Identifiability of Relational Queries in Multi-View Pretraining

2026-07-06

AI Summary

This work addresses structural ambiguity in downstream relational queries arising from interface design in multi-view pretraining, which can render answers non-identifiable. The paper establishes the first theoretical framework for query identifiability, formalizing it through interface laws—functional dependencies that hold consistently across all valid worlds—and proves a minimax error lower bound of 1/2 for non-identifiable queries. It further reduces the minimal augmentation problem to set cover and proposes two efficient algorithms: CheckCert, based on attribute closure, for identifiability verification, and Greedy-MinAug, a greedy algorithm for minimal augmentation. Both achieve millisecond-level runtime at scale (thousands of attributes). Experiments confirm the existence of the theoretical error bound and demonstrate abrupt performance gains in models as interfaces are enhanced.

Abstract

When data sources are integrated through a shared interface, a downstream query may or may not be determined by what the interface exposes: two globally consistent worlds can agree on every shared attribute yet disagree on the query answer. This ambiguity is structural -- a property of the interface design, not the data volume -- and cannot be resolved by collecting more records or training a larger model. We formalize query identifiability for data integration under interface laws (functional dependencies that hold uniformly across all legal worlds rather than within a single instance) and prove three results. (i) A polynomial-time certificate (CheckCert) decides identifiability via attribute closure, and is exact on instances that expose any residual ambiguity (closure-separable). (ii) Non-identifiable queries face an irreducible 1/2 minimax error floor for any estimator using only interface evidence, bounding multi-view pretraining systems from below. (iii) A minimum-augmentation algorithm (Greedy-MinAug) finds the smallest set of interface additions to certify a query, reducing to Set Cover (logarithmic approximation). Experiments on synthetic benchmarks, real integration datasets spanning three domains (scholarly, product, restaurant), and schemas up to 10^3 attributes confirm CheckCert is exact, both algorithms run in single-digit milliseconds, and ML classifiers exhibit the predicted error floor and abrupt capability gains.

Problem

• query identifiability
• data integration
• multi-view pretraining
• interface design
• structural ambiguity

Innovation

• query identifiability
• multi-view pretraining
• functional dependencies
• data integration
• minimax error