Self-Verbalized Uncertainty Quantification

• Self-verbalized uncertainty quantification is a method where models express their epistemic confidence using numeric scores or natural language cues, bridging raw probabilities and semantic judgments.
• It employs techniques like supervised fine-tuning, calibrator models, and dual-agent architectures to align confidence estimates with output accuracy, mitigating error cascades in agentic workflows.
• Empirical results demonstrate improved model transparency and calibration, making self-verbalized UQ crucial for reliable autonomous systems and enhanced decision control.

Self-verbalized uncertainty quantification (UQ) refers to methods that endow LLMs or agentic systems with the capacity to express their own epistemic confidence or doubt, either numerically or in natural language, about specific outputs or actions. Unlike ensemble-based, Bayesian, or token-level probabilistic UQ strategies, self-verbalized UQ utilizes the generative properties of LLMs to emit human-readable statements—typically scalar confidences or textual explanations—that reflect model-internal estimates of correctness, reliability, or risk. This paradigm has seen rapid development as both a means of calibration and as a mechanism for active control in sequential decision-making agents, particularly in settings where the so-called Spiral of Hallucination and cascading epistemic errors threaten the reliability of autonomous workflows (Shorinwa et al., 2024, Jang et al., 4 Jun 2025, Zhang et al., 22 Jan 2026).

1. Principles and Distinction from Other UQ Paradigms

Self-verbalized UQ denotes approaches in which a model is explicitly prompted, fine-tuned, or supervised to verbalize its own degree of certainty regarding its outputs. This is realized either as numeric probabilities (e.g., “I am 80% sure”), qualitative statements (“I am quite confident”), or both. The methodology contrasts with:

• Ensemble/Bayesian UQ: leverage multiple forward passes or weight/posterior sampling, providing uncertainty via statistical dispersion.
• Token-level probability-based UQ: interrogate internal per-token probability distributions or sequence entropy.
• Semantic/Consistency UQ: estimate uncertainty by assessing semantic agreement with trusted knowledge bases or fact-checkers.

Self-verbalized UQ is semi-black-box, requiring only the ability to prompt/generate, and is distinct from fully white-box access to internal model states (Shorinwa et al., 2024).

Within contemporary taxonomies, self-verbalized UQ is positioned between token-level and semantic UQ, bridging the gap between raw probabilistic outputs and purely semantic, post hoc quality judgments (Shorinwa et al., 2024).

2. Methodologies for Self-Verbalized Uncertainty Quantification

A diverse set of training and inference techniques underlie self-verbalized UQ systems:

1. Calibrator + Controlled Generation: Small calibrator models predict correctness scores given prompt and response, used to supervise LLM generations that must emit confidence-aligned markers (Shorinwa et al., 2024).
2. Supervised Confidence Fine-tuning: Models are fine-tuned on datasets (e.g., CalibratedMath) with target confidence labels, typically via cross-entropy loss, to reproduce numeric confidences following solution outputs (Jang et al., 4 Jun 2025).

• For example, for question $q$, sample $K$ CoT generations $(r^{(i)}, a^{(i)})_{i=1}^K$, compute empirical correctness $\hat{p}(q) = \frac{1}{K}\sum_{i=1}^K \mathbbm{1}[a^{(i)}=a^\star]$, then set scalar label $c = \lfloor 100\cdot \hat{p}(q)\rfloor$ (Jang et al., 4 Jun 2025).

1. RLHF-based Calibration: Human feedback is utilized to jointly optimize for both factuality and alignment of the verbalized confidence with correctness (e.g., SaySelf, TrustFine) (Shorinwa et al., 2024).
2. Dual-Agent Architectures: A speaker LLM emits answers with confidences, while a listener LLM or external supervisor scores output correctness, aligning speaker confidence via reward signals (e.g., LACIE) (Shorinwa et al., 2024).
3. Knowledge Distillation with Confidence Transfer: Confidence-labeled outputs from a capable teacher LLM (e.g., GPT-4) are used to supervise student model training, producing both answers and accompanied numeric confidences (Shorinwa et al., 2024).
4. Abstention Training: The LLM is trained to abstain (“I don’t know”) when confidence is low, thus quantizing self-verbalized uncertainty into actionable abstention signals (Shorinwa et al., 2024).

