How Much Does One Wrong Answer Cost? Error Propagation in Constraint Pruning with Noisy LLM Oracles

Zhengtao Gui, Weining Shen

Constraint pruning saves queries to a large language model (LLM) or another noisy oracle by skipping each yes/no question implied by answers accepted earlier, for example through transitivity. Entity-resolution systems and LLM-based rankers use this idea. However, their analyses typically assume a correct oracle. We argue that pruning should be judged by its risk when the oracle errs, since an accepted wrong answer spreads to every question it implies. When each answer is wrong independently with small probability $\varepsilon$, the first-order risk is set by how many facts one wrong answer corrupts on average. We consider two kinds of constraints. For implication rules, as in taxonomies, pruning in a random order adds no first-order risk: a wrong answer that would change $k$ facts is accepted with probability $1/k$, so it costs one fact on average. Rules with $s$ premises break this balance: a wrong answer at a premise shared by $r$ rules can cost order $r^{1-1/s}$ facts. For entity resolution with $m$ records of one entity, the first-order risk equals $\varepsilon$ times the Wiener index (the total pairwise distance) of the spanning tree built by the query order. Pivot orders,…