Manuscript OpenAI@2026-10-07 · OpenAI.tex · remark · 6a931f8f
Remark: 139-01. Subpolynomial query complexity for well-conditioned log-concave sampling
Manuscript map · lines 5085–5094
OpenAI@2026-10-07#rem:oai-p-139-01
Authors: OpenAI. Family 139.
Title: Subpolynomial query complexity for well-conditioned log-concave sampling.
Abstract: For every fixed ε > 0, we give a sampling algorithm using at most $C_{}varepsilon d{}{}varepsilon$ exact first-order queries on every execution for C2 potentials on ℝd with a known minimizer and Hessian between Id and $2I_d$. The output has total-variation distance at most 1/10 from the target Gibbs law. Computation between queries is unrestricted. We also prove an ${}Omega({}log d)$ query lower bound for arbitrary randomized adaptive algorithms, determining the optimal dimension exponent to be zero.
This abstract is a catalogue record. It is not a verification and not a premise. It does not close O.1. O.1 stays NOT_CLOSED. No quantum coefficient is admitted. No compilation is asserted.
Nearby in this section
- section: Manuscript map
- remark: Remark: 001-01. Milne's rationality conjecture for abelian varieties
- remark: Remark: 002-01. Exact Birch–Swinnerton-Dyer Formula from Low Selmer Corank
- remark: Remark: 002-02. The Selmer converse for elliptic curves at every prime
- remark: Remark: 002-03. The two-primary Birch–Swinnerton-Dyer formula in Selmer corank at most one
- remark: Remark: 003-01. The Quasi-Riemann Hypothesis: A Zero-Free Half-Plane s 7/8
- remark: Remark: 003-02. The Quasi-Riemann Hypothesis (alternate 11/12 proof)
- remark: Remark: 003-03. Uniform exclusion of Landau–Siegel zeros