Interactive Proofs for General Distribution Properties

2026-07-16 · Source: Apple Machine Learning Research · Field: Science & Research — Mathematics & Computational Sciences, Artificial Intelligence & Machine Learning · Depth: Expert, quick

Summary

Interactive Proofs for General Distribution Properties introduces novel interactive proof systems designed to efficiently verify claims about unknown distributions from a small number of samples. These systems address scenarios where an untrusted analyst (Bob) makes assertions about a distribution Alice has sampled. The research constructs proof systems for properties decidable by bounded-depth circuits, where N is the distribution's support size and D is the circuit depth. The verifier's sample, running, and communication complexity are bounded by Õ(D+N^0.99), with O(D·log(N)) rounds. The honest prover operates in polynomial time with quasi-linear sample complexity, making the system doubly-efficient. This work extends prior research, which was limited to label-invariant distribution properties, to a much broader class.

Key takeaway

For research scientists developing verifiable computation methods, this work demonstrates a significant advancement in efficiently verifying complex distribution properties. You can now consider interactive proof systems for a broader range of properties beyond label-invariance, potentially reducing the computational burden of verifying claims from untrusted sources. This enables more robust and resource-efficient data analysis verification in your projects.

Key insights

Interactive proof systems can efficiently verify general distribution properties using limited samples and resources.

Principles

• Doubly-efficient proof systems reduce verification costs.
• Bounded-depth circuits define verifiable property classes.
• Sublinear verification is possible for general properties.

Method

Construct interactive proof systems for distribution properties decidable by bounded-depth circuits, achieving verifier complexity Õ(D+N^0.99) and O(D·log(N)) rounds, with a polynomial-time, quasi-linear sample complexity prover.

In practice

• Verify untrusted data analysis claims efficiently.
• Reduce resource needs for distribution property checks.
• Extend verifiable properties beyond label-invariance.

Topics

• Interactive Proofs
• Distribution Properties
• Bounded-Depth Circuits
• Sample Complexity
• Verifiable Computation
• Data Analysis Verification

Best for: AI Scientist, Research Scientist

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Editorial summary, takeaway, and curation by AIssential. Original article published by Apple Machine Learning Research.