arxiv: 2601.04731 · v2 · submitted 2026-01-08 · 💻 cs.AI · cs.CL

Recognition: no theorem link

Miner:Mining Intrinsic Mastery for Data-Efficient RL in Large Reasoning Models

Shuyang Jiang , Yuhao Wang , Ya Zhang , Yanfeng Wang , Yu Wang

Authors on Pith no claims yet

Pith reviewed 2026-05-16 16:32 UTC · model grok-4.3

classification 💻 cs.AI cs.CL

keywords intrinsic uncertaintyself-supervised rewardtoken-level credit assignmentadaptive advantage calibrationreasoning modelsdata-efficient RLcritic-free RLlarge language models

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The pith

Policy uncertainty serves as a self-supervised reward to fix zero-advantage waste in critic-free RL for reasoning models.

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

The paper shows that current RL methods for large reasoning models waste rollouts on prompts where every answer is correct because advantage estimates drop to zero. Miner solves this by turning the policy's own token-level uncertainty into an internal reward signal that requires no extra models, labels, or inference passes. Two mechanisms do the work: a focal credit assignment that strengthens gradients only on uncertain tokens and an adaptive calibration that blends the uncertainty signal with any verifiable rewards. On Qwen3-4B and 8B models across six benchmarks the method raises Pass@1 by as much as 4.58 points and Pass@K by 6.66 points over GRPO while using the same rollout budget. The central claim is that exploiting this latent uncertainty is both necessary and sufficient for scalable, data-efficient RL training of reasoning models.

Core claim

Miner repurposes the policy's intrinsic uncertainty as a self-supervised reward signal, with no external supervision, auxiliary models, or additional inference cost. It introduces token-level focal credit assignment that dynamically amplifies gradients on critical uncertain tokens while suppressing overconfident ones, together with adaptive advantage calibration to integrate intrinsic and verifiable rewards. Evaluated on Qwen3-4B and Qwen3-8B across six reasoning benchmarks, the approach yields up to 4.58 absolute gains in Pass@1 and 6.66 gains in Pass@K compared with GRPO, establishing that latent uncertainty exploitation is both necessary and sufficient for efficient and scalable RL of the

What carries the argument

Token-level focal credit assignment that amplifies gradients on uncertain tokens while suppressing overconfident ones, combined with adaptive advantage calibration to blend intrinsic uncertainty with verifiable rewards.

If this is right

Rollout budgets on easy prompts are no longer wasted because uncertainty supplies non-zero advantage estimates.
Training remains critic-free and incurs zero extra inference cost at every step.
The same two innovations outperform other exploration-targeted methods on the reported benchmarks.
The method scales from 4B to 8B base models without architectural changes.
Performance gains appear consistently across six distinct reasoning benchmarks.

Where Pith is reading between the lines

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

The same uncertainty signal could be applied in any sparse-reward RL setting where verifiable outcomes are infrequent.
Combining focal credit assignment with other exploration bonuses might compound gains without new hyper-parameters.
If uncertainty estimates become overconfident in later training stages, performance could plateau unless the calibration rule is updated.
The approach opens a route to purely self-supervised RL loops that gradually reduce reliance on external verifiers.

Load-bearing premise

The policy's intrinsic uncertainty supplies a reliable and unbiased signal for credit assignment that mixes cleanly with verifiable rewards without introducing new biases or needing extra tuning.

What would settle it

Run the same training loop on a set of positive homogeneous prompts; if Miner produces no higher final Pass@1 or Pass@K than a plain GRPO baseline that receives zero advantage on every rollout, the central claim is false.

Figures

Figures reproduced from arXiv: 2601.04731 by Shuyang Jiang, Yanfeng Wang, Ya Zhang, Yuhao Wang, Yu Wang.

