Neural Network Toolbox™

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 = []

and returns

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

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.)
2. Set net.adaptFcn to 'trains'. (net.adaptParam automatically becomes trains's default parameters.)
3. 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),

1. Set net.trainParam (or net.adaptParam) properties to desired values.
2. 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
  

See Also

learnh, adapt, train

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