Generalization ability of a perceptron with non-monotonic transfer function

Details Generalization ability of a perceptron with non-monotonic transfer function Generalization ability of a perceptron with non-monotonic transfer function

1997-05-19

arxiv.org/abs/cond-mat/9705190v3

Physics

Condensed Matter

Disordered Systems and Neural Networks

Latex 20 pages with 10 figures

Scientific paper

10.1103/PhysRevE.58.849

We investigate the generalization ability of a perceptron with non-monotonic transfer function of a reversed-wedge type in on-line mode. This network is identical to a parity machine, a multilayer network. We consider several learning algorithms. By the perceptron algorithm the generalization error is shown to decrease by the ${\alpha}^{-1/3}$-law similarly to the case of a simple perceptron in a restricted range of the parameter $a$ characterizing the non-monotonic transfer function. For other values of $a$, the perceptron algorithm leads to the state where the weight vector of the student is just opposite to that of the teacher. The Hebbian learning algorithm has a similar property; it works only in a limited range of the parameter. The conventional AdaTron algorithm does not give a vanishing generalization error for any values of $a$.We thus introduce a modified AdaTron algorithm which yields a good performance for all values of $a$. We also investigate the effects of optimization of the learning rate as well as of the learning algorithm. Both methods give excellent learning curves proportional to ${\alpha}^{-1}$. The latter optimization is related to the Bayes statistics and is shown to yield useful hints to extract maximum amount of information necessary to accelerate learning processes.

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