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arXiv · 2606.29054

When Can Conformal Risk Control Certify LLM Outputs? Bounds, Impossibility, and Adaptation for Structured Generation

Varun Kotte
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Abstract

Large language models (LLMs) deployed for structured generation (NER, JSON extraction, QA, and classification) lack formal reliability guarantees, and standard heuristic abstention policies violate user-specified risk targets on 7.5--12.5% of settings, with no per-deployment guarantee. We characterize when conformal risk control (CRC) can certify structured LLM outputs and when it provably cannot. First, we prove a sharpened, attained feasibility frontier: when base risk μexceeds target α, any distribution-free method must abstain on at least (μ-α)/(M-α) of inputs, yielding a closed-form feasibility test that decides whether CRC can work before running it. Second, we establish a proven certification phase diagram across Hoeffding, empirical Bernstein, and a betting-based e-CRC bound, verified over 716 configurations (six open-weight models 3B--72B, eight datasets, six scores): at strict targets (α<= 0.20) the certified sets are nested (51/72/80 certified; Hoeffding-to-Bernstein the largest upgrade, +41%; e-CRC best under calibration scarcity), while at relaxed targets the Hoeffding-Bernstein ordering reverses at a closed-form frontier. Third, we show a negative shift result with a constructive counterpart: under cross-dataset shift the target is violated on 14 of 16 transfers by static CRC and every tested adaptive-conformal-inference (ACI) step size, yet a full-feedback anytime-valid monitor certifies 0 of 16 while remaining non-vacuous. Relaxing the target to α= 0.40 unlocks practical certification (28% NER, 13% QA, 19% CLS). The framework gives a three-step deployment recipe: check feasibility, select the bound and score, then re-check under shift.

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Varun Kotte. 2026-09-07. When Can Conformal Risk Control Certify LLM Outputs? Bounds, Impossibility, and Adaptation for Structured Generation. https://arxiv.org/abs/2606.29054

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