**Figure 1.** Figure 1: (a) Traditional GRPO algorithms produce a credible number of rollouts that do not contribute to RL updates, due to indistinguishable top rewards. (b) MINER introduce intrinsic rewards to each rollout, injecting beneficial dense reward signals, achieving the same peak performance with only 50% training steps, and up to 23% higher performance on Qwen3-4B-Base. large-scale post-training. Yet, this multi-rollo… view at source ↗

**Figure 2.** Figure 2: Framework of MINER. We focus on introducing intrinsic rewards to positive homogeneous prompts (PH). Upper Center: We use sequence-level uncertainty computed via the old policy πold as the intrinsic rewards, to reinforce correct yet uncertain rollouts, without overfitting to already-mastered sequences; Upper Right: Then, we leverage token-level focal credit assignment to specifically rewarding critical toke… view at source ↗

**Figure 3.** Figure 3: Comparison with other exploration-enhanced [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗

**Figure 4.** Figure 4: (a) Ablation study with three innovations (Intrinsic Reward (IR), Focal Weighting (FW) and Advantage [PITH_FULL_IMAGE:figures/full_fig_p007_4.png] view at source ↗

**Figure 5.** Figure 5: Pass@K scaling of MINER and Base model on Qwen3-4B (Upper) and Qwen3-8B (Lower) models, where MINER still demonstrates improvements for a sufficiently large K. we adopt self-consistency (SC; Wang et al. (2023)) as the evaluation method under multiple parallel samples. We do not compare sequential scaling as it is empirically verified to be highly inefficient compared to the parallel scaling paradigm (Ghosa… view at source ↗

**Figure 6.** Figure 6: Training and evaluation prompt for any token. For w/o AC, the Afinal i,j equals to the original A˜ i,j without calibration. C.6 Details of Experiments of RQ2 These experiments involve many other baselines to enhance the model exploration. The following baselines are fetched directly from their officially released codebase. For BAPO, it controls the clip range in an asymmetric manner, which allows the clip_… view at source ↗

**Figure 7.** Figure 7: (a) Pass@K scaling comparison of MINER against other GRPO variants; (b) Maintain performance on easy queries and breaking boundaries on challenging problems when evaluating MINER on six difficulty levels sourced from MATH500 and AIME2024; (c) Negligible extra computational overhead compared to GRPO. computing advantages against that for completing a training step during a whole training epoch. Results in … view at source ↗

**Figure 8.** Figure 8: Training rewards, master ratio (PH ratio) and AIME24 dev set score of GRPO and our method trained [PITH_FULL_IMAGE:figures/full_fig_p017_8.png] view at source ↗

**Figure 9.** Figure 9: Training rewards, master ratio (PH ratio) and AIME24 dev set score of GRPO and our method trained [PITH_FULL_IMAGE:figures/full_fig_p017_9.png] view at source ↗

**Figure 10.** Figure 10: Training rewards, master ratio (PH ratio) and MedQA dev set score of GRPO and our method trained [PITH_FULL_IMAGE:figures/full_fig_p018_10.png] view at source ↗

**Figure 11.** Figure 11: The KL loss, gradient norm and entroy dynamics of applying [PITH_FULL_IMAGE:figures/full_fig_p018_11.png] view at source ↗

**Figure 12.** Figure 12: The KL loss, gradient norm and entroy dynamics of applying [PITH_FULL_IMAGE:figures/full_fig_p019_12.png] view at source ↗

**Figure 13.** Figure 13: Advantage distribution of MINER. The problem is sourced from the MATH500 dataset. The darker the token, the more advantage credit is assigned. The maximum token advantage equals to the sequence advantage value. 20 [PITH_FULL_IMAGE:figures/full_fig_p020_13.png] view at source ↗

read the original abstract

Current critic-free RL methods for large reasoning models suffer from severe inefficiency when training on positive homogeneous prompts (where all rollouts are correct), resulting in waste of rollouts due to zero advantage estimates. We introduce a radically simple yet powerful solution to \uline{M}ine \uline{in}trinsic mast\uline{er}y (Miner), that repurposes the policy's intrinsic uncertainty as a self-supervised reward signal, with no external supervision, auxiliary models, or additional inference cost. Our method pioneers two key innovations: (1) a token-level focal credit assignment mechanism that dynamically amplifies gradients on critical uncertain tokens while suppressing overconfident ones, and (2) adaptive advantage calibration to seamlessly integrate intrinsic and verifiable rewards. Evaluated across six reasoning benchmarks on Qwen3-4B and Qwen3-8B base models, Miner achieves state-of-the-art performance among the other four algorithms, yielding up to \textbf{4.58} absolute gains in Pass@1 and \textbf{6.66} gains in Pass@K compared to GRPO. Comparison with other methods targeted at exploration enhancement further discloses the superiority of the two newly proposed innovations. This demonstrates that latent uncertainty exploitation is both necessary and sufficient for efficient and scalable RL training of reasoning models. Code is available at https://github.com/pixas/Miner.

