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
Os pares de arredondamento aleatório ocultos causam a perda de privacidade de libertações inteiras sucessivas. Nós estudamos um mecanismo de feedback racional sob participação de unidade assinada previsível e observação completa de cada saída física. O tempo de feedback de uma preparação conecta três resultados. Primeiro, preservar a perda completa até que um eco observado sincronize os mundos dá uma compilação precisa de ponto de lei finito, com um exponente de largura de suporte de $3C-2$ em cada orçamento fixo de $C\ge2$. Em segundo lugar, os compromissos de liberação anteriores dão uma hierarquia monótona cujo ponto final exato, lacunas rigorosas e brackets numéricos quantificam a perda de calibração. Em um erro discreto fixo de Gaussia, uma
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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