Quantifying and Understanding Uncertainty in Large Reasoning Models
Yangyi Li, Chenxu Zhao, Mengdi Huai
Abstract
Large Reasoning Models (LRMs) have recently demonstrated significant improvements in complex reasoning. While quantifying generation uncertainty in LRMs is crucial, traditional methods are often insufficient because they do not provide finite-sample guarantees for reasoning-answer generation. Conformal prediction (CP) stands out as a distribution-free and model-agnostic methodology that constructs statistically rigorous uncertainty sets. However, existing CP methods ignore the logical connection between the reasoning trace and the final answer. Additionally, prior studies fail to interpret the origins of uncertainty coverage for LRMs as they typically overlook the specific training factors driving valid reasoning. Notably, it is challenging to disentangle reasoning quality from answer correctness when quantifying uncertainty, while simultaneously establishing theoretical guarantees for computationally efficient explanation methods. To address these challenges, we first propose a novel methodology that quantifies uncertainty in the reasoning-answer structure with statistical guarantees. Subsequently, we develop a unified example-to-step explanation framework using Shapley values that identifies a provably sufficient subset of training examples and their key reasoning steps to preserve the guarantees. We also provide theoretical analyses of our proposed methods. Extensive experiments on challenging reasoning datasets verify the effectiveness of the proposed methods.
AI Impact Assessments
(3 models)Scientific Impact Assessment
Core Contribution
This paper tackles uncertainty quantification (UQ) for Large Reasoning Models (LRMs) — models that generate explicit reasoning traces before final answers. Two main contributions are proposed: (1) CoRAP (Conformal Reasoning-Answer Prediction), a conformal prediction framework that jointly quantifies uncertainty over reasoning-answer pairs with finite-sample guarantees, and (2) a hierarchical Shapley value explanation framework that identifies which training examples and reasoning steps are sufficient to maintain coverage guarantees.
The key insight is that existing CP methods either ignore reasoning traces entirely or treat the full generation holistically, failing to verify whether reasoning logically supports the answer. CoRAP introduces three quality functions (sequence quality, set confidence, conditional answer quality) and calibrates threshold triplets via the Learn Then Test (LTT) framework with FWER control.
Methodological Rigor
Conformal prediction component: Theorem 3.1 provides a valid risk control guarantee, leveraging the established LTT framework. The proof is a relatively direct application of binomial-tail p-values with FWER correction. While technically correct, the novelty in the statistical machinery is modest — the contribution lies in the problem formulation (the three-threshold structure and the loss function capturing reasoning-answer validity).
Explanation component: Theorem 3.2 provides a two-level guarantee, but relies on a key assumption — the "diminishing returns" condition v(P\U) ≥ v(P) − Σϕ_u − ξ — whose validity in practice is neither verified nor characterized. The slack terms ξ_ex, ξ_st appear in bounds but remain abstract. The Monte Carlo Shapley approximation with Hoeffding-based confidence bounds is standard.
Critical weakness in reasoning validation: The admission function V(z_i, r̂_k) uses ROUGE-L ≥ 0.2 against reference rationale. This surface-level lexical overlap metric is a poor proxy for logical reasoning validity. A reasoning trace could have high ROUGE-L while containing logical errors, or valid reasoning could score low due to paraphrasing. This fundamentally undermines the paper's central claim of verifying "logical connection between reasoning trace and final answer."
Potential Impact
The problem is well-motivated: as LRMs become prevalent, understanding when and why their reasoning is trustworthy is important. However, several factors limit practical impact:
Timeliness & Relevance
The paper addresses a genuinely timely topic — UQ for reasoning models is an open and important problem as o-series and DeepSeek-R1 models proliferate. The connection between uncertainty quantification and training data attribution is a fresh angle. However, the execution does not yet match the ambition of the problem statement.
Strengths
1. Well-structured problem formulation that explicitly disentangles reasoning quality from answer correctness within a statistical framework.
