Recognition: 2 theorem links
· Lean TheoremCan LLMs Express Their Uncertainty? An Empirical Evaluation of Confidence Elicitation in LLMs
Pith reviewed 2026-05-13 08:35 UTC · model grok-4.3
The pith
LLMs tend to be overconfident when verbalizing answers but human-inspired prompts and consistency across multiple responses reduce the bias and narrow the gap to white-box methods.
A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.
Core claim
LLMs are overconfident when asked to state verbalized confidence, imitating human patterns, yet this improves with model scale. Human-inspired prompts, consistency among multiple responses, and refined aggregation strategies mitigate overconfidence from several angles. On confidence calibration and failure prediction, black-box methods reach AUROC values such as 0.605 compared with 0.522 for weaker baselines and approach white-box results, though no single technique dominates and performance remains poor on tasks requiring professional knowledge.
What carries the argument
Three-component black-box framework of prompting strategies to elicit verbalized confidence, sampling methods to generate multiple responses, and aggregation techniques that measure consistency across those responses.
If this is right
- Larger models yield better calibration and failure-prediction performance.
- Human-inspired prompts, multi-response consistency, and improved aggregation each reduce overconfidence.
- Black-box methods achieve AUROC scores up to 0.605, closing much of the gap to white-box approaches.
- No single combination of strategies consistently outperforms the others.
- All tested methods perform poorly on tasks that require professional knowledge.
Where Pith is reading between the lines
- Black-box elicitation techniques could enable uncertainty-aware use of commercial APIs that provide no internal access.
- The pattern of overconfidence may reflect biases in training data rather than model architecture alone.
- Extending the three-component framework to new domains would test whether the mitigation effects are task-specific.
Load-bearing premise
The five dataset types and five LLMs represent the range of tasks where uncertainty expression matters, and verbalized confidence serves as a meaningful proxy for actual model uncertainty.
What would settle it
A replication on a fresh professional-knowledge dataset where the proposed prompting, sampling, and aggregation strategies produce no AUROC gain above random baseline would show the mitigation claims do not hold.
read the original abstract
Empowering large language models to accurately express confidence in their answers is essential for trustworthy decision-making. Previous confidence elicitation methods, which primarily rely on white-box access to internal model information or model fine-tuning, have become less suitable for LLMs, especially closed-source commercial APIs. This leads to a growing need to explore the untapped area of black-box approaches for LLM uncertainty estimation. To better break down the problem, we define a systematic framework with three components: prompting strategies for eliciting verbalized confidence, sampling methods for generating multiple responses, and aggregation techniques for computing consistency. We then benchmark these methods on two key tasks-confidence calibration and failure prediction-across five types of datasets (e.g., commonsense and arithmetic reasoning) and five widely-used LLMs including GPT-4 and LLaMA 2 Chat. Our analysis uncovers several key insights: 1) LLMs, when verbalizing their confidence, tend to be overconfident, potentially imitating human patterns of expressing confidence. 2) As model capability scales up, both calibration and failure prediction performance improve. 3) Employing our proposed strategies, such as human-inspired prompts, consistency among multiple responses, and better aggregation strategies can help mitigate this overconfidence from various perspectives. 4) Comparisons with white-box methods indicate that while white-box methods perform better, the gap is narrow, e.g., 0.522 to 0.605 in AUROC. Despite these advancements, none of these techniques consistently outperform others, and all investigated methods struggle in challenging tasks, such as those requiring professional knowledge, indicating significant scope for improvement. We believe this study can serve as a strong baseline and provide insights for eliciting confidence in black-box LLMs.
Editorial analysis
A structured set of objections, weighed in public.
