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# learnhd

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.

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

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

and returns

 dW S-by-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

info = 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

## 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,

1. Set net.trainFcn to 'trainr'. (net.trainParam automatically becomes trainr's default parameters.)

3. Set each net.inputWeights{i,j}.learnFcn to 'learnhd'.

4. 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),

1. Set net.trainParam (or net.adaptParam) properties to desired values.

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