# AdaBoost Does Not Always Cycle: A Computer-Assisted Counterexample

arXiv: https://arxiv.org/abs/2604.07055 · HTML: https://mlsanity.com/paper/2604.07055/

## Key facts

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- First posted on arXiv 8 Apr 2026.

## Abstract (arXiv)

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.