Gradient Optimization Procedures

Introduction:-The most interesting characteristic of neural networks is their capability to familiarize with problems by means of training and, after sufficient training, to be able to solve unknown problems of the same class. This approach is referred to as generalization.

Learning is a comprehensive term. A learning system changes itself in order to adapt to e.g. environmental changes. A neural network could learn from many things but, of course, there will always be the question of how to implement it.

Theoretically, a neural network could learn by

• Developing new connections,
• Deleting existing connections,
• Changing connecting weights,
• Changing the threshold values of neurons,
• Varying one or more of the three neuron functions (remember: activation function, propagation function and output function),
• Developing new neurons, or
• Deleting existing neurons (and so, of course, existing connections).

1).A learning procedure is always an algorithm that can easily be implemented by means of a programminglanguage.Atraining set is a set of training patterns, which we use to train our neural net.

Unsupervised learning is the biologically most plausible method, but is not suitable for all problems. The training set only consists of input patterns; the network tries by itself to detect similarities and to generate pattern classes.

2).Inreinforcement learning the network receives a logical or a real value after completion of a sequence, which defines whether the result is right or wrong. Intuitively it is clear that this procedure should be more effective than unsupervised learning since the network receives specific criteria for problem-solving.

The training set consists of input patterns, after completion of a sequence a value is returned to the network indicating whether the result was right or wrong and, possibly,how right or wrong it was.

3).In supervised learningthe training set consists of input patterns as well as their correct results in the form of the precise activation of all output neurons. Thus, for each training set that is fed into the network the output, for instance, can directly becompared with the correct solution andthe network weights can be changedaccording to their difference. The objective is to change the weights to the effect that the network cannot only associate input and output patterns independently after the training, but can provide plausible results to unknown, similar input patterns, i.e. it generalises.

The training set consists of input patterns with correct results so that the network canreceive a precise error vectorcan be returned. This learning procedure is not always biologicallyplausible, but it is extremely effectiveand therefore very practicable.At first we want to look at the supervisedlearning procedures in general which - in this text - are correspondingto the following steps:

Entering the input pattern (activation ofinput neurons).

Forward propagation of the input by the network, generation of the output.

Comparing the output with the desired output (teaching input), provides error vector (difference vector).

Corrections of the network are calculated based on the error vector.