OpenAI · 139-01 · 2026-09-26 · Theoretical computer science
Subpolynomial query complexity for well-conditioned log-concave sampling
preprints/Subpolynomial-query-complexity-for-well-conditioned-log-concave-sampling-September-26-2026
Family 139. Subpolynomial queries for log-concave sampling.
The authors are OpenAI. This companion does not verify the proof and does not adopt it as a theorem of Ngo Cheung’s series. It is not a premise. O.1 stays NOT_CLOSED. Anti-de Sitter results are not a de Sitter state, not Em02-E’s relational lapse, not XVI-P’s QdS scheme, and not XVI-Q’s sigma-image record. No quantum coefficient is admitted. No compilation is asserted.
Read against the standing problems
Standing problems. No standing problem is named in this text. It was still read against the nine problems and does not close any of them. The authors are OpenAI. The companion does not verify the proof. This is not a premise of a manuscript by Ngo Cheung. O.1 stays NOT_CLOSED. No quantum coefficient is admitted. No compilation is asserted. XVI-P · XVI-N
For potentials with a supplied minimizer and , proves that sampling within total variation requires only exact value-and-gradient queries for every fixed . The bound holds on every run, with unrestricted computation between queries. A logarithmic lower bound also holds, so the optimal power-law exponent in this oracle model is zero.
For every fixed ε > 0, we give a sampling algorithm using at most exact first-order queries on every execution for C2 potentials on ℝd with a known minimizer and Hessian between Id and . The output has total-variation distance at most 1/10 from the target Gibbs law. Computation between queries is unrestricted. We also prove an query lower bound for arbitrary randomized adaptive algorithms, determining the optimal dimension exponent to be zero.
Preprint source and Lean scope
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This preprint is named in the Lean scope note for 139: Subpolynomial query complexity for log-concave sampling. The authors are OpenAI. This companion does not verify the formalization. It is not a premise. The OAI library is not imported. No compilation is asserted. O.1 stays NOT_CLOSED.