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Conformal Prediction Beyond the Seen: A Missing Mass Perspective for Uncertainty Quantification in Generative Models
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Proposes Conformal Prediction with Query Oracle (CPQ), which uses missing-mass theory (a derivative estimator and Good-Turing estimates) to set adaptive query budgets and conformity scores for black-box LLM prediction sets with an EE fallback label.
Problem
Conformal prediction for open-ended generative models that only expose a sampling oracle, where prediction sets must balance coverage, query budget, and informativeness, and sets often need a fallback "everything else" label when the correct output was not sampled.
Approach
Derives an optimal query policy that stops querying when the derivative of the missing mass falls below a threshold, and an optimal set map that thresholds a score based on the missing mass (estimated via Good-Turing), then estimates the missing-mass derivative with a new doubleton-based estimator -2N2/t^2.
Key results
- On GSM8K at 95% nominal coverage, CPQ reaches 0.95 empirical coverage with an EE fraction of 0.16, versus 0.70 for CLM and 0.61 for SCOPE-Gen under the same budget.
- On BBH Geometric Shapes at 60% nominal coverage, CPQ's EE fraction is 0.07 versus 0.40 for CLM and 0.38 for SCOPE-Gen.
- On BBH Date at 70% nominal coverage, CPQ's EE fraction is 0.25 versus 0.32 for CLM and 0.51 for SCOPE-Gen.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use CPQ instead of CLM | Conformal prediction for generative models · Geo | EE fraction: 0.40 ± 0.047 -> 0.07 ± 0.07 | Helped |
| Use CPQ instead of SCOPE-Gen | Conformal prediction for generative models · Geo | EE fraction: 0.38 ± 0.22 -> 0.07 ± 0.07 | Helped |
| Use CPQ instead of CLM | Conformal prediction for generative models · GSM8K | EE fraction: 0.70 ± 0.11 -> 0.16 ± 0.14 | Helped |
| Use CPQ instead of SCOPE-Gen | Conformal prediction for generative models · GSM8K | EE fraction: 0.61 ± 0.26 -> 0.16 ± 0.14 | Helped |
| Use CPQ instead of CLM | Conformal prediction for generative models · Date | EE fraction: 0.32 ± 0.11 -> 0.25 ± 0.08 | Helped |
| Use CPQ instead of SCOPE-Gen | Conformal prediction for generative models · Date | EE fraction: 0.51 ± 0.11 -> 0.25 ± 0.08 | Helped |
| Add adaptive querying based on estimated missing-mass derivative (ablation) | Vanilla · Geo Shapes, GSM8K, and BBH-Date | EE fraction | Helped |
| Add optimal conformal calibration using missing-mass estimates (ablation) | CPQ with adaptive querying · Geo Shapes, GSM8K, and BBH-Date | EE fraction | Helped |
Surprising findings
- Standard CLM and SCOPE-Gen fail to achieve valid coverage at high nominal levels without including EE, since they ignore the unseen label mass.
Limitations
- Missing-mass and derivative estimates can be noisy in very-low query regimes.
- Clustering into semantic equivalence classes uses an LLM judge and is an approximation; the method relies on well-defined cluster probabilities.
- Theoretical optimality is derived in a population setting assuming the oracle equals the true conditional distribution, so the decoupled analysis only approximates the joint optimum.
Experimental setup
Datasets: BBH Geometric Shapes GSM8K BBH Date Understanding
Benchmarks: BBH Geometric Shapes GSM8K BBH Date Understanding
Metrics: empirical coverage EE fraction average set size
Baselines: CLM SCOPE-Gen Vanilla fixed-query CP
Builds on: conformal language modeling Good-Turing estimator split conformal prediction SCOPE-Gen
Closest papers by meaning
- Generative Conformal Prediction with Optimized Coverage Allocation (NeurIPS 2026 · similarity 0.91)
- Conformal Prediction with Paraphrase-Aware Scoring for LLM Uncertainty Quantification (NeurIPS 2026 · similarity 0.91)
- Reliable Uncertainty Quantification in Machine Learning via Conformal Prediction (AAAI 2025 · similarity 0.89)
- Prune 'n Predict: Optimizing LLM Decision-making with Conformal Prediction (ICML 2025 · similarity 0.88)
- Large language model validity via enhanced conformal prediction methods (NeurIPS 2024 · similarity 0.88)
- Geometry-Calibrated Conformal Abstention for Language Models (NeurIPS 2026 · similarity 0.88)
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