Ganxuan Yang, Siqi Wen, Shuyan Yu, Jidong Yuan · 2026 · arXiv (Cornell University)
DOI: 10.48550/arxiv.2610.26442 · cited by 0 works (OpenAlex) · open-access PDF
私たちは、予測可能な署名ユニット参加とすべての物理出力の完全な観察下で合理的なフィードバックメカニズムを研究します。 準備の生涯は3つの結果を結びつける。 第一に、観測されたエコーが世界を同期するまで完全な損失を維持することにより、予測可能な署名ユニット参加とすべての物理出力の完全な観察が行われます。 第二に、準備の生涯は3つの結果を結びつける。 第一に、観測されたエコーが世界を同期するまで完全な損失を維持することにより、正確なフィードバックポイントのコンパイルが提供されます。 固定ガウシアの差別的なエラーでは、サポート幅が4つの約束を必要とします。 第三に、
Machine translation (Meta M2M100); the English original follows.
Hidden randomized rounding couples the privacy loss of successive integer releases. We study a rational-feedback mechanism under predictable signed-unit participation and full observation of every physical output. A preparation's lifetime connects three results. First, preserving complete carries until an observed echo synchronizes the worlds gives exact finite-law point compilation, with support-width exponent $3C-2$ at every fixed budget $C\ge2$. Second, releasing commitments earlier gives a monotone hierarchy whose exact endpoint, strict gaps and numerical brackets quantify calibration loss. At one fixed discrete Gaussian, a loss allowance of 0.09 requires all four commitments. Third, legal regeneration yields an unrestricted KL rate with a square-root testing remainder and a complete asymptotic frontier under joint physical-time and participation constraints. At fixed rational parameters, finite-window occupation programs approximate that frontier to error $2^{-b}$ in polynomial bit time in $b$. Verified countable-transcript semantics and independently checked finite certificates support these analyses. A matched static workload illustrates the resulting design tradeoff: a structured finite integer matrix improves error and fresh randomness, while the scalar feedback instance retains fewer noise-state and source-table bits.
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Topics: Integer (computer science), Mathematics, Rounding, Fixed point, Equivalence (formal languages), Polynomial
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