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# learnh

Hebb weight learning rule

## Syntax

[dW,LS] = learnh(W,P,Z,N,A,T,E,gW,gA,D,LP,LS)
info = learnh('code')

## Description

learnh is the Hebb weight learning function.

[dW,LS] = learnh(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 learnh's learning parameter, shown here with its default value.

 LP.lr - 0.01 Learning rate

info = learnh('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 and output A for a layer with a two-element input and three neurons. Also define the learning rate LR.

```p = rand(2,1);
a = rand(3,1);
lp.lr = 0.5;
```

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

```dW = learnh([],p,[],[],a,[],[],[],[],[],lp,[])
```

## Network Use

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

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

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

4. Set each net.layerWeights{i,j}.learnFcn to 'learnh'. (Each weight learning parameter property is automatically set to learnh's default parameters.)

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

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

expand all

### Algorithms

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

```dw = lr*a*p'
```

## References

Hebb, D.O., The Organization of Behavior, New York, Wiley, 1949