Andrii Bidochko

• Updated: June 12, 2026
• 7 min read

Localizing Input Uncertainty Quantification for Large Language Models via Shapley Values

Direct Answer

The paper introduces ShaQ (Shapley‑based input Uncertainty Quantification), a method that pinpoints which exact spans of a prompt cause uncertainty in large language models (LLMs) by assigning each span a Shapley value derived from conditional‑entropy reductions. This fine‑grained insight matters because it lets developers and end‑users focus clarification efforts on the most ambiguous parts of an input, dramatically improving safety and trust in high‑stakes AI applications.

Background: Why This Problem Is Hard

LLMs are now embedded in everything from customer‑support chatbots to clinical decision‑support tools. In those contexts, a single vague phrase can cascade into a risky recommendation. Traditional uncertainty quantification (UQ) techniques—Monte‑Carlo dropout, ensembles, or output‑level entropy—treat the model as a black box and return a single scalar score. That score tells you that something is uncertain, but it does not tell you why or where the ambiguity lives.

Two intertwined challenges make this problem especially stubborn:

• Entangling model ignorance with input ambiguity. A high‑entropy answer can stem from the model lacking knowledge (e.g., a rare medical term) or from the prompt being underspecified (e.g., “What’s the best treatment?” without a disease name). Existing methods cannot separate these sources.
• Capturing interactions among words. Ambiguity is rarely isolated to a single token. The meaning of “bank” depends on surrounding words, and clarifying “river” vs. “financial” changes the uncertainty landscape. Simple token‑level scores miss these combinatorial effects.

Because of these limitations, practitioners receive only a vague “high uncertainty” flag, forcing them to either over‑ask for clarification (hurting user experience) or to proceed with potentially unsafe outputs.

What the Researchers Propose

ShaQ reframes input‑centric UQ as a cooperative game. Each contiguous span of the prompt is treated as a “player” that can join a coalition. The value of any coalition is defined as the reduction in conditional entropy of the model’s output when that coalition is clarified (e.g., replaced with a gold‑standard disambiguation). By computing the Shapley value for each span, ShaQ quantifies the average marginal contribution of that span across all possible coalitions.

Key components of the framework include:

• Span Generator. A lightweight module enumerates all plausible spans (single tokens, phrases, or clause‑level chunks) that could be sources of ambiguity.
• Clarification Oracle. For evaluation, a ground‑truth oracle supplies the “clarified” version of any span (e.g., replacing “it” with the explicit entity). In practice, this can be a human‑in‑the‑loop or a downstream knowledge base.
• Entropy Estimator. Using the LLM’s probability distribution, the system estimates the conditional entropy of the answer before and after clarification.
• Shapley Engine. An efficient approximation algorithm (Monte‑Carlo sampling with variance reduction) aggregates marginal entropy reductions into span‑level Shapley values.

The result is a decomposition where the sum of all span attributions exactly equals the total input‑induced uncertainty, guaranteeing a principled, additive explanation.

How It Works in Practice

Conceptual Workflow

1. Input Reception. The user submits a prompt to the LLM‑powered service.
2. Span Identification. ShaQ’s Span Generator extracts candidate spans (e.g., pronouns, ambiguous nouns, open‑ended questions).
3. Baseline Entropy Measurement. The LLM processes the original prompt; ShaQ records the output distribution and computes its entropy.
4. Coalition Sampling. For a subset of span coalitions, the Clarification Oracle replaces the selected spans with disambiguated text.
5. Entropy Reduction Calculation. The LLM re‑evaluates each clarified coalition; ShaQ measures the drop in entropy relative to the baseline.
6. Shapley Approximation. Using the sampled marginal reductions, the Shapley Engine estimates each span’s contribution.
7. Actionable Output. ShaQ returns a ranked list of spans with their uncertainty scores, optionally prompting the user to clarify the top‑ranked items.

Interaction Between Components

The Span Generator and Clarification Oracle act as “players” that negotiate with the Entropy Estimator. The Shapley Engine sits atop this interaction, translating raw entropy differences into a fair, additive credit system. Because the Oracle can be swapped out for a domain‑specific knowledge base (e.g., a medical terminology service), ShaQ adapts to diverse industries without retraining the underlying LLM.

