Uncertainty Quantification › Verbalized Uncertainty

Beyond numerical confidence scores, models can express uncertainty in natural language. Rather than producing a probability value, the model says something like "I'm not certain about this, but..." or "I believe this is correct, though you should verify with a primary source." This is called verbalized uncertainty or linguistic uncertainty expression.

Numerical confidence scores are not human-readable by default. When you deploy an LLM in a product, the end user receives text, not logits. Verbalized uncertainty lets models communicate the same information in a form users can act on, directly in the response.

Verbalized uncertainty can convey more detail than a single probability. A model can distinguish between different types of uncertainty within a single response:

• "I'm confident this happened but unsure of the exact date" (factual uncertainty with partial knowledge)
• "This is a contested topic among experts" (epistemic disagreement in the world)
• "This falls outside my knowledge cutoff" (temporal uncertainty about recent events)
• "I may be confusing this with a similar event" (confusion or conflation uncertainty)

These distinctions matter for how a user should respond. Knowing to check a specific date is different from knowing to consult an expert on a contested topic, which is different again from knowing that the answer simply isn't knowable from an LLM's training data. A single numeric confidence score collapses all of these into a single value and loses the actionable structure.

There is also a practical benefit in user experience. Research on trust in AI systems shows that users who receive explicit uncertainty information make better decisions than users who receive confident answers without uncertainty markers. When a model says "I believe this is correct, but you should verify," users check more often and catch errors more reliably. The uncertainty expression acts as a metacognitive cue that activates verification behavior.

The uncertainty quantification field distinguishes two fundamental types of uncertainty that appear throughout statistics and machine learning:

In language models, the distinction is blurry in practice. The model cannot distinguish "I don't know because I wasn't trained on this" from "nobody knows because it is inherently uncertain." A question about a contested historical interpretation and a question about a fact the model simply wasn't trained on look the same from the model's perspective: both produce uncertainty in the output, but for very different reasons.

The distinction matters practically because the appropriate response differs. Epistemic uncertainty can often be resolved by retrieval or tool use: if the model doesn't know something, fetching a document might provide the answer. Aleatoric uncertainty cannot be resolved this way: no amount of retrieval will tell you exactly when an earthquake will happen. A well-designed system that can distinguish the two would route differently: retrieval augmentation for epistemic uncertainty, clear communication of irreducible uncertainty for aleatoric cases.

Some researchers have proposed using sampling-based methods to proxy this distinction. The intuition is that epistemic uncertainty (things the model learned inconsistently across different parts of training) would produce high sampling variance, while aleatoric uncertainty (inherently uncertain facts) would produce consistently uncertain outputs. This intuition doesn't always hold in practice, but it motivates semantic entropy and related techniques as approximate probes of epistemic uncertainty.

The challenge with verbalized uncertainty is that models must learn to say "I don't know" when they do not know, not just when prompted to hedge. Several training approaches have been developed:

Supervised fine-tuning on uncertainty-labeled data. Collect question-answer pairs where the model's answers are scored for correctness. Fine-tune the model to produce hedged responses when it gets the answer wrong and confident responses when correct. This requires a labeled dataset of model errors, which is expensive to construct. The model must learn what to say and when saying "I'm not sure" is appropriate, which depends on having a reliable internal signal of its own knowledge boundaries.

RLHF with calibration reward. Include a calibration signal in the reward function during RLHF. Responses that accurately hedge on difficult questions get higher reward; overconfident wrong responses get penalized. The challenge is operationalizing "accurate hedging" as a reward. One approach: use an external verifier to check factual claims, then reward hedging when claims are wrong and penalize hedging when claims are correct.

Prompting. Large models can be prompted to verbalize uncertainty without fine-tuning. A system prompt like "If you are not certain about something, say so explicitly and explain why" can improve verbal calibration for models with sufficient instruction-following ability. The effect is stronger in larger models that have better instruction comprehension. This is the most practically accessible approach for most deployment teams, requiring no additional training infrastructure.

RLAIF (reinforcement learning from AI feedback). An AI judge evaluates whether the model's expressed uncertainty matches its actual correctness. This creates a scalable signal for calibration without requiring human labeling of every question. The judge assesses: "This model said it was 'fairly confident' and was correct. Did the expressed confidence match the actual outcome?" Aggregated over many examples, this signal trains toward verbal calibration.

Verbalized uncertainty has a fundamental problem: the model can say "I'm not sure" without being uncertain internally. It's a surface-level behavior that can be decoupled from the model's internal confidence state.

Studies have found that LLMs often produce calibrated-sounding hedges without having lower token-level confidence on the content they're hedging. The model has learned that certain phrasings ("it may be", "I believe") are stylistically appropriate in certain contexts. This is sometimes called sycophantic hedging: the model hedges to seem appropriately humble rather than because its confidence is lower. If you measure the token-level probability on responses where the model verbally hedges versus responses where it doesn't hedge, you often find very little difference.

A related problem is topic-based hedging: models learn to hedge on topics that are stereotypically uncertain (emerging science, predictions about the future, contested political topics) and to express confidence on topics that are stereotypically factual (historical dates, mathematical facts), regardless of whether they know the specific answer. A model might say "I'm confident that World War II ended in 1945" (correct) but also "I'm confident that the Battle of Maldon was fought in 981" (incorrect) because historical dates pattern-match to the confident register, not because the model has verified the date.

A practical consequence: you cannot take verbalized uncertainty at face value. If a model says "I'm quite certain that...", that phrase may reflect the model's writing style for that topic type more than its actual reliability on that specific claim. Sampling-based methods and calibration analysis provide stronger evidence because they measure behavioral consistency rather than surface language patterns.