Apple 研究提出位置不变性属性统一检验框架，区分函数与分布验证

Apple 机器学习研究团队提出一种位置不变性（location-invariant）属性的统一检验框架，该属性可通过频率特征进行表征。

研究指出，函数与分布的位置不变性在统计检验层面可统一处理，但在验证（verification）层面存在本质差异。

该工作为对称性属性的理论分析与实际检测提供了更清晰的数学基础。

Location-Invariant Properties of Functions Versus Properties of Distributions: United in Testing but Separated in Verification

Authors Oded Goldreich†, Guy N. Rothblum

View publication：https://eccc.weizmann.ac.il/report/2025/105/

Interactive Proofs for General Distribution Properties

July 16, 2026 research area Methods and Algorithms：/research/?domain=Methods%20and%20Algorithms conference FOCS：/research/?event=FOCS

Suppose Alice has collected a small number of samples from an unknown distribution, and would like to learn about the distribution. Bob, an untrusted data analyst, claims to have run a sophisticated data analysis on the distribution and makes assertions about its properties. When and how is it possible for Alice to efficiently verify Bob’s claims (using fewer resources than would be needed to run the analysis herself)? We construct interactive…

How to Verify Any (Reasonable) Distribution Property: Computationally Sound Argument Systems for Distributions

April 24, 2025 research area Methods and Algorithms：/research/?domain=Methods%20and%20Algorithms conference ICLR：/research/?event=ICLR

As statistical analyses become more central to science, industry and society, there is a growing need to ensure correctness of their results. Approximate correctness can be verified by replicating the entire analysis, but can we verify without replication? Building on a recent line of work, we study proof-systems that allow a probabilistic verifier to ascertain that the results of an analysis are approximately correct, while drawing fewer samples…

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