Can LLMs Learn to Reason Robustly under Noisy Supervision?

Shenzhi Yang; Guangcheng Zhu; Bowen Song; Sharon Li; Haobo Wang; Xing Zheng; Yingfan Ma; Zhongqi Chen

cs.LGApr 5, 2026

Can LLMs Learn to Reason Robustly under Noisy Supervision?

Authors: Shenzhi Yang, Guangcheng Zhu, Bowen Song, Sharon Li, Haobo Wang, Xing Zheng, Yingfan Ma, Zhongqi Chen, +2 more

Organizations: Zhejiang University · Ant Group · University of Wisconsin-Madison

Abstract

Reinforcement Learning with Verifiable Rewards (RLVR) effectively trains reasoning models that rely on abundant perfect labels, but its vulnerability to unavoidable noisy labels due to expert scarcity remains critically underexplored. In this work, we take the first step toward a systematic analysis of noisy label mechanisms in RLVR. In contrast to supervised classification, most RLVR algorithms incorporate a rollout-based condition: a label's influence on training is contingent on whether the current policy can generate rollouts that realize it, a property that naturally extends to noisy labels. Based on this observation, we distinguish two types of noise: inactive noisy labels, which reduce data efficiency, and active noisy labels, which are reinforced and risk skewing the model toward incorrect distributions. From experiments on training with noisy samples, we identify an Early Correctness Coherence phenomenon: although noisy samples begin to lag behind in later stages, accuracy on both clean and noisy samples increases similarly in early training. Motivated by this dynamic, we propose Online Label Refinement (OLR), which progressively corrects potentially noisy labels with majority-voted answers when two conditions hold: a positive slope in the majority answer's rollout pass rate and stable historical consistency across updates, enabling gradual self-correction as the policy improves. We evaluate OLR on six in-distribution mathematical reasoning benchmarks (AIME24/25, AMC, MATH-500, Minerva, and Olympiad) and three out-of-distribution tasks (ARC-c, GPQA-diamond, and MMLU-pro). Across noise ratios from 0.1 to 0.9, OLR consistently improves robustness under both inactive and active noisy-label settings, achieving average gains of 3.6% to 3.9% on in-distribution benchmarks and 3.3% to 4.6% on out-of-distribution evaluations.

Figures & tables

Figure 1: Two types of noisy labels in RLVR. Inactive noisy label (left): an incorrect initial label that the model cannot trigger the corresponding reasoning path for and reinforce, so it remains inactive. Active noisy label (right): an incorrect label that the model has a probability of triggering the corresponding reasoning path for and reinforcing, so it remains active.

Panel of Figure 2 — Figure 2: Early Correctness Coherence. Training accuracy of Qwen3-4B-Base ( Yang et al., 2025 ) under noisy supervision (noise ratio 0.5). For each sample, we take the majority answer as the model’s prediction. Clean and noisy samples exhibit similar learning dynamics early in training but gradually diverge as training progresses. (i) In the initial phase, the accuracy of correct answers from both groups increases steadily , suggesting that the model already contains latent correct answers for noisy samples that are not fully exploited . (ii) In later stages, accuracy on clean samples continues to improve while performance on noisy samples lags behind. Our method, O nline L abel R efinement ( OLR ), utilizes