Editing Perceptron (section)

=== Perceptron cycling theorem ===
When the dataset is not linearly separable, then there is no way for a single perceptron to converge. However, we still have<ref>{{Cite journal |last1=Block |first1=H. D. |last2=Levin |first2=S. A. |date=1970 |title=On the boundedness of an iterative procedure for solving a system of linear inequalities |url=https://www.ams.org/proc/1970-026-02/S0002-9939-1970-0265383-5/ |journal=Proceedings of the American Mathematical Society |language=en |volume=26 |issue=2 |pages=229–235 |doi=10.1090/S0002-9939-1970-0265383-5 |issn=0002-9939|doi-access=free }}</ref>
{{Math theorem
| name = Perceptron cycling theorem
| note = 
| math_statement = If the dataset <math>D</math> has only finitely many points, then there exists an upper bound number <math>M</math>, such that for any starting weight vector <math>w_0</math> all weight vector <math>w_t</math> has norm bounded by <math>\|w_t\| \leq \|w_0\|+M</math>
}}This is proved first by [[Bradley Efron]].<ref>Efron, Bradley. "The perceptron correction procedure in nonseparable situations." ''Rome Air Dev. Center Tech. Doc. Rept'' (1964).</ref>