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# learngdm

Gradient descent with momentum weight and bias learning function

## Syntax

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

## Description

learngdm is the gradient descent with momentum weight and bias learning function.

[dW,LS] = learngdm(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 learngdm's learning parameters, shown here with their default values.

 LP.lr - 0.01 Learning rate LP.mc - 0.9 Momentum constant

info = learngdm('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 gradient G for a weight going to a layer with three neurons from an input with two elements. Also define a learning rate of 0.5 and momentum constant of 0.8:

```gW = rand(3,2);
lp.lr = 0.5;
lp.mc = 0.8;
```

Because learngdm only needs these values to calculate a weight change (see "Algorithm" below), use them to do so. Use the default initial learning state.

```ls = [];
[dW,ls] = learngdm([],[],[],[],[],[],[],gW,[],[],lp,ls)
```

learngdm returns the weight change and a new learning state.

## Network Use

You can create a standard network that uses learngdm with newff, newcf, or newelm.

To prepare the weights and the bias of layer i of a custom network to adapt with learngdm,

2. Set each net.inputWeights{i,j}.learnFcn to 'learngdm'. Set each net.layerWeights{i,j}.learnFcn to 'learngdm'. Set net.biases{i}.learnFcn to 'learngdm'. Each weight and bias learning parameter property is automatically set to learngdm'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

learngdm calculates the weight change dW for a given neuron from the neuron's input P and error E, the weight (or bias) W, learning rate LR, and momentum constant MC, according to gradient descent with momentum:

```dW = mc*dWprev + (1-mc)*lr*gW
```

The previous weight change dWprev is stored and read from the learning state LS.