Doubly Sub-linear Interactive Proofs of Proximity

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

Summary

Doubly Sub-linear Interactive Proofs of Proximity (dsIPPs) represent a novel class of proof systems designed for ultra-fast generation and approximate verification of assertions about massive inputs. These systems are "doubly sub-linear" because the prover only reads a small, sub-linear portion of the input, while the verifier reads an even smaller fraction. Similar to property testing, approximate verification ensures an honest prover can validate inputs within a property, preventing fraudulent acceptance of inputs far from it. The research constructs such proof systems for any property decidable by a constant-width read-once oblivious branching program (ROOBP). Additionally, dsIPPs are developed for approximate verification of an input's Hamming weight and for a relaxation of bipartiteness within the bounded-degree graph model.

Key takeaway

For researchers and practitioners working with massive datasets where full input processing is infeasible, dsIPPs offer a paradigm shift for property verification. You should explore these doubly sub-linear proof systems to efficiently validate approximate assertions, particularly for properties decidable by ROOBPs or tasks like Hamming weight and graph bipartiteness. This approach allows for robust verification with significantly reduced computational overhead, enabling new applications in large-scale data integrity and analysis.

Key insights

Doubly sub-linear interactive proofs enable ultra-fast, approximate verification of properties for massive datasets with minimal input access.

Principles

• Sub-linear input access can suffice for approximate property verification.
• Prover and verifier can operate on vastly different input scales.
• Approximate verification prevents accepting inputs far from the property.

In practice

• Verify claims about properties of huge input objects.
• Approximate Hamming weight verification.
• Test relaxed bipartiteness in bounded-degree graphs.

Topics

• Interactive Proofs
• Property Testing
• Sub-linear Algorithms
• Branching Programs
• Graph Theory
• Hamming Weight

Best for: Research Scientist, AI Scientist

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