Interactive Proofs of Proximity for Model Evaluation

2026-09-25

AI Summary

This study addresses how a resource-constrained verifier can efficiently audit the statistical properties of an untrusted model under unknown input distributions. To this end, it proposes a fault-tolerant, doubly-sublinear interactive proximity proof system that decouples sampling from querying and supports both black-box and gray-box data access. By integrating weighted Hamming weight analysis with a multi-evaluator discrepancy resolution algorithm, the approach reduces the verification complexity of Hamming weight testing from cubic to near-linear while proving matching query lower bounds. The proposed framework significantly decreases the computational overhead for both the verifier and the honest prover. Furthermore, it is successfully applied to core auditing scenarios, including model accuracy, fairness, calibration, and robustness.

Abstract

We study interactive proofs of proximity (IPPs) for model evaluation, where a resource-limited verifier interacts with an untrusted prover, typically the model owner, to certify statistical properties of a model under an unknown input distribution. Our formulation separates sampling the input distribution from querying the model and evaluating its output; distinguishes real audit data (black-box sampling) from generated data (chosen-randomness, or gray-box, access to the sampler); and allows the prover and verifier to use different evaluators. We focus on doubly-sublinear IPPs, where both the verifier and honest prover use sublinear resources, and on (weighted) Hamming weight properties. For ordinary Hamming weight, we give a tolerant doubly-sublinear IPP. For completeness and soundness radii $\varepsilon_c<\varepsilon_f$ and gap $g=\varepsilon_f-\varepsilon_c$, a logarithmic-round instantiation uses $\widetilde{O}(1/g)$ verifier queries and $O(1/g^2)$ honest-prover queries, improving the cubic dependence of Amir, Goldreich, and Rothblum (ITCS 2025). We prove matching query lower bounds up to polylogarithmic factors. For distribution-weighted Hamming weight, black-box sampling requires $\Theta(1/g^2)$ verifier samples but only $\widetilde{O}(1/g)$ evaluations; the quadratic sample complexity is necessary in the interior regime. With chosen-randomness access, the problem reduces to ordinary Hamming weight, yielding $\widetilde{O}(1/g)$ calls and evaluations. If the parties'evaluators disagree arbitrarily on a $\rho$-fraction of the distribution and by at most $\gamma$ elsewhere, our protocols remain doubly sublinear whenever $g>2\kappa$, where $\kappa=\rho+(1-\rho)\gamma$. Applications include auditing accuracy, group fairness, calibration, harmlessness, usefulness, and average-case robustness.

Problem

• Interactive Proofs of Proximity
• Model Evaluation
• Doubly-Sublinear
• Hamming Weight Properties
• Statistical Certification

Innovation

• Interactive Proofs of Proximity
• Doubly-Sublinear Complexity
• Model Evaluation
• Hamming Weight Properties
• Tolerant Testing