# Limit Cycles of AdaBoost

arXiv: https://arxiv.org/abs/2209.06928 · HTML: https://mlsanity.com/paper/2209.06928/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 1 of its 25 references that are in the map.
- First posted on arXiv 14 Sep 2022.

## Builds on (most cited first, 1 of 1)

- [Some Open Problems in Optimal AdaBoost and Decision Stumps](https://mlsanity.com/paper/1505.06999/) (2015)

## Built on by (most cited first, 1 of 1)

- [Optimal AdaBoost Converges](https://mlsanity.com/paper/2210.07808/) (2022)

## Abstract (arXiv)

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.