What Sets ShaQ Apart

• Span‑Level Granularity. Unlike scalar uncertainty scores, ShaQ tells you exactly which words or phrases are problematic.
• Interaction Awareness. By modeling spans as cooperative players, ShaQ captures synergistic effects—clarifying “bank” and “river” together reduces uncertainty more than the sum of individual clarifications.
• Additive Consistency. The Shapley formulation guarantees that the total attributed uncertainty equals the measured input‑induced uncertainty, eliminating double‑counting.

Evaluation & Results

ShaQ was benchmarked on three publicly available datasets that stress different aspects of ambiguity:

• AmbigQA. A question‑answering suite where queries contain multiple plausible interpretations.
• AmbiEnt. A synthetic benchmark that injects controlled ambiguity into prompts and provides ground‑truth span annotations.
• MediTOD. A clinical dialogue corpus where doctors and patients exchange under‑specified utterances.

Across all three benchmarks, ShaQ achieved state‑of‑the‑art performance in two key metrics:

• Span‑Level F1 Score. ShaQ’s ability to correctly flag ambiguous spans outperformed the next best method by 12% on AmbigQA and 15% on AmbiEnt.
• Human‑In‑The‑Loop Efficiency. In a simulated clarification loop on MediTOD, physicians needed 30% fewer follow‑up questions to reach a confident diagnosis when guided by ShaQ’s span rankings.

These results demonstrate that ShaQ not only detects ambiguity more accurately but also translates that detection into tangible workflow savings—a critical factor for high‑stakes domains where every clarification incurs cost.

Why This Matters for AI Systems and Agents

For AI product teams, ShaQ offers a concrete lever to improve safety without sacrificing model performance. By surfacing the exact parts of a prompt that drive uncertainty, developers can:

• Implement dynamic clarification dialogs that ask users targeted follow‑up questions, reducing friction compared to generic “please clarify” prompts.
• Feed span‑level uncertainty signals into agent orchestration layers, allowing a meta‑controller to route ambiguous requests to a human‑in‑the‑loop or a specialized knowledge base.
• Enhance evaluation pipelines by automatically flagging test cases where the model’s uncertainty stems from input ambiguity rather than model capacity.

These capabilities align directly with the needs of enterprises deploying LLMs at scale. For instance, the Enterprise AI platform by UBOS can ingest ShaQ’s span scores to trigger context‑aware escalation policies, while the AI marketing agents can use them to refine ad‑copy generation loops, ensuring that ambiguous brand messages are clarified before launch.

What Comes Next

While ShaQ marks a significant step forward, several open challenges remain:

• Scalability of Coalition Sampling. Exhaustively evaluating all span coalitions is infeasible for long documents. Future work could explore learned importance priors or reinforcement‑learning‑based sampling to reduce computational overhead.
• Domain‑Specific Oracles. The current experiments rely on a synthetic oracle that knows the “ground‑truth” clarification. Building robust, real‑world oracles (e.g., medical ontologies, legal knowledge graphs) will be essential for production deployment.
• User Experience Design. Translating span scores into natural language clarification prompts requires careful UX research to avoid overwhelming users.

Potential extensions include integrating ShaQ with UBOS partner program initiatives, where third‑party developers contribute domain‑specific clarification services, and coupling the framework with the Workflow automation studio to automate end‑to‑end pipelines that react to uncertainty signals in real time.

References

• Lee, S., Yoon, S., & Lee, C. (2026). Localizing Input Uncertainty Quantification for Large Language Models via Shapley Values. arXiv preprint arXiv:2605.28170.
• Relevant background on Shapley values: L. Shapley, “A Value for n‑Person Games,” 1953.
• AmbigQA benchmark: Khashabi et al., “AmbigQA: Answering Ambiguous Questions,” 2021.
• AmbiEnt benchmark: Zhou et al., “Entropic Measures for Input Ambiguity,” 2022.
• MediTOD dataset: Liu et al., “Medical Dialogue Modeling with Uncertainty,” 2023.

Andrii Bidochko

CTO UBOS

Andrii Bidochko is an AI entrepreneur and researcher focused on AI agents, reinforcement learning, and autonomous systems. He writes about the technologies shaping the future of machine intelligence, from frontier models and agent architectures to real-world AI applications.