Referee Report
Summary. The manuscript presents a systematic framework for black-box confidence elicitation in LLMs consisting of prompting strategies, sampling methods for multiple responses, and aggregation techniques. It evaluates these on confidence calibration and failure prediction tasks using five dataset types (commonsense reasoning, arithmetic reasoning, and others) and five LLMs (GPT-4, LLaMA 2 Chat, etc.). Key findings include that LLMs are overconfident in verbalized confidence, performance improves with model scale, the proposed strategies mitigate overconfidence, and black-box methods achieve AUROC scores close to white-box methods (0.522 to 0.605), although all methods perform poorly on professional knowledge tasks. The work aims to serve as a baseline for future research.
Significance. If the empirical results are robust, this paper makes a significant contribution by establishing a strong baseline for black-box uncertainty estimation in LLMs, an area of growing importance for closed-source models. The demonstration that human-inspired prompts, response consistency, and aggregation can narrow the performance gap to white-box methods without requiring internal access or fine-tuning is practically valuable. The scaling law observation and identification of limitations in professional domains provide useful insights. The use of standard metrics like AUROC and calibration error allows for direct comparison with future work.
major comments (2)
- §4.1 (Datasets and Models): The assumption that the five dataset types and five LLMs adequately represent the range of real-world tasks is load-bearing for the mitigation claims but unverified. The paper notes that all methods struggle on professional knowledge tasks; if the selected tasks under-sample domains where verbalized confidence diverges from internal uncertainty, the reported AUROC improvement from 0.522 to 0.605 and the 'narrow gap' may not generalize, weakening the central claim that the strategies mitigate overconfidence broadly.
- §5 (Results): The specific AUROC values (0.522 to 0.605) for the black-box vs. white-box comparison are presented without detailing the exact methods, datasets, and statistical significance; this makes it difficult to evaluate whether the gap is consistently narrow or varies substantially across conditions, which is central to the comparison claim.
minor comments (2)
- Abstract: The list of five dataset types should be explicitly enumerated rather than using 'e.g.' to improve clarity.
- Throughout: Ensure all prompts used in the experiments are provided in the appendix for reproducibility.
Simulated Author's Rebuttal
We thank the referee for their constructive comments on our manuscript. We address each major comment point by point below, clarifying our choices and indicating where revisions have been made to improve transparency and scope.
read point-by-point responses
-
Referee: §4.1 (Datasets and Models): The assumption that the five dataset types and five LLMs adequately represent the range of real-world tasks is load-bearing for the mitigation claims but unverified. The paper notes that all methods struggle on professional knowledge tasks; if the selected tasks under-sample domains where verbalized confidence diverges from internal uncertainty, the reported AUROC improvement from 0.522 to 0.605 and the 'narrow gap' may not generalize, weakening the central claim that the strategies mitigate overconfidence broadly.
Authors: We agree that the representativeness of the chosen datasets and models is important for assessing the breadth of our mitigation claims. Section 4.1 explicitly selects the five dataset types to cover a spectrum from commonsense and arithmetic reasoning to professional knowledge tasks, using standard benchmarks to enable reproducibility. The poor performance on professional knowledge tasks is highlighted in the results and abstract precisely to illustrate limitations rather than to claim broad coverage. We acknowledge that no fixed set of tasks can exhaustively sample all domains where verbalized confidence may diverge from internal uncertainty. In the revised manuscript, we have expanded the Limitations section to state that our findings apply to the evaluated benchmarks and that future work should test additional domains for stronger generalization claims. We have also qualified the 'narrow gap' language to refer specifically to the tasks studied. revision: partial
-
Referee: §5 (Results): The specific AUROC values (0.522 to 0.605) for the black-box vs. white-box comparison are presented without detailing the exact methods, datasets, and statistical significance; this makes it difficult to evaluate whether the gap is consistently narrow or varies substantially across conditions, which is central to the comparison claim.