2. End-to-end framework connecting UQ to explanation via a principled hierarchical approach.
3. Computational optimizations (grouping, influence functions, warm-start preselection) show practical awareness.
4. Consistent validity: Empirical losses stay below target α across configurations, while the baseline frequently violates risk control.
5. Efficiency gains: CoRAP produces notably more compact prediction sets than CP-Router.
Limitations
1. Admission function quality: ROUGE-L is inadequate for validating reasoning logic — this is the framework's Achilles' heel.
2. Theoretical assumptions insufficiently validated: The diminishing returns condition for Theorem 3.2 is assumed but not empirically verified.
3. Task simplicity mismatch: CLEVR-Math arithmetic and ScienceQA MCQs don't stress-test the reasoning capabilities that distinguish LRMs from LLMs.
4. No text-only evaluation: Despite LRMs being primarily language models, all experiments are multimodal — acknowledged as a limitation.
5. Reproducibility concerns: Some important details (grid Λ specification, influence function implementation details) are underspecified.
Overall Assessment
This paper makes a reasonable methodological contribution by extending conformal prediction to the reasoning-answer structure of LRMs and proposing a hierarchical attribution framework. The theoretical results are sound within their assumptions, and the experimental results demonstrate validity. However, the weak admission function, narrow experimental scope, and gap between the paper's ambitious framing and its actual demonstrations significantly limit the contribution's impact. The work would benefit from stronger reasoning validators, more challenging benchmarks, and comparisons with a broader set of UQ methods.
Generated Apr 16, 2026
Comparison History (55)
Paper 2 likely has higher impact: it introduces a clear missing primitive (intervention identifiability) for tool-using agents, a timely and broadly relevant problem for reliable real-world deployment. The CIVeX framework operationalizes causal identification with auditable certificates and decision verdicts, and is evaluated across synthetic/adversarial confounding plus real production-log benchmarks with strong safety/utility tradeoffs. This bridges causal inference and agent systems, with immediate applications in high-stakes automation. Paper 1 is novel and rigorous, but its application scope is narrower (uncertainty for LRMs) and may see slower adoption.
Paper 1 introduces a novel, interpretable framework for understanding LLM planning by extracting search trees from reasoning traces, revealing the striking finding that LLMs exhibit myopic planning despite generating deep deliberation. This provides actionable insights for improving reasoning models and bridges cognitive science with AI. Paper 2 addresses uncertainty quantification with conformal prediction—a more incremental contribution combining existing tools (CP, Shapley values). Paper 1's findings are more surprising, broadly applicable across strategic domains, and directly relevant to the timely question of whether reasoning models truly reason.
Paper 2 introduces a comprehensive benchmark revealing fundamental limitations in LLMs' metacognitive capabilities and self-calibration. Its large-scale empirical findings directly challenge current assumptions about autonomous AI safety, suggesting a paradigm shift towards external scaffolding. This will likely have a broader and more immediate impact across AI safety and deployment than the specialized methodological advancements in uncertainty quantification presented in Paper 1.
Paper 2 introduces a comprehensive benchmark revealing fundamental limitations in LLM metacognition and self-prediction. By demonstrating that models systematically fail to translate self-knowledge into appropriate action-selection, it provides actionable, paradigm-shifting insights for AI safety and agentic deployment—specifically, the necessity of external scaffolding over internal self-knowledge. This broad empirical evaluation across multiple models will likely drive widespread future research in autonomous AI, giving it a broader and more immediate scientific impact than the methodological advancements of Paper 1.
Paper 2 demonstrates exceptional breadth of impact by bridging AI architectures with fundamental complex systems dynamics across quantum, biophysical, and social sciences. While Paper 1 addresses a highly timely issue in LLM uncertainty with rigorous methodology, Paper 2 introduces a profoundly novel concept—Dynamical Temporal Attention—that modulates emergent phenomena and mitigates catastrophic forgetting in Hopfield networks. This profound interdisciplinary applicability and fundamental scientific innovation give Paper 2 a higher potential for widespread, paradigm-shifting impact across multiple scientific domains.
