GPT-5.6 and Fable 5 Team Up to Solve a 25-Year-Old Math Problem

Dimitris Papailiopoulos, a principal researcher at Microsoft Research and an associate professor at the University of Wisconsin–Madison, collaborated with AI models GPT-5.6 and Fable 5 to prove that a two-step algorithm can achieve exact recovery in MIMO detection at the maximum likelihood threshold, a problem that had remained unsolved for 25 years. MIMO detection is a classic problem in wireless communications where the receiver must recover the transmitted bits from a noisy, mixed signal. The naive maximum likelihood detection requires exhaustive search, which is exponential. In 2001, Hassibi and Vikalo proposed a sphere decoder that they claimed ran in polynomial time, but in 2005 Jaldén and Ottersten proved its expected complexity was actually exponential. Subsequent approaches like semidefinite relaxation, bit-flipping local search, AMP, and statistical physics methods all failed to exactly match the threshold. The AI models provided proof paths: GPT-5.6 used an AMP-based approach, while Fable 5 used a 'signed LMMSE plus greedy bit-flipping' approach, which Papailiopoulos chose and then had GPT refine. After a week of iterative simplification, they obtained a proof that the algorithm works in polynomial time O(N^3), with the greedy step requiring O(N log N) steps. The algorithm first performs LMMSE rounding, then greedy bit-flipping, and the proof shows it always terminates at the true transmitted bit string.