 0.01`	Learning rate
`LP.mc - 0.9`	Momentum constant

learngdm(code) returns useful information for each code string:

'pnames'
Names of learning parameters

'pdefaults'
Default learning parameters

'needg'
Returns 1 if this function uses gW or gA

`'pnames'`	Names of learning parameters
`'pdefaults'`	Default learning parameters
`'needg'`	Returns 1 if this function uses `gW` or `gA`

Examples

Here you define a random gradient G for a weight going to a layer with three neurons from an input with two elements. Also define a learning rate of 0.5 and momentum constant of 0.8:

gW = rand(3,2);
lp.lr = 0.5;
lp.mc = 0.8;

Because learngdm only needs these values to calculate a weight change (see algorithm below), use them to do so. Use the default initial learning state.

ls = [];
[dW,ls] = learngdm([],[],[],[],[],[],[],gW,[],[],lp,ls)

learngdm returns the weight change and a new learning state.

Network Use

You can create a standard network that uses learngdm with newff, newcf, or newelm.

To prepare the weights and the bias of layer i of a custom network to adapt with learngdm,

Set net.adaptFcn to 'trains'. net.adaptParam automatically becomes trains's default parameters.
Set each net.inputWeights{i,j}.learnFcn to 'learngdm'. Set each net.layerWeights{i,j}.learnFcn to 'learngdm'. Set net.biases{i}.learnFcn to 'learngdm'. Each weight and bias learning parameter property is automatically set to learngdm's default parameters.

To allow the network to adapt,

Set net.adaptParam properties to desired values.
Call adapt with the network.

See newff or newcf for examples.

Algorithm

learngdm calculates the weight change dW for a given neuron from the neuron's input P and error E, the weight (or bias) W, learning rate LR, and momentum constant MC, according to gradient descent with momentum:

```
dW = mc*dWprev + (1-mc)*lr*gW
```

The previous weight change dWprev is stored and read from the learning state LS.