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

Miner gives workable tweaks for zero-advantage cases in critic-free RL on reasoning models, but the necessity claim goes beyond what the four-algorithm comparison shows.

read the letter

The main takeaway is that Miner repurposes the policy's own uncertainty for token-level credit assignment and adaptive calibration, which produces measurable gains over GRPO on Qwen3 models. The two mechanisms target the waste on positive homogeneous prompts where all rollouts are correct and advantages hit zero. That part looks like a straightforward engineering fix with no added models or inference cost, and the code release is a plus for anyone who wants to try it directly.

Referee Report

3 major / 2 minor

Summary. The manuscript presents Miner, a critic-free RL method for large reasoning models that repurposes the policy's intrinsic uncertainty as a self-supervised reward signal to mitigate zero-advantage issues on positive homogeneous prompts. It introduces token-level focal credit assignment to dynamically amplify gradients on uncertain tokens and adaptive advantage calibration to integrate intrinsic and verifiable rewards. On Qwen3-4B and Qwen3-8B models across six reasoning benchmarks, Miner reports gains of up to 4.58 Pass@1 and 6.66 Pass@K over GRPO and three other exploration baselines, concluding that latent uncertainty exploitation is both necessary and sufficient for efficient and scalable RL training of reasoning models. Code is released.

Significance. If the empirical results hold under broader scrutiny, the approach could meaningfully advance data-efficient RL for reasoning models by avoiding auxiliary critics or extra inference. The open-sourced code is a clear strength for reproducibility. The sufficiency claim within the tested regime is plausible given the reported gains, but the necessity direction requires additional support beyond the four-algorithm comparison.

major comments (3)

[Abstract] Abstract: The statement that the results 'demonstrate that latent uncertainty exploitation is both necessary and sufficient' is not supported by the evidence. The experiments compare Miner only to GRPO plus three exploration-targeted baselines; this can support sufficiency in the tested setting but does not establish necessity, as alternative credit-assignment schemes (entropy bonuses, prompt-level diversity, or learned critics) are not evaluated or ruled out.
[Experiments] Experiments section: The absolute gains (4.58 Pass@1, 6.66 Pass@K) are reported without standard deviations, number of independent runs, or statistical significance tests. This weakens confidence in the superiority claims and the cross-benchmark conclusions.
[Method] Method description: The focal amplification thresholds and adaptive calibration weights are free parameters. No sensitivity analysis or ablation isolating their contribution is provided, which undercuts the claim that the method is 'radically simple' with no extensive hyperparameter tuning.

minor comments (2)

[Abstract] Abstract: The method-name description contains a visible LaTeX artifact (uline); this should be cleaned for the final version.
[Method] Method: Explicit equations or pseudocode for the token-level focal credit assignment and adaptive advantage calibration would improve clarity and reproducibility.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the thoughtful and constructive comments. We address each major point below and have prepared revisions to the manuscript where the feedback identifies areas for improvement.

read point-by-point responses

Referee: [Abstract] Abstract: The statement that the results 'demonstrate that latent uncertainty exploitation is both necessary and sufficient' is not supported by the evidence. The experiments compare Miner only to GRPO plus three exploration-targeted baselines; this can support sufficiency in the tested setting but does not establish necessity, as alternative credit-assignment schemes (entropy bonuses, prompt-level diversity, or learned critics) are not evaluated or ruled out.

Authors: We agree that the current experiments establish sufficiency relative to the four compared methods but do not rule out all alternative credit-assignment approaches, so the necessity claim is not fully supported. We will revise the abstract to state that the results demonstrate sufficiency for efficient and scalable RL training within the evaluated regime, while noting that broader comparisons would be required to strengthen any necessity argument. revision: yes
Referee: [Experiments] Experiments section: The absolute gains (4.58 Pass@1, 6.66 Pass@K) are reported without standard deviations, number of independent runs, or statistical significance tests. This weakens confidence in the superiority claims and the cross-benchmark conclusions.

Authors: This is a valid observation. The current manuscript reports point estimates only. In the revised version we will report standard deviations across multiple independent runs (at least three random seeds per setting), specify the number of runs, and include statistical significance tests (e.g., paired t-tests) for the key comparisons to increase confidence in the reported gains. revision: yes
Referee: [Method] Method description: The focal amplification thresholds and adaptive calibration weights are free parameters. No sensitivity analysis or ablation isolating their contribution is provided, which undercuts the claim that the method is 'radically simple' with no extensive hyperparameter tuning.

