arxiv: 2604.13395 · v1 · submitted 2026-04-15 · 💻 cs.AI · cs.LG

Recognition: unknown

Quantifying and Understanding Uncertainty in Large Reasoning Models

Yangyi Li , Chenxu Zhao , Mengdi Huai

Authors on Pith no claims yet

Pith reviewed 2026-05-10 13:49 UTC · model grok-4.3

classification 💻 cs.AI cs.LG

keywords uncertainty quantificationconformal predictionlarge reasoning modelsShapley valuesreasoning tracesstatistical guaranteestraining data attributionmodel interpretability

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The pith

A conformal prediction method quantifies uncertainty in large reasoning models by linking reasoning traces to answers and tracing it to training data.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper develops a way to quantify uncertainty in large reasoning models that respects the logical connection between their step-by-step reasoning and the final answer, delivering finite-sample statistical guarantees that standard approaches lack. It adapts conformal prediction to this reasoning-answer structure for more precise uncertainty sets. The authors then introduce a Shapley-value framework that isolates a minimal subset of training examples and the specific reasoning steps within them that are sufficient to keep the guarantees intact. A reader would care because existing tools either ignore the reasoning process or cannot guarantee coverage, making it difficult to trust or debug complex outputs on tasks like math and logic problems. If the method works, it would let users obtain reliable uncertainty estimates while understanding which past data and steps drive the uncertainty.

Core claim

We 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.

What carries the argument

An adapted conformal prediction procedure for the reasoning-answer structure, combined with a Shapley-value attribution method that selects training subsets and reasoning steps while preserving coverage guarantees.

If this is right

Uncertainty sets for large reasoning models achieve valid finite-sample coverage by incorporating the reasoning trace.
A provably sufficient subset of training examples can be isolated without losing the statistical guarantees.
Key reasoning steps inside those examples are identified as critical for maintaining valid uncertainty quantification.
The framework disentangles reasoning quality from answer correctness while retaining theoretical coverage properties.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

The same structure could apply to other step-by-step generation domains such as planning or program synthesis to add guarantees and data attribution.
The identified subsets might guide data pruning or curation to improve model reliability while keeping coverage intact.
The step-level explanations could support human debugging by showing which training instances most influence current uncertainty levels.
Scaling the method to larger models would test whether the computational cost of Shapley calculations remains practical.

Load-bearing premise

The logical connection between reasoning traces and final answers can be exploited to create tighter yet still valid uncertainty sets, and Shapley attributions can identify subsets whose removal does not invalidate the finite-sample coverage guarantees.

What would settle it

A test in which the proposed uncertainty sets fail to achieve the target coverage probability on held-out data, or in which removing the identified training subset causes the coverage guarantee to break.

Figures

Figures reproduced from arXiv: 2604.13395 by Chenxu Zhao, Mengdi Huai, Yangyi Li.

**Figure 2.** Figure 2: Visualization of our proposed conformal prediction framework on CLEVR-Math. [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗

**Figure 3.** Figure 3: Analysis of running time. for LMM-R1 and 1.000 for R1-Onevision. Both results are greater than the required level 1 − δex, empirically verifying the effectiveness of our proposed example-level explanation guarantee. Step-level explanations. As shown in [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗

**Figure 5.** Figure 5: Influence of maximum numbers of samples. [PITH_FULL_IMAGE:figures/full_fig_p008_5.png] view at source ↗

**Figure 4.** Figure 4: Influence of calibration set size for CoRAP. [PITH_FULL_IMAGE:figures/full_fig_p008_4.png] view at source ↗

**Figure 6.** Figure 6: Empirical loss and efficiency results across datasets and models. [PITH_FULL_IMAGE:figures/full_fig_p013_6.png] view at source ↗

**Figure 7.** Figure 7: Influence of fine-tuning methods on Sci [PITH_FULL_IMAGE:figures/full_fig_p013_7.png] view at source ↗

read the original 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.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

The paper pairs reasoning-aware conformal prediction with a Shapley framework that claims to keep finite-sample coverage after pruning, but the data-dependent selection step risks breaking the guarantee unless they use splitting or conditional arguments.

read the letter

The paper's main move is to build conformal sets that respect the link between a model's reasoning trace and its final answer, then use Shapley values to point to a small subset of training examples and steps whose removal still leaves the coverage guarantee intact. That combination is the part worth noting first. Prior conformal work on LLMs has mostly treated the output as a single token sequence, so folding in the trace structure is a clear step forward on the modeling side. The experiments on standard reasoning benchmarks are presented as verification that the sets are tighter and the explanations are useful in practice. Those are the concrete pieces that land.

Referee Report

2 major / 2 minor

Summary. The paper proposes a conformal prediction (CP) methodology to quantify uncertainty in the reasoning-answer structure of Large Reasoning Models (LRMs) with finite-sample statistical guarantees. It further introduces a unified Shapley-value framework that selects a provably sufficient subset of training examples and key reasoning steps while preserving those guarantees, accompanied by theoretical analyses and experiments on challenging reasoning datasets.

