A block-product gadget with shared period-2 orbits but irrational eigenvalue log-ratios produces an AdaBoost burst-winner sequence with irrational asymptotic frequency, proving non-periodicity.
Schapire and Yoav Freund.Boosting: Foundations and Algorithms
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AdaBoost Does Not Always Cycle: A Computer-Assisted Counterexample
A block-product gadget with shared period-2 orbits but irrational eigenvalue log-ratios produces an AdaBoost burst-winner sequence with irrational asymptotic frequency, proving non-periodicity.