Authors: We thank the referee for pointing out the need for greater detail in the black-box versus white-box comparison. In the revised Section 5, we now provide a full breakdown of AUROC scores by individual prompting/sampling/aggregation method, by each dataset type, and by each of the five LLMs. We have also added statistical significance analysis (bootstrap confidence intervals and paired tests where appropriate) to quantify whether the observed gap remains consistently narrow across conditions. These additions directly address the request for transparency and allow readers to assess variation across settings. revision: yes
Circularity Check
Empirical study uses external benchmarks and off-the-shelf models with no self-referential reductions
full rationale
The paper defines a three-component framework (prompting strategies, sampling methods, aggregation techniques) and evaluates it empirically on five dataset types and five LLMs using standard external metrics (AUROC, calibration error). No equations, fitted parameters, or derivations are shown that reduce reported performance numbers (e.g., AUROC 0.522 to 0.605) to quantities defined inside the same experiment. All claims rest on comparisons against independent white-box baselines and real model outputs rather than self-definition or self-citation chains. The study is therefore self-contained against external benchmarks.
Axiom & Free-Parameter Ledger
axioms (1)
- domain assumption Verbalized confidence from LLMs can serve as a usable signal for calibration and failure prediction
Forward citations
Cited by 26 Pith papers
-
Grounded or Guessing? LVLM Confidence Estimation via Blind-Image Contrastive Ranking
BICR uses blind-image contrastive ranking on frozen LVLM hidden states to train a lightweight probe that penalizes confidence on blacked-out inputs, yielding top calibration and discrimination across five models and m...
-
EquiMem: Calibrating Shared Memory in Multi-Agent Debate via Game-Theoretic Equilibrium
EquiMem calibrates shared memory in multi-agent debate by computing a game-theoretic equilibrium from agent queries and paths, outperforming heuristics and LLM validators across benchmarks while remaining robust to ad...
-
MRI-Eval: A Tiered Benchmark for Evaluating LLM Performance on MRI Physics and GE Scanner Operations Knowledge
MRI-Eval benchmark shows frontier LLMs scoring 93-97% on MRI MCQs but falling to 37-61% on stem-only questions, with GE scanner operations as the weakest category for all models.
-
The First Token Knows: Single-Decode Confidence for Hallucination Detection
First-token normalized entropy (phi_first) from one greedy decode reaches mean AUROC 0.820 for hallucination detection, matching or exceeding semantic self-consistency (0.793) and surface self-consistency (0.791) acro...
-
Don't Start What You Can't Finish: A Counterfactual Audit of Support-State Triage in LLM Agents
LLM agents overcommit on non-complete tasks at 41.7% unless given explicit support-state categories, which raise typed deferral accuracy to 91.7%.
-
MIRROR: A Hierarchical Benchmark for Metacognitive Calibration in Large Language Models
MIRROR benchmark shows LLMs universally fail at compositional self-prediction and cannot translate partial self-knowledge into better agentic actions, with external metacognitive control reducing confident failures by...
-
SciPredict: Can LLMs Predict the Outcomes of Scientific Experiments in Natural Sciences?
LLMs predict outcomes of real scientific experiments at 14-26% accuracy, comparable to human experts, but lack calibration on prediction reliability while humans demonstrate strong calibration.
-
Evaluating the False Trust engendered by LLM Explanations
A user study finds that LLM reasoning traces and post-hoc explanations create false trust by increasing acceptance of incorrect answers, whereas contrastive dual explanations improve users' ability to detect errors.
-
Measuring Black-Box Confidence via Reasoning Trajectories: Geometry, Coverage, and Verbalization
Trajectory geometry in embedding space fused with coverage and verbalization yields better black-box CoT confidence estimation than self-consistency at lower sample counts across six benchmark-reasoner pairs.
-
Temporal Reasoning Is Not the Bottleneck: A Probabilistic Inconsistency Framework for Neuro-Symbolic QA
Temporal reasoning is not the core bottleneck for LLMs on time-based QA; the real issue is unstructured text-to-event mapping, addressed by a neuro-symbolic system with PIS that reaches 100% accuracy on benchmarks whe...
