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Conformal Language Modeling via Posterior Sampling

NeurIPS 2026 · Large language models › Language, safety and interpretability · approach: Uncertainty quantification for LLMs · 0 citations (OpenAlex)

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Proposes conformal language modeling via posterior sampling: calibrates a threshold on a family of score-thresholded LM posteriors (with an abstention atom) using off-policy particles, giving finite-sample risk control with higher utility than post-hoc conformal filtering.

Problem

Post-hoc conformal filtering of LLM outputs for hallucination control yields incoherent or unhelpful responses because it edits samples after generation rather than shifting the generative distribution.

Approach

Treat risk control as posterior sampling: condition the LM prior (mixed with a factual abstention atom) on a cumulative claim-score threshold, and calibrate the threshold off-policy from prior particles with monotonized empirical-posterior risk, yielding finite-sample guarantees.

Key results

• Ours achieves valid risk control on FActScore and MATH, tracking target factuality with empirical risk near target and slightly conservative at low targets.
• On MATH, MH begins generating incomplete answers at high rates for targets >= 0.6, while the proposed method's completeness increases with target factuality among non-abstaining outputs.
• On FActScore, non-abstaining generations from the proposed method degrade less than MH as target factuality rises, mainly in completeness and helpfulness; unconditional average is lower than MH due to more abstentions.

Surprising findings

• Unconditional utility underperforms MH on FActScore because the LM judge prefers an edited answer over abstention.
• Fraction of non-abstaining outputs that are entirely factual slightly decreases versus MH on FActScore.

Limitations

• Posterior sampling cannot move far from the LM prior support, so poorly known instances can only be made factual by abstaining.
• Utility evaluated with LLM-judge rather than human evaluation.
• Small beta affects convergence to population posterior; finite-particle guarantee is for the empirical posterior.

Experimental setup

Datasets: FActScore MATH

Benchmarks: FActScore MATH

Metrics: empirical risk vs target factuality Likert completeness/fluency/helpfulness completeness rate claims per output claim precision hallucination-free rate

Baselines: MH (conformal language modeling post-hoc filtering)

Builds on: conformal risk control conformal language modeling fixed sequence testing sequential Monte Carlo steering

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