Selective prediction systems can mitigate harms resulting from language model hallucinations by abstaining from answering in high-risk cases. Uncertainty quantification techniques are often employed to identify such cases, but are rarely evaluated in the context of the wider selective prediction policy and its ability to operate at low target error rates. We identify a model-dependent failure mode of entropy-based uncertainty methods that leads to unreliable abstention behaviour, and address it by combining entropy scores with a correctness probe signal. We find that across three QA benchmarks (TriviaQA, BioASQ, MedicalQA) and four model families, the combined score generally improves both the risk--coverage trade-off and calibration performance relative to entropy-only baselines. Our results highlight the importance of deployment-facing evaluation of uncertainty methods, using metrics that directly reflect whether a system can be trusted to operate at a stated risk level.
Figures & tables
Figure 1: Performance of the PC probe and combined method relative to entropy-only baselines, averaged across all four evaluated models. Positive values denote an improvement in the target metric (i.e., higher AUROC/AUPRC or lower E-AURC/TCE). Abbreviations: NLL (Sequence NLL), SE (Semantic Entropy), SEP (Semantic Entropy Probe). The combined method consistently outperforms both the entropy baselines and the standalone PC probe across most configurations, with the notable exception of SE on the MedicalQA dataset.
Figure 2: SE score vs. PC probe logit for Qwen on TriviaQA. Many answers, both correct and hallucinated, collapse to SE=0 , yet receive distinct PC probe scores.
Model
SE AUROC
PC AUROC
ρs
Llama 3.2 3B
0.884
0.813
0.51
Qwen3 4B
0.844
0.888
0.54
Gemma 3 4B
0.752
0.752
0.34
Ministral 8B
0.823
0.750
0.50
Table 1: Hallucination detection AUROC for SE and PC probe on TriviaQA, with Spearman correlation ρs between their risk scores. The best method varies across models, with only moderate correlation between scores.
Figure 3: Ministral 8B selective prediction on BioASQ. Left: risk–coverage curves; the shaded region marks a high-trust regime ( α≤0.15 ). Entropy based methods fail to enter this regime at non-trivial coverage. Right: realized hallucination rate vs. target α ; a perfect system lies on the diagonal. Entropy-based methods diverge sharply at strict targets; combined methods do not.
Appendix figures & tables5 assets
Supplementary material from the paper’s appendix.
Appendix
Dataset
Method
AUROC ↑
AUPRC ↑
E-AURC ↓
TCE ↓
TriviaQA
Sequence NLL
0.64611.5
0.5443.4
0.2179.9
0.18911.5
Semantic Entropy
0.8265.5
0.7326.7
0.0945.5
0.0848.7
SE Probe
0.7452.5
0.6439.9
0.1221.4
0.0834.3
PC Probe
0.8016.5
0.71212.9
0.1034.1
0.0611.8
BioASQ
Sequence NLL
0.6621.4
0.6944.8
0.2452.6
0.27812.9
Semantic Entropy
0.7604.2
0.7715.4
0.1643.3
0.1096.0
Appendix
Table A1: Performance of base hallucination detection methods across datasets, averaged over all models.
Method
TriviaQA
BioASQ
MedicalQA
AUROC
AUPRC
AUROC
AUPRC
AUROC
AUPRC
Llama 3.2 3B
Acc: 64.2%
Acc: 48.3%
Acc: 22.0%
Sequence NLL
0.6644.5
0.5317.2
0.6564.0
0.6335.5
0.6905.5
0.8534.3
Semantic Entropy
0.8842.7
0.7675.8
0.7374.2
0.6995.8
0.6885.6
0.8663.4
SE Probe
0.7234.4
0.6066.8
0.6974.3
0.7215.4
0.6265.4
0.8643.2
PC Probe
0.8133.5
0.6916.6
0.6693.6
0.6835.4
0.6425.3
0.8683.3
Appendix
Table A2: Detailed hallucination detection classification metrics (AUROC and AUPRC) for all evaluated models and datasets. Results are reported as MeanStd across 200 bootstrap iterations. The best performing method per column is highlighted in bold, and Acc denotes the base model accuracy at full coverage.
Method
TriviaQA
BioASQ
MedicalQA
E-AURC ↓
TCE ↓
E-AURC ↓
TCE ↓
E-AURC ↓
TCE ↓
Llama 3.2 3B
Sequence NLL
0.1944.2
0.1818.1
0.2443.9
0.1987.6
0.2253.4
0.4377.7
Semantic Entropy
0.0451.3
0.0411.2
0.1633.2
0.0731.2
0.2103.7
0.3329.7
SE Probe
0.1192.5
0.0734.8
0.2143.9
0.29415.1
0.2663.6
0.3571.3
PC Probe
0.0872.2
0.0734.3
0.2373.3
0.26316.8
0.2423.6
0.4034.1
Appendix
Table A3: Detailed selective prediction metrics: Full-coverage Excess Area Under the Risk–Coverage Curve (E-AURC) and Target Calibration Error (TCE) for all evaluated models and datasets. TCE is averaged over operational target risk levels α∈[0.05,0.3] . Lower values indicate better performance, with the best method per column highlighted in bold. In cases where coverage is zero over the whole operational range, we report TCE as the model base hallucination rate.