Paper 2 addresses a critical challenge in Large Reasoning Models: quantifying uncertainty with statistical guarantees. By linking reasoning traces to final answers using Conformal Prediction and Shapley values, it provides rigorous methodological advancements applicable across any domain utilizing LRMs. While Paper 1 offers a novel and highly practical approach to AI governance and content moderation, Paper 2's theoretical depth, methodological rigor, and broader applicability to foundational AI safety and reliability give it a higher potential for widespread scientific impact.
Paper 1 introduces a novel interdisciplinary bridge between AI attention mechanisms and complex dynamical systems. Its broad applicability to quantum, biophysical, and social systems, along with addressing catastrophic forgetting in neural networks, gives it profound cross-field scientific implications. While Paper 2 offers timely and rigorous improvements for LLM reliability, Paper 1's foundational approach to emergent phenomena promises a wider and more fundamental scientific impact.
Paper 2 addresses a fundamental challenge in understanding uncertainty in Large Reasoning Models with broad applicability across AI. It combines conformal prediction with Shapley-value explanations, offering distribution-free statistical guarantees and theoretical analyses that generalize beyond any single domain. Paper 1, while rigorous and practically valuable for content moderation evaluation, targets a narrower application domain. Paper 2's methodological contributions—linking reasoning traces to answers in uncertainty quantification with provable guarantees—are likely to influence a wider range of fields including safe AI deployment, interpretability, and trustworthy reasoning systems.
Paper 2 addresses a more broadly impactful problem—uncertainty quantification for Large Reasoning Models—combining conformal prediction with Shapley-value explanations and providing theoretical guarantees. This intersects multiple high-demand areas: LLM reasoning, uncertainty quantification, and trustworthy AI. Paper 1 makes a solid contribution extending mechanistic interpretability to vision transformers, but it is more incremental (adapting existing circuit discovery methods to a new modality). Paper 2's methodological novelty (reasoning-aware CP, unified explanation framework with provable guarantees) and timeliness given the surge in reasoning models give it broader potential impact.
Paper 1 tackles a fundamental challenge in Large Reasoning Models by introducing statistically rigorous uncertainty quantification using conformal prediction and Shapley values. Its provision of finite-sample theoretical guarantees and model-agnostic methods offers high methodological rigor. While Paper 2 addresses an important societal bias in RAG systems, Paper 1's theoretical contributions and focus on the reliability of complex reasoning processes have broader, foundational implications across the AI field, making its potential scientific impact significantly higher.
Paper 2 is likely higher impact: it introduces statistically rigorous, distribution-free uncertainty quantification for LRMs via conformal prediction while explicitly modeling reasoning–answer structure, plus an explanation framework with theoretical guarantees. This targets pressing real-world needs (reliable deployment, calibrated decision-making, interpretability) across many domains using LRMs, and offers methodological rigor and timeliness. Paper 1 is novel and conceptually important (transformers executing a universal language), but its practical applications are less immediate and may be more sensitive to experimental setup and bounded-context assumptions.
Paper 2 likely has higher impact due to its timely focus on uncertainty quantification for large reasoning models and its combination of distribution-free statistical guarantees (conformal prediction) with structure-aware reasoning/answer coupling and interpretable attribution (Shapley-based explanations). This targets immediate real-world needs (reliable deployment, calibration, auditing, safety) across many domains using LRMs, and offers methodological rigor with theoretical analysis plus empirical validation. Paper 1 is novel and conceptually important, but its applicability may be narrower and more dependent on synthetic program-distribution training and bounded-context execution assumptions.
Paper 2 offers broader scientific and practical impact by challenging the prevailing assumption that LLMs are merely cost-saving fallbacks for human annotation. By demonstrating statistically when LLMs are superior frontline estimators of group perspectives, it fundamentally shifts methodologies across NLP, social sciences, and HCI. While Paper 1 provides rigorous methodological advancements in uncertainty quantification, Paper 2's findings have more immediate, widespread real-world applications and cross-disciplinary relevance, altering how researchers globally approach data collection and human-centric evaluation.
