Apple researchers propose interactive proof systems to verify distribution property claims with sublinear overhead

Apple’s Machine Learning Research team published a paper introducing interactive proof systems designed to verify general distribution properties with bounded-depth circuits. The framework addresses a practical verification problem: when an analyst (Bob) makes claims about an unknown distribution based on samples, how can the data owner (Alice) efficiently validate those claims without re-running the full analysis? The proposed solution enables Alice to verify Bob’s assertions using fewer computational resources than would be required to perform the analysis herself.

The authors formalize the problem and provide complexity bounds for the verifier’s overhead. Specifically, for an unknown distribution with support size bounded by N and a property decidable by a uniform Boolean circuit of depth D, the verifier’s sample complexity, running time, and communication complexity are all bounded by Õ(D+N^0.99). The number of rounds in the interactive protocol is O(D·log(N)).

The proof system is described as doubly-efficient: the honest prover runs in polynomial time and quasi-linear sample complexity. This contrasts with the baseline requirement where deciding the property without a prover would demand quasi-linear sample complexity and running time, even for simple properties.

The work builds on prior results from the same authors presented at FOCS 2023, which addressed only the more restricted class of label-invariant distribution properties. The new framework generalizes these results to general distribution properties decidable by bounded-depth circuits or Turing machines.

The paper situates this contribution within a broader research agenda on verification of statistical analyses, noting the growing need to ensure correctness of results in science, industry, and society without full replication. The authors highlight that approximate correctness can be verified more efficiently using proof systems, avoiding the need to re-run entire analyses.