Authors: The thresholds and weights are set once via a simple quantile-based heuristic on a small validation subset and then held fixed across all six benchmarks and both model sizes, which is consistent with limited tuning. Nevertheless, we accept that an explicit sensitivity study and ablation isolating each component would strengthen the simplicity claim. We will add both a sensitivity table and component-wise ablations to the revised manuscript. revision: yes

Circularity Check

0 steps flagged

No circularity in derivation chain

full rationale

The paper defines Miner by repurposing the policy's intrinsic uncertainty as a self-supervised reward signal and introduces two explicit mechanisms (token-level focal credit assignment and adaptive advantage calibration) that are combined with verifiable external rewards. These steps are presented as algorithmic innovations without any equation or derivation reducing the final advantage estimate to a fitted parameter or input by construction. The necessity-and-sufficiency claim rests on empirical benchmark comparisons rather than a mathematical chain that loops back to the method's own definitions. No self-citation load-bearing step, uniqueness theorem, or ansatz smuggling appears in the derivation; the approach remains self-contained against external benchmarks and falsifiable via the reported experiments.

Axiom & Free-Parameter Ledger

2 free parameters · 1 axioms · 0 invented entities

The approach rests on standard policy-gradient assumptions plus the unproven premise that uncertainty correlates with useful learning signal; no new physical entities or ad-hoc constants are introduced beyond typical RL hyperparameters.

free parameters (2)

focal amplification thresholds
Parameters controlling how strongly uncertain tokens are up-weighted; values chosen to balance the signal.
adaptive calibration weights
Mixing coefficients between intrinsic uncertainty reward and verifiable reward; fitted or tuned per experiment.

axioms (1)

standard math Policy gradient updates remain valid when rewards are augmented by internal uncertainty estimates
Invokes the standard policy-gradient theorem without additional proof.

pith-pipeline@v0.9.0 · 5547 in / 1310 out tokens · 45252 ms · 2026-05-16T16:32:47.476455+00:00 · methodology

discussion (0)

Reference graph

Works this paper leans on

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augment correctness with proper scoring- rule–based rewards so the model learns to output calibrated confidence alongside answers. However, the first two paradigms overlook the advantage shaping of PH trajectories and fail to utilize them, while calibrated methods destroy the objective of the maximization of correctness, and achieve bad performance compar...

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AMC23(AI-MO, 2024): This dataset is sourced from American Mathematics Competitions sys- tem in 2023, which contains 40 problems with hybrid question types

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We adopt its 5-options English version, taking the 1,273 test problems as the evaluation benchmark

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It focuses on yes/no/- maybe questions that require reasoning over biomedical literature

PubmedQA(Jin et al., 2019) is a specialized benchmark for biomedical question answer- ing, consisting of question-answer pairs derived from PubMed abstracts. It focuses on yes/no/- maybe questions that require reasoning over biomedical literature. We use the human-labeled question test set, with 500 problems for evalu- ation. Note that we include relevant...

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MedMCQA(Pal et al., 2022) is a large-scale benchmark for medical question answering, fea- turing over 194,000 multiple-choice questions sourced from Indian medical entrance exams and other educational resources. It spans a wide range of medical topics, including anatomy, pharmacology, and pathology, and is designed to evaluate the reasoning and knowledge ...

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We only maintain health and biology subsets for testing medical reason- ing abilities, which includes 1535 problems

MMLU-Pro(Wang et al., 2024) is a chal- lenging multi-task benchmark containing over 12,000 multiple-choice questions across 14 di- verse domains, including subjects in STEM (e.g., math, physics, chemistry), social sciences, law, and humanities. We only maintain health and biology subsets for testing medical reason- ing abilities, which includes 1535 problems

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Please reason step by step and output the final answer as ‘The answer is’

MedXpertQA(Zuo et al., 2025) is an expert- level medical benchmark comprising 4,460 questions spanning 17 medical specialties and 11 body systems. It includes two subsets: a text-only version for evaluating textual medi- cal reasoning and a multimodal version (MM) with images, aimed at assessing advanced clini- cal knowledge comparable to medical licensin...

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