Structured Knowledge Dependency Estimation for Question Answering

Question answering (QA) systems draw on knowledge from task context, retrieval, decomposition, and intermediate reasoning. These sources form a candidate knowledge space whose units may be redundant, complementary, noisy, or incorrect, making their influence difficult to assess independently. In particular, the effect of removing a knowledge subset can differ from the sum of its individual parts, while exhaustive subset interventions are costly. We formulate this challenge as knowledge dependency estimation, defining dependency by the behavioral change of a fixed QA model when subsets of candidate knowledge are removed. We propose KNOT, a structured estimator learned from offline interventions. KNOT maps candidates into shared latent factors and uses removal–retention coverage to model both the coverage carried by a removed subset and the coverage preserved by the remaining candidates. The same function predicts subset effects and yields unit-level dependency scores through singleton evaluation. Across five QA benchmarks, KNOT improves zero-call subset-effect prediction and knowledge ranking over amortized attribution baselines, and supports substantial context compression while preserving near-full-context answer quality.