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
Les couples d'arrondissement randomisé caché entraînent la perte de confidentialité des sorties entières successives. Nous étudions un mécanisme de rétroaction rationnel sous une participation prévisible à l'unité signée et une observation complète de chaque sortie physique. La durée de vie d'une préparation connecte trois résultats. Premièrement, la préservation des résultats complets jusqu'à ce qu'un écho observé synchronise les mondes donne une compilation exacte de points de loi finie, avec un exponent de largeur de support de $3C-2$ à chaque budget fixe de $C\ge2. Deuxièmement, la libération d'engagements antérieurs donne une hiérarchie monotone dont le point final exact, les lacunes strictes et les
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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