Generalization errors of the simple perceptron
Jianfeng Feng · Journal of Physics A Mathematical and General · 1998
To find an exact form for the generalization error of a learning machine is an open problem, even in the simplest case: simple perceptron learning. We introduce a new approach to tackle the problem. The generalization error of the simple perceptron is expressed as a linear combination of extreme values of inputs. With the help of extreme value theory in statistics we then obtain an exact form of the generalization error of the simple perceptron in the case of the worst learning. Generalization errors of the higher-order perceptron taking the form of an inverse power law in the number of examples are also considered.