OpenAI research collection · 1 manuscript · Source checked 2026-10-19
OpenAI's result summary
Proves exponential threshold repetition for every finite two-player one-round game: if its entangled value is v < 1, the probability of winning at least a fraction v+δ of k independent repetitions decays exponentially in k, for 0< δ< 1-v. Arbitrary joint finite-dimensional entangled strategies and correlated question distributions are allowed.
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MANUSCRIPT 01
Threshold parallel repetition for finite-dimensional entangled games
For every finite two-player game with entangled value v < 1, we prove exponential decay for the probability of winning at least a v+δ fraction of k independent repetitions, uniformly over all finite-dimensional joint strategies. The result allows arbitrary correlated question distributions and holds for every 0< δ< 1-v and k ≥…
Full source abstract
For every finite two-player game with entangled value v < 1, we prove exponential decay for the probability of winning at least a v+δ fraction of k independent repetitions, uniformly over all finite-dimensional joint strategies. The result allows arbitrary correlated question distributions and holds for every 0< δ< 1-v and k ≥ 1. Its universal rate is proportional to δ^5/(1+log(|\mathcal A||\mathcal B|)), where \mathcal A,\mathcal B are the answer alphabets. For each fixed question distribution, we also obtain an explicit cubic rate in δ.
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New mathematical reasoning could help AI tackle harder scientific and computational problems. How reliably these skills transfer beyond mathematics will determine how much they contribute to general intelligence.