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
La pérdida de privacidad de pares de redondeo aleatorio oculta la pérdida de privacidad de sucesivos lanzamientos de números enteros. Estudiamos un mecanismo de retroalimentación racional bajo la participación de unidad firmada predecible y la observación completa de cada salida física. La vida útil de una preparación conecta tres resultados. En primer lugar, la preservación de las cargas completas hasta que un eco observado sincroniza los mundos da una compilación exacta de puntos de ley finita, con un exponente de ancho de soporte de $3C-2$ en cada presupuesto fijo de $C\ge2$. En segundo lugar, la liberación de compromisos anteriores da una jerarquía monótona cuyo punto final exacto, brechas estrictas y brackets numéricos cuantifican la pér
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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