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🎉🥳 After another 20 hours with GPT-5.6 Sol, we have substantially improved the lower bound on worst-case FDR(BHq) for correlated Gaussian two-sided tests: https://lihualei71.github.io/FDR_BH_gaussian_stronger_lower_bound.pdf GPT’s amazing capability to construct examples with desired properties is instrumental! 🧵(1/5)
New paper🚨After 10h w/ GPT-5.6 Sol, I made exciting progress on worst-case FDR of BH for correlated two-sided Gaussian tests @edgardobriban showed FDR(BH_q)/q can exceed 1 Q (a folklore conjecture): Is the ratio universally bounded? A: No👇 https://lihualei71.github.io/FDR_BH_gaussian_lower_bound.pdf 🧵(1/8) https://twitter.com/edgardobriban/status/2077082912021786660
🎉🥳 After another 20 hours with GPT-5.6 Sol, we have substantially improved the lower bound on worst-case FDR(BHq) for correlated Gaussian two-sided tests: https://lihualei71.github.io/FDR_BH_gaussian_stronger_lower_bound.pdf GPT’s amazing capability to construct examples with desired properties is instrumental! 🧵(1/5)
New paper🚨After 10h w/ GPT-5.6 Sol, I made exciting progress on worst-case FDR of BH for correlated two-sided Gaussian tests @edgardobriban showed FDR(BH_q)/q can exceed 1 Q (a folklore conjecture): Is the ratio universally bounded? A: No👇 https://lihualei71.github.io/FDR_BH_gaussian_lower_bound.pdf 🧵(1/8) https://twitter.com/edgardobriban/status/2077082912021786660
Pretty sure from this point on, there will constantly be people running frontier LLM’s over open research problems, hoping that it solves them. We’re now trying to turn electricity into net new knowledge for humanity – and it's working! Truly the stuff of science fiction.
This conjecture was, by far, the most interesting open problem in my area of statistics. Any statistician would have been excited to construct this counterexample, and I’d have been thrilled for them. GPT-5.6 solved it, but I wish a human had. https://twitter.com/edgardobriban/status/2077082912021786660