Notes

• Protocol extends sum-check for approximate computations, supporting adjustable error parameters δ
• Soundness error gracefully decreases with δ/Δ, validators may reject with initial error Δ large
• Utilizes the metric structure of low-degree polynomials, distinct from classic algebraic methods
• Natural instantiation over complex numbers, analysis based on polynomial behavior on the unit circle
• New intermediate security phenomena appear under Fiat-Shamir transformation, related to approximation
• Achieves black-box feasibility, compiler independent of arithmetic operations, only needing to satisfy error bounds

• 协议扩展sum-check以处理近似计算，支持可调误差参数δ
• 可靠性误差随δ/Δ优雅下降，初始误差Δ大时验证者更易拒绝
• 利用低度多项式的度量结构，区别于经典代数方法
• 复数域实例化最自然，分析基于单位圆上的多项式行为
• Fiat-Shamir变换下出现新的中间安全现象，与近似相关
• 实现黑盒可行性，编译器独立于算术操作实现，仅需满足误差界