Paper 2 addresses a more fundamental and broadly impactful problem—uncertainty quantification for Large Reasoning Models—combining conformal prediction with Shapley-value explanations and providing theoretical guarantees. This has wider applicability across safety-critical AI deployments and contributes to both the theoretical foundations and practical interpretability of reasoning models. Paper 1, while practically useful for inference efficiency, is more incremental (training-free heuristic for prefill speedup) and addresses a narrower engineering bottleneck. Paper 2's methodological novelty and cross-cutting relevance to AI safety, trustworthiness, and interpretability give it higher potential impact.
Paper 1 proposes a transformative paradigm for autonomous agents by enabling spontaneous, reward-free self-evolution without human supervision at inference. This offers immense real-world application potential for adaptable AI systems. While Paper 2 provides rigorous theoretical contributions to uncertainty quantification, Paper 1's highly innovative approach to self-improving agents addresses a critical bottleneck in AI autonomy, likely resulting in broader and more immediate impact across the rapidly growing field of agentic AI.
Paper 2 likely has higher scientific impact due to its broad, reusable benchmark resource: a large-scale, multilingual, multimodal Olympiad dataset plus the first dedicated math-retrieval benchmark. Public release enables widespread adoption across academia/industry, influencing evaluation standards, retrieval-augmented generation research, multilingual modeling, and multimodal reasoning. Its timeliness aligns with current emphasis on benchmarks and RAG. Paper 1 is methodologically innovative (conformal guarantees + Shapley explanations) but is narrower in scope and may see slower, more specialized uptake compared to a widely used dataset/benchmark.
Paper 2 has higher likely scientific impact due to its methodological novelty and rigor: it advances conformal prediction to account for reasoning–answer structure with finite-sample statistical guarantees, and adds theoretically grounded interpretability via Shapley-based example/step attributions. This is broadly applicable across many LRM settings (evaluation, safety, calibration, dataset curation, debugging) and is highly timely given rapid deployment of reasoning models. Paper 1 is strong and application-driven, but is more domain-specific (mobile mapping/navigation in cluttered spaces) and appears to offer fewer general theoretical contributions.
LACE introduces a fundamentally novel architectural paradigm—enabling parallel reasoning paths to interact via cross-thread attention—which represents a significant departure from existing approaches where reasoning traces are independent. This has broad implications for how LLMs perform inference and could influence future model architectures and training paradigms. Paper 1 contributes solid methodology (conformal prediction + Shapley values for LRM uncertainty), but builds more incrementally on existing CP and explainability frameworks. LACE's 7+ point accuracy improvement and its potential to reshape parallel reasoning make it more likely to drive widespread adoption and follow-up research.
Paper 2 likely has higher impact due to broader and more timely relevance: numerical instability affects essentially all Transformer-based LLM deployments, especially agentic systems needing reproducibility and safety. Its framing of universal chaos regimes and mechanistic layerwise error propagation could influence hardware/software stacks, evaluation protocols, and reliability engineering across ML and HPC. Paper 1 is novel and rigorous (CP with reasoning-answer structure + Shapley explanations), but its applicability is narrower to uncertainty quantification workflows and depends on adoption of specific calibration/explanation pipelines, whereas Paper 2 targets a fundamental, cross-cutting failure mode.
Paper 2 likely has higher scientific impact: it introduces a statistically grounded, broadly applicable uncertainty quantification framework for large reasoning models with finite-sample guarantees (conformal prediction) that explicitly models reasoning–answer structure, plus a theoretically supported explanation method (Shapley-based) tying uncertainty to training examples/steps. This combination of rigor, generality, and direct utility for reliable deployment and evaluation can influence multiple areas (ML theory, interpretability, safety, and applied decision-making). Paper 1 is timely and important for evaluation security, but is more narrowly scoped and primarily diagnostic.