AdaBoost Does Not Always Cycle: A Computer-Assisted Counterexample
Machine Learning
2026-04-20 v2
Abstract
We give a computer-assisted counterexample to the open question, posed by Rudin, Schapire, and Daubechies in COLT 2012, of whether exhaustive AdaBoost always converges to a finite cycle. The construction is based on a block-product gadget whose two factors share an exact period-2 orbit for their 5-step branch maps, but whose linearized return maps have dominant eigenvalues with an irrational logarithmic ratio. This irrationality forces the burst-winner sequence to have an irrational asymptotic frequency, precluding eventual periodicity. All assertions are certified by exact rational arithmetic. This work was developed in collaboration with GPT-5.4 Pro and Claude Opus 4.6.
Cite
@article{arxiv.2604.07055,
title = {AdaBoost Does Not Always Cycle: A Computer-Assisted Counterexample},
author = {Erik Y. Wang},
journal= {arXiv preprint arXiv:2604.07055},
year = {2026}
}