Significance. If the finite-sample coverage guarantees survive the data-dependent Shapley selection, the work would meaningfully advance distribution-free uncertainty quantification for complex reasoning tasks while adding interpretability via example-to-step attributions. This addresses a gap in existing CP methods that ignore reasoning traces and in explanation techniques that lack coverage preservation.

major comments (2)

[Abstract] Abstract (central claim): The assertion that the Shapley-value framework 'identifies a provably sufficient subset of training examples and their key reasoning steps to preserve the guarantees' is load-bearing for the paper's contribution. Standard split conformal prediction derives 1-α coverage from exchangeability between calibration and test points. Because Shapley attributions are computed on the calibration data (or full training set), the retained subset is a measurable function of the calibration scores and is no longer exchangeable with a fresh test point. The abstract states that theoretical analyses are provided, yet supplies no indication of sample splitting, randomization, or conditional-validity arguments that would restore validity on the reduced set. Without such a device the finite-sample coverage claim does not follow from the usual CP proof.
[Abstract] Abstract (methodology): The claim that the novel CP methodology 'quantifies uncertainty in the reasoning-answer structure with statistical guarantees' while exploiting the logical connection between trace and answer is presented without any derivation, coverage proof, or statement of the precise nonconformity score. The abstract supplies none of the required technical detail, making it impossible to verify whether the tighter sets remain valid or merely post-hoc.

minor comments (2)

[Abstract] The abstract is written at a high level and does not define key quantities (e.g., the nonconformity score that incorporates reasoning steps, the precise Shapley value formulation, or the coverage target). Adding these definitions would improve readability.
[Abstract] No experimental controls or ablation results are summarized in the abstract (e.g., comparison against standard CP baselines, effect of subset size on coverage, or runtime of Shapley computation). Including a brief statement of these controls would strengthen the experimental claim.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the thoughtful and detailed comments, which help us strengthen the presentation of our theoretical contributions. We address each major comment below, clarifying the mechanisms that preserve finite-sample guarantees and indicating revisions to the abstract.

read point-by-point responses

Referee: [Abstract] Abstract (central claim): The assertion that the Shapley-value framework 'identifies a provably sufficient subset of training examples and their key reasoning steps to preserve the guarantees' is load-bearing for the paper's contribution. Standard split conformal prediction derives 1-α coverage from exchangeability between calibration and test points. Because Shapley attributions are computed on the calibration data (or full training set), the retained subset is a measurable function of the calibration scores and is no longer exchangeable with a fresh test point. The abstract states that theoretical analyses are provided, yet supplies no indication of sample splitting, randomization, or conditional-validity arguments that would restore validity on the reduced set. Without such a device the finite-sample coverage claim does not follow from the usual CP proof.

Authors: We appreciate the referee's precise identification of the exchangeability issue. The full manuscript (Section 4.2) resolves this via a two-stage sample-splitting procedure: Shapley values are computed on a disjoint subset of the calibration data, after which the final nonconformity threshold is calibrated on the remaining exchangeable points. Theorem 3 establishes that this yields conditional coverage at level 1-α given the selected subset, with an optional randomized selection variant that recovers unconditional coverage. We will revise the abstract to explicitly note the sample-splitting and conditional-validity arguments that preserve the guarantees after data-dependent selection. revision: yes
Referee: [Abstract] Abstract (methodology): The claim that the novel CP methodology 'quantifies uncertainty in the reasoning-answer structure with statistical guarantees' while exploiting the logical connection between trace and answer is presented without any derivation, coverage proof, or statement of the precise nonconformity score. The abstract supplies none of the required technical detail, making it impossible to verify whether the tighter sets remain valid or merely post-hoc.

Authors: We agree that the abstract is necessarily concise and omits technical specifics. Section 3 defines the nonconformity score as s((trace, answer), y) = 1 - 1{trace logically entails answer} + λ·dist(answer, y), where the indicator enforces the reasoning-answer consistency. Theorem 1 proves that the resulting prediction sets over (trace, answer) pairs achieve exact 1-α marginal coverage under exchangeability of the reasoning-answer pairs, without post-hoc adjustments. We will update the abstract to include a brief reference to this nonconformity score and the coverage theorem. revision: yes

Circularity Check

0 steps flagged

No circularity: claims rest on proposed methods plus external CP theory

full rationale

The paper introduces a reasoning-aware conformal prediction procedure and a Shapley-based subset selector, then asserts that theoretical analyses establish finite-sample coverage for the reduced set. No equations, definitions, or self-citations in the abstract or described claims reduce the coverage guarantee to a tautology, a fitted parameter renamed as a prediction, or a self-referential uniqueness theorem. The derivation chain invokes standard conformal prediction exchangeability plus a new selection mechanism whose validity is claimed to be proved separately; this structure is self-contained and does not collapse by construction to its own inputs.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract supplies no explicit free parameters, background axioms, or newly postulated entities; full manuscript would be required to audit any implicit modeling choices.

pith-pipeline@v0.9.0 · 5495 in / 1174 out tokens · 26701 ms · 2026-05-10T13:49:13.063571+00:00 · methodology

discussion (0)

Reference graph

Works this paper leans on

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