Abstract: We extend the convergence of the simple perceptron learning rule to the case that the set of inputs is infinity or a region. When the set of inputs is linearly separable, we prove that a simple perceptron always improves its performance. As the set of the inputs is 'strong' linearly separable, then within finite time the connections among units converge to a limit which separates the inputs. The convergence rate is also estimated.

Key words: simple perceptron, supermartingale, linearly separable

摘要： 当输入是无穷集或区域时，通过构造一个上鞅，本文证明了简单Perceptron学习算法的收敛性。

关键词: 简单Perceptron, 上鞅, 线性可分