Model
NLL
SE
SE Probe
LR
MLP
LR
MLP
LR
MLP
Llama 3.2 3B ( TriviaQA )
0.8263.4
0.8313.3
0.8632.9
0.8642.8
0.8363.2
0.8363.2
Llama 3.2 3B ( BioASQ )
0.6743.6
0.6743.6
0.7023.5
0.7073.5
0.6933.6
0.6933.6
Llama 3.2 3B ( MedicalQA )
0.6495.2
0.5606.2
0.6665.2
0.6395.3
0.6545.4
0.6505.5
Qwen3 4B ( TriviaQA )
0.8882.6
0.8912.5
0.9102.1
0.9112.1
0.8942.4
0.8892.5
Qwen3 4B ( BioASQ )
0.7114.3
0.7214.3
0.7224.1
0.7214.2
0.7074.3
0.6944.4
Appendix
Table A4: Ablation study comparing the classification performance (AUROC) of Logistic Regression (LR) and Multi-Layer Perceptron (MLP) combiners for fusing correctness and entropy signals.
Figure A1: Risk–coverage curves for all four model families on TriviaQA. The shaded region marks the high-trust regime ( α≤0.15 ). The relative ranking of methods varies substantially across models, motivating model-aware evaluation of uncertainty quantification approaches.
Large language models (LLMs) are increasingly deployed in question answering (QA) systems, yet they may generate hallucinated or misaligned responses without reliable confidence estimates. Uncertainty quantification (UQ) offers a natural basis for selective answering, where a system answers only when its prediction is deemed reliable and abstains otherwise. However, existing uncertainty scores for LLMs are often heuristic: a threshold chosen on such scores does not, by itself, provide statistical guarantees on the error rate among accepted answers. We propose CIC, a confidence-interval-based calibration framework that converts arbitrary uncertainty scores into risk-controlled selective answering rules. Given a held-out calibration set, CIC evaluates each generated response using an application-specific alignment criterion and associates it with an uncertainty score and a binary error label. For each candidate uncertainty threshold, CIC estimates the acceptance-conditioned error rate and constructs a high-probability upper confidence bound using either Hoeffding-style or Clopper-Pearson confidence intervals. It then selects the largest threshold whose upper bound is below a user-specified risk level α, thereby maximizing the answering rate subject to a finite-sample reliability constraint. Under exchangeability, CIC guarantees with probability at least 1−δ that the selected threshold, if non-null, controls the error rate among accepted answers at level α. We evaluate CIC on both closed-ended and open-ended QA benchmarks across seven LLMs and multiple uncertainty estimators. Experimental results show that CIC consistently achieves valid risk control while retaining strong answering efficiency, providing a practical and statistically grounded mechanism for deploying LLMs in reliability-sensitive QA workflows.
LLMs' overconfidence, particularly when hallucinating, poses a significant challenge for the deployment of the models in safety-critical settings and makes a reliable estimation of uncertainty necessary. Existing approaches for uncertainty quantification typically prioritize lexical or probabilistic measures; however, these techniques often ignore the semantic variance of different responses with similar meaning. In this paper, we propose Adaptive Conformal Semantic Entropy (ACSE), a method for estimating prompt-level uncertainty by adaptively measuring semantic dispersion in LLMs outputs. Our uncertainty scoring function is based on clustering semantic entropy of multiple diverse responses to the same prompt. The function adaptively adjusts the uncertainty score based on semantic features of each cluster. To ensure statistical reliability of our score, we use conformal calibration to apply a decision rule to accept/abstain the prompts, providing a finite-sample, distribution-free guarantee such that the error rate among the accepted responses remains bounded by a user-specified tolerance. Our extensive experimental evaluations using different LLMs and datasets, demonstrate that our approach consistently outperforms state-of-the-art uncertainty quantification baselines using discriminative performance, conformal guarantees, and probabilistic calibration indicators. As a highlight, for TriviaQA dataset, AUROC of our approach is 0.88 compared to 0.65 produced by the token entropy approach.
Hamed Karimi, Vaishali Meyappan, Reza Samavi
Toronto Metropolitan University, Toronto, Ontario, Canada · Vector Institute, Toronto, Ontario, Canada
Large language models (LLMs) can reduce hallucination by abstaining from questions they would likely get wrong. Abstention can be implemented outside the model (selective answering) using a confidence threshold that controls the answer rate (coverage), or learned inside it (abstention training), which can perform better but fixes coverage once trained. To compare the two, we match their coverage and decompose risk (error rate) into answering ability and distinguishing ability, i.e., how well the model answers and how accurately it abstains, respectively. The decomposition shows that abstention training performs better mainly by answering better: with strong confidence estimators, the two have nearly equal distinguishing ability. This motivates Train for Accuracy, then Post-hoc Select (TAPS), a modular approach that keeps coverage controllable, needs only standard post-training and an off-the-shelf confidence estimator, and benefits from advances in either component. Across three LLMs and three factual QA benchmarks, TAPS with a probing-based confidence estimator attains 1.5--9.4 percentage points lower mean risk than three representative abstention training methods at matched coverage. Within TAPS, accuracy training often weakens the model's own confidence signals, yet refitting the estimator largely preserves distinguishing ability. Together, these results establish TAPS as a strong yet controllable baseline and raise the bar for future abstention training: sacrificing control over coverage should yield gains beyond what can be achieved by optimizing answering and abstaining separately.
Junwei Zhang, Yifei Wang, Wanli Yang +6
State Key Laboratory of AI Safety, Institute of Computing Technology, CAS · University of Chinese Academy of Sciences · Beijing Institute of Technology