-
What Single-Prompt Accuracy Misses: A Multi-Variant Reliability Audit of Language Models
Multi-variant testing reveals that prompt design and evaluator choices can change apparent model reliability by large margins, with verbal confidence often overstated and robustness uncorrelated with size.
-
Spatiotemporal Hidden-State Dynamics as a Signature of Internal Reasoning in Large Language Models
Large reasoning models show measurable hidden-state dynamics that a new statistic can use to distinguish correct reasoning trajectories without labels.
-
Confidence Estimation in Automatic Short Answer Grading with LLMs
A hybrid confidence framework for LLM-based short answer grading combines model signals with aleatoric uncertainty from semantic clustering of responses and improves selective grading reliability over single-source methods.
-
MarketBench: Evaluating AI Agents as Market Participants
LLMs show poor calibration in predicting task success and token use on software engineering benchmarks, causing market auctions to underperform compared to perfect information scenarios, with limited improvement from ...
-
How LLMs Detect and Correct Their Own Errors: The Role of Internal Confidence Signals
LLMs implement a second-order confidence architecture where the PANL activation encodes both error likelihood and the ability to correct it, beyond verbal confidence or log-probabilities.
-
Verbal Confidence Saturation in 3-9B Open-Weight Instruction-Tuned LLMs: A Pre-Registered Psychometric Validity Screen
Seven 3-9B instruction-tuned LLMs produce verbal confidence that saturates at high values and fails psychometric validity criteria for Type-2 discrimination under minimal elicitation.
-
Enhancing Confidence Estimation in Telco LLMs via Twin-Pass CoT-Ensembling
Twin-Pass Chain-of-Thought Ensembling cuts Expected Calibration Error by up to 88% in Gemma-3 models on TeleQnA, ORANBench, and srsRANBench.
-
Calibration-Aware Policy Optimization for Reasoning LLMs
CAPO improves LLM calibration by up to 15% while matching or exceeding GRPO accuracy through logistic AUC loss and noise masking, enabling better abstention and scaling performance.
-
CLSGen: A Dual-Head Fine-Tuning Framework for Joint Probabilistic Classification and Verbalized Explanation
CLSGen is a dual-head LLM fine-tuning framework that enables joint probabilistic classification and verbalized explanation generation without catastrophic forgetting of generative capabilities.
-
Assessing and Mitigating Miscalibration in LLM-Based Social Science Measurement
LLM confidence for social science text measurements is poorly calibrated across models, and a soft-label distillation pipeline reduces expected calibration error by 43% and Brier score by 34%.
-
Decodable but Not Corrected by Fixed Residual-Stream Linear Steering: Evidence from Medical LLM Failure Regimes
Overthinking in medical QA is linearly decodable at 71.6% accuracy yet fixed residual-stream steering yields no correction across 29 configurations, while enabling selective abstention with AUROC 0.610.
-
Confidence Estimation in Automatic Short Answer Grading with LLMs
A hybrid confidence framework for LLM-based automatic short answer grading integrates model-based signals with aleatoric uncertainty from semantic clustering of responses and yields more reliable estimates than single...
-
Measuring the metacognition of AI
Meta-d' and signal detection theory provide quantitative tools to assess metacognitive sensitivity and risk-based regulation in large language models.
-
"I Don't Know" -- Towards Appropriate Trust with Certainty-Aware Retrieval Augmented Generation
CERTA adds relevance-based certainty estimation to RAG so LLMs can better signal uncertainty on non-objective questions, reducing overconfidence.
-
Towards Trustworthy Report Generation: A Deep Research Agent with Progressive Confidence Estimation and Calibration
A deep research agent incorporates progressive confidence estimation and calibration to produce trustworthy reports with transparent confidence scores on claims.
-
Do Small Language Models Know When They're Wrong? Confidence-Based Cascade Scoring for Educational Assessment
Verbalized confidence from small LMs enables cost-effective cascade routing for automated educational scoring, matching large-model accuracy at 76% lower cost when discrimination is strong.
discussion (0)
Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.