We generate and from by randomly flipping bits in with probability p. The probability that the class of a training example or a testing example matches the target is , but the probability that the class of the training example matches the class of the testing example is . target
t 1 … t 32 , , t = = train α 1 … α 32 , , α = = test β 1 … β 32 , , β = = t i α i β i 0 1 , { } ∈ , , α β t t 1 p - 1 2p - 2p 2 + P α i t i = ( ) 1 p - = P β i t i = ( ) 1 p - = P α i β i = ( ) 1 2p - 2p 2 + = α i β i t i = = 1 p - ( ) 2 α i β i t i ≠ = p 2 1 p - ( ) 2 p 2 + 1 2p - 2p 2 + = α β t 2 n (9)(10)
If the i-th bias strength gene has a value , then there is a probability that the individual will guess ; otherwise, there is a probability that the individual will guess . This simplified model does not describe the learning mechanism. We are dealing with a level of abstraction where the exact learning mechanism is not important. Since we assume that all 32 possible cases are in the training **data** , the individual can learn by simply storing the training data. In a more complex model, the genotype could encode the architecture of a neural network, and back propagation could be used to learn from the training **data** (Balakrishnan and Honavar, 1995).