  The iterative weight update for the AdaBoost machine learning algorithm may
be realized as a dynamical map on a probability simplex. When learning a
low-dimensional data set this algorithm has a tendency towards cycling
behavior, which is the topic of this paper. AdaBoost's cycling behavior lends
itself to direct computational methods that are ineffective in the general,
non-cycling case of the algorithm. From these computational properties we give
a concrete correspondence between AdaBoost's cycling behavior and continued
fractions dynamics. Then we explore the results of this correspondence to
expound on how the algorithm comes to be in this periodic state at all. What we
intend for this work is to be a novel and self-contained explanation for the
cycling dynamics of this machine learning algorithm.
