Feasibility Preservation under Monotone Retrieval Truncation
Sean Plummer
TL;DR
Feasibility preservation under retrieval truncation reframes correctness beyond relevance ranking, modeling retrieval as a budgeted truncation of the evidence pool and analyzing when a feasible witness persists at finite depth. The core results show that monotone retrieval guarantees finite witnessability for individual queries, while uniform feasibility across query classes requires finite generation of witness certificates; without these conditions, uniform bounds can fail and non-monotone truncation can destroy feasibility. The work highlights sharp boundaries, including the necessity of monotonicity and finite generation, and demonstrates that feasibility depends on global constraints rather than per-slot coverage. Overall, the authors propose a structural, feasibility-centric view of validated retrieval, with implications for correctness guarantees independent of scoring or optimization.
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.