learnhd :: Functions (Neural Network Toolbox™)

learnhd

Purpose

Hebb with decay weight learning rule

Syntax

[dW,LS] = learnhd(W,P,Z,N,A,T,E,gW,gA,D,LP,LS)
info = learnhd(code)

Description

learnhd is the Hebb weight learning function.

learnhd(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 learnhd's learning parameters, shown here with default values.

LP.dr - 0.01
Decay rate

LP.lr - 0.1
Learning rate

`LP.dr - 0.01`	Decay rate
`LP.lr - 0.1`	Learning rate

learnhd(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 input P, output A, and weights W for a layer with a two-element input and three neurons. Also define the decay and learning rates.

p = rand(2,1);
a = rand(3,1);
w = rand(3,2);
lp.dr = 0.05;
lp.lr = 0.5;

Because learnhd only needs these values to calculate a weight change (see algorithm below), use them to do so.

dW = learnhd(w,p,[],[],a,[],[],[],[],[],lp,[])

Network Use

To prepare the weights and the bias of layer i of a custom network to learn with learnhd,

Set net.trainFcn to 'trainr'. (net.trainParam automatically becomes trainr's default parameters.)
Set net.adaptFcn to 'trains'. (net.adaptParam automatically becomes trains's default parameters.)
Set each net.inputWeights{i,j}.learnFcn to 'learnhd'. Set each net.layerWeights{i,j}.learnFcn to 'learnhd'. (Each weight learning parameter property is automatically set to learnhd's default parameters.)

To train the network (or enable it to adapt),

Set net.trainParam (or net.adaptParam) properties to desired values.
Call train (adapt).

Algorithm

learnhd calculates the weight change dW for a given neuron from the neuron's input P, output A, decay rate DR, and learning rate LR according to the Hebb with decay learning rule:

```
dw = lr*a*p' - dr*w
```