Excited to share an AI-driven solution to the open problem posed by Rudin, Schapire, and Daubechies in COLT 2012: "Does AdaBoost Always Cycle?"
arxiv.org/abs/2604.07055
This was an attempt to push the limits of autonomous mathematical research. It's stunning to see what GPT 5.4 Pro & Opus 4.6 are capable of.
AdaBoost is among the most widely used boosting algorithms, but its asymptotic behavior still isn't fully understood. This particular problem asks if its distributions always converge to a cycle for every {-1, 1}-valued matrix, and has been open for the past 14 years!
Working with GPT and Claude, we identify a counterexample and show that it does not converge with a certificate. What's most striking to me is just how much heavy-lifting the models did to get to the solution. The whole process was also shockingly quick.
This result further signals AI's ability to advance real scientific research. While many Erdős problems have (very impressively) been solved, this exact question was published as an open research problem of real interest to the CS and ML theory communities.
Certificate:
github.com/ewang26/AdaBoost Many thanks to
@EdgarDobriban for very helpful feedback on this work and his efforts on
SolveAll.org. Onwards and upwards!