Feasibility Preservation under Monotone Retrieval Truncation

TL;DR

This paper models retrieval as a feasibility problem under truncation, showing conditions under which relevant evidence can be guaranteed to be retrieved despite truncation limitations.

Contribution

It formalizes retrieval as a structural feasibility problem, identifying conditions for finite retrieval guarantees under monotone truncation and highlighting limitations of non-monotone truncation.

Findings

Monotone truncation guarantees finite witnessability for individual queries.

Finite generation of witness certificates is necessary for uniform retrieval bounds.

Counterexamples demonstrate failure modes under non-monotone truncation and other conditions.

Abstract

Retrieval-based systems approximate access to a corpus by exposing only a truncated subset of available evidence. Even when relevant information exists in the corpus, truncation can prevent compatible evidence from co-occurring, leading to failures that are not captured by relevance-based evaluation. This paper studies retrieval from a structural perspective, modeling query answering as a feasibility problem under truncation. We formalize retrieval as a sequence of candidate evidence sets and characterize conditions under which feasibility in the limit implies feasibility at finite retrieval depth. We show that monotone truncation suffices to guarantee finite witnessability for individual queries. For classes of queries, we identify finite generation of witness certificates as the additional condition required to obtain a uniform retrieval bound, and we show that this condition is necessary. We further exhibit sharp counterexamples demonstrating failure under non-monotone truncation, non-finitely-generated query classes, and purely slotwise coverage. Together, these results isolate feasibility preservation as a correctness criterion for retrieval independent of relevance scoring or optimization, and clarify structural limitations inherent to truncation-based retrieval.