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
Versteckte randomisierte Umrundung Paare den Verlust der Privatsphäre der aufeinanderfolgenden gesamten Releases. Wir untersuchen einen rationalen Feedback-Mechanismus unter vorhersehbarer unterzeichneter Einheit Beteiligung und vollständige Beobachtung jeder physischen Ausgabe. Die Lebensdauer einer Vorbereitung verbindet drei Ergebnisse. Erstens, die Erhaltung der vollständigen Beförderungen bis zu einem beobachteten Echo synchronisiert die Welten gibt genaue finite-law-Punkt-Kompilation, mit einem Support-Breite-Exponent von $3C-2$ bei jedem festen Budget $C\ge2$. Zweitens, die Freigabe von Verpflichtungen früher gibt eine monotone Hierarchie, deren genaue Endpunkt, strenge L
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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