Neural Network Toolbox

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.

learnh(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 = []

and returns,

• dW -- S x 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

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 we define a random input P and output A for a layer with a two-element input and three neurons. We also define the learning rate LR.

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

Since learnh only needs these values to calculate a weight change (see algorithm below), we will 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 will automatically become trainr's default parameters.)
2. Set net.adaptFcn to 'trains'. (net.adaptParam will automatically become trains's default parameters.)
3. Set each net.inputWeights{i,j}.learnFcn to 'learnh'. Set each net.layerWeights{i,j}.learnFcn to 'learnh'. Each weight learning parameter property will automatically be set to learnh's default parameters.)

To train the network (or enable it to adapt)

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

Algorithm

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'
  

See Also

• learnhd, adapt, train
  

References

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

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learnhd

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