Doubly Sub-linear Interactive Proofs of Proximity
| Source: Apple ML Research
Tags: Apple-ML-Research, interactive-proofs, theoretical-CS, ITCS, property-testing, verification, complexity-theory
Weizmann/Apple researchers introduce doubly sub-linear interactive proofs of proximity (dsIPPs) at ITCS 2026 — a class where both proof generation and verification are faster than reading the full input — demonstrated for branching program properties, Hamming weight approximation, and approximate graph bipartiteness.
Details
This ITCS 2026 paper from Noga Amir, Oded Goldreich, and Guy Rothblum defines and constructs doubly sub-linear interactive proofs of proximity (dsIPPs): proof systems where the honest prover generates a proof without reading the full input (sub-linear prover complexity) and the verifier confirms it even faster (also sub-linear, and strictly smaller than the prover's complexity). The approach targets approximate assertions: the prover proves that an input is close to having a property, not that it has the property exactly. This mirrors property testing — the verifier accepts inputs in the property and rejects those far from it — but with a prover who guides verification efficiently without processing the entire object. Concrete constructions are demonstrated for: (1) properties decidable by constant-width read-once oblivious branching programs (ROOBPs), (2) approximate Hamming weight verification, and (3) a relaxation of bipartiteness in bounded-degree graph models. These benchmark cases illustrate the framework's scope. This is part of a cluster of Apple/Weizmann IPP papers published at FOCS and ITCS in July 2026, progressively building a complexity theory for verified statistical computation. The immediate practical gap is large — bounded-degree and ROOBP constraints are narrow — but the direction matters as ML pipelines operate on datasets too large to audit by direct inspection.