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# learngd

Gradient descent weight and bias learning function

## Syntax

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

## Description

learngd is the gradient descent weight and bias learning function.

[dW,LS] = learngd(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 output gradient with respect to performance x 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 learngd's learning parameter, shown here with its default value.

 LP.lr - 0.01 Learning rate

info = learngd('code') returns useful information for each supported 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 gradient gW for a weight going to a layer with three neurons from an input with two elements. Also define a learning rate of 0.5.

```gW = rand(3,2);
lp.lr = 0.5;
```

Because learngd only needs these values to calculate a weight change (see "Algorithm" below), 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 automatically becomes 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 is automatically 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 help newff or help newcf for examples.

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### Algorithms

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.