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This paper introduces Knot, a method for estimating the dependency of LLM-based question answering systems on different candidate knowledge units (context, retrieved documents, intermediate reasoning steps). Knot learns from subset-level counterfactual supervision and models subset sensitivity through coverage over latent dependency factors to derive rank-aware unit scores. Experiments on multiple-choice and generative QA benchmarks show that Knot outperforms baselines in subset-sensitivity prediction and produces more faithful unit rankings, enabling practical risk screening by flagging error-prone QA predictions.
LLMs' reliance on specific knowledge sources during question answering can now be reliably estimated without extensive perturbation, enabling better error detection and risk screening.
Reliable question answering requires identifying not only whether an answer is correct, but also which available knowledge the prediction depends on. In realistic LLM-based QA, this knowledge may come from context, retrieval, decomposition, or intermediate reasoning, forming a noisy and redundant candidate space rather than a clean gold evidence set. We study \emph{knowledge dependency estimation}: estimating the sensitivity of a fixed black-box QA model to different candidate knowledge units. The challenge is to obtain fine-grained dependency scores without exhaustive test-time perturbation while modeling redundancy, substitutability, and complementarity. We propose \textbf{Knot}, a structured rank-aware knowledge dependency estimator. Knot learns from subset-level counterfactual supervision, models subset sensitivity through coverage over latent dependency factors, and derives rank-aware unit scores to identify influential candidates. Across multiple-choice and generative QA benchmarks, Knot outperforms all compared baselines in subset-sensitivity prediction and produces more faithful unit rankings than deployable baselines without extra QA-model calls; when used for practical risk screening, its dependency scores help flag error-prone QA predictions early.
