Neural Network Toolbox

learngd

Gradient descent weight and bias learning function

Syntax

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

[db,LS] = learngd(b,ones(1,Q),Z,N,A,T,E,gW,gA,D,LP,LS)

info = learngd(code)

Description

learngd is the gradient descent weight and bias learning function.

learngd(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 learngd's learning parameter shown here with its default value.

• LP.lr - 0.01 - Learning rate.

learngd(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 gradient gW for a weight going to a layer with 3 neurons, from an input with 2 elements. We also define a learning rate of 0.5.

• gW = rand(3,2);
  lp.lr = 0.5;
  

Since learngd only needs these values to calculate a weight change (see algorithm below), we will use them to do so.

• dW = learngd([],[],[],[],[],[],[],gW,[],[],lp,[])
  

Network Use

You can create a standard network that uses learngd with newff, newcf, or newelm. To prepare the weights and the bias of layer i of a custom network to adapt with learngd:

1. Set net.adaptFcn to 'trains'. net.adaptParam will automatically become trains's default parameters.
2. Set each net.inputWeights{i,j}.learnFcn to 'learngd'. Set each net.layerWeights{i,j}.learnFcn to 'learngd'. Set net.biases{i}.learnFcn to 'learngd'. Each weight and bias learning parameter property will automatically be set to learngd's default parameters.

To allow the network to adapt:

1. Set net.adaptParam properties to desired values.
2. Call adapt with the network.

See newff or newcf for examples.

Algorithm

learngd calculates the weight change dW for a given neuron from the neuron's input P and error E, and the weight (or bias) learning rate LR, according to the gradient descent: dw = lr*gW.

See Also

learngdm, newff, newcf, adapt, train

learncon

learngdm