These methodologies support both scalar (numeric) and natural language confidence outputs. Fine-tuning on domain-relevant (prompt, answer, confidence) triplets is common, and post-hoc calibrators (e.g., logistic regression on confidence spans) can be applied where direct training is infeasible.

3. Self-Verbalized UQ in Agentic Frameworks: The AUQ Paradigm

The Dual-Process Agentic Uncertainty Quantification (AUQ) framework operationalizes self-verbalized uncertainty as an active, bidirectional control signal in autonomous agents, aiming to curtail cascading error propagation—termed the Spiral of Hallucination—during long-horizon reasoning (Zhang et al., 22 Jan 2026). AUQ comprises two integrated subsystems:

• System 1: Uncertainty-Aware Memory (UAM)
  • At each step $t$, the agent emits a triplet $(a_t, \hat{c}_t, \hat{e}_t)$ where $a_t$ is the action, $\hat{c}_t\in [0,1]$ is verbatim confidence, and $\hat{e}_t$ is a short natural-language uncertainty explanation.
  • The sequence is stored in memory $$\mathcal{M}_t = \{(o_i, a_i, \hat{c}_i, \hat{e}_i)\}_{i=0}^{t-1}$$. Including prior $(\hat{c}_i, \hat{e}_i)$ in prompts for $t+1$ steers future generations away from overcommitted trajectories.
  • Confidence is propagated multiplicatively or via a min-operator: $C_t = \prod_{i=0}^t \hat{c}_i$ or $C_t = \min_{0\leq i\leq t} \hat{c}_i$.
• System 2: Uncertainty-Aware Reflection (UAR)
  • If $\hat{c}_t < \tau$ (with $\tau$ a reliability threshold, e.g., 0.8–0.95), UAR samples $N$ candidate actions and confidence tuples from an inverse prompt containing $\hat{e}_t$.
  • A consistency-weighted score for each action is computed:

  $$S_{\mathrm{cons}}(a) = \frac{1}{N} \sum_{k=1}^N \hat{c}_t^{(k)} \mathbb{I}[a_t^{(k)} \equiv a]$$

  The maximal scorer is selected, and in low-confidence cases, memory expansion plus reflection is retried.

The dual-process loop dynamically alternates between fast execution (System 1) and expensive deliberation (System 2), optimizing decision reliability and computational efficiency (Zhang et al., 22 Jan 2026).

4. Emergent Behaviors and Interpretability

Supervised fine-tuning with scalar confidence labels induces not only well-calibrated confidence spans but also distinctive self-verification behavior. Empirical studies show:

• Response Length vs. Confidence: Low-confidence generations are longer, with frequent self-checking or error-correction phrases (e.g., “Let me double-check…”), while high-confidence responses are concise (Jang et al., 4 Jun 2025).
• Emergence of Verification without Explicit Supervision: Models trained only on scalar confidence labels internalize a mapping: low-confidence → more chain-of-thought (CoT) debugging steps; high-confidence → confident, direct answers (Jang et al., 4 Jun 2025).
• Generalizability: This length–confidence relationship generalizes across datasets (e.g., GSM8K, MATH-500, ARC-Challenge), suggesting that self-verbalized UQ induces internal representational modulation beyond mere dataset artifacts (Jang et al., 4 Jun 2025).

A plausible implication is that confidence-aware fine-tuning enhances both transparency—by exposing the model’s epistemic stance—and controllability, by enabling downstream agents/users to interpret model behaviors contextually.

5. Calibration Metrics and Empirical Evaluation

Standard and bespoke metrics are adopted for evaluating self-verbalized UQ:

Metric	Description	Application
Expected Calibration Error (ECE)	$$\sum_{m=1}^M \frac{|B_m|}{N} |\mathrm{acc}(B_m) - \mathrm{conf}(B_m)|$$	Bin-based discrepancy between accuracy and mean confidence (Shorinwa et al., 2024, Jang et al., 4 Jun 2025, Zhang et al., 22 Jan 2026)
Brier Score (BS)	$\frac{1}{N} \sum_{i=1}^N (p_i - y_i)^2$	Mean squared error of predicted confidence vs correctness
AUROC	Area under ROC for confidence as predictor of correctness	Discriminative power for detecting errors
Trajectory-ECE / Brier	Aggregated over agentic roll-outs using $\Phi_\text{last}$, $\Phi_\text{min}$, $\Phi_\text{avg}$	Used in AUQ frameworks (Zhang et al., 22 Jan 2026)

Empirical findings include:

• Large LLMs (e.g., GPT-4 scale) achieve ECE ≈ 5%, smaller (Vicuna-7B) ≈ 15% (Shorinwa et al., 2024).
• Fine-tuning on confidence labels reduces ECE and boosts accuracy/interpretability (e.g., LLaMA3.2-3B on GSM8K: ECE drops from 0.2065 to 0.0568, ACC rises from 68.68% to 71.34%) (Jang et al., 4 Jun 2025).
• AUQ framework yields trajectory-level ECE as low as 0.109 (vs 0.306 for ReAct) and end-state AUROC > 0.96 on ALFWorld, demonstrating that self-verbalized signals, when used as control, outperform baseline memory-less or purely reactive protocols (Zhang et al., 22 Jan 2026).
• Combining self-verbalization with calibrators or reflection mechanisms further reduces Brier score by up to 20% relative to naïve scoring (Shorinwa et al., 2024).

6. Applications, Limitations, and Challenges

Applications span single-turn chatbot scenarios, chain-of-thought math/logic reasoning, and long-horizon agentic workflows where autonomous agents must manage compounding uncertainty over multiple steps (Shorinwa et al., 2024, Zhang et al., 22 Jan 2026).

Limitations and Pathologies:

• Persistent overconfidence—verbalized estimates frequently cluster near the upper end (80–100%) even for erroneous responses (Shorinwa et al., 2024).
• Calibration and fluency can drift under distribution shift, with numeric verbalizations losing fidelity on OOD tasks (Shorinwa et al., 2024, Jang et al., 4 Jun 2025).
• Human-like rounding or anchoring biases (preference for 5%-steps) are evident.
• Additional resource cost: fine-tuning with human or automated labels, dual-agent RLHF, and listener feedback all require new data and compute (Shorinwa et al., 2024).

Challenges:

• Prompt robustness—eliciting well-calibrated outputs with prompt engineering alone remains open (Shorinwa et al., 2024).
• Multi-turn propagation and updating of uncertainty in dialog agents.
• Adversarial robustness (e.g., prompt injection attacks targeting confidence expressions).

7. Practical Strategies and Future Research Directions

Best practices for effective deployment and continued improvement of self-verbalized UQ include:

• Prefer numeric probability outputs and avoid vague lexical hedges.
• Employ few-shot prompting with explicit (question, answer, confidence) exemplars or domain-specific calibration data (Shorinwa et al., 2024).
• Fine-tune on small in-domain datasets or, where infeasible, apply post-hoc calibrators to verbalized outputs.
• Combine self-verbalized UQ with secondary checks (token entropy or semantic consistency) to mitigate overconfidence.
• Incorporate bidirectional signal propagation (as in AUQ) to convert passive uncertainty into actionable triggers for reflection, memory weighting, or rethinking (Zhang et al., 22 Jan 2026).
• Regularly evaluate calibration (ECE, Brier, AUROC) and adapt prompting/calibration strategies accordingly.

Open research directions include leveraging mechanistic interpretability to probe the internals of confidence formation, developing standardized multi-domain benchmarks, and designing adversarially robust verbalization protocols (Shorinwa et al., 2024).

Self-verbalized uncertainty quantification represents both an interpretability tool and an agentic feedback signal, blurring the line between “sensor” and “actuator” in model-internal epistemics. Through dual-process control, calibration-aware fine-tuning, and careful evaluation, it is an increasingly foundational component of reliable, transparent AI systems (Zhang et al., 22 Jan 2026, Shorinwa et al., 2024, Jang et al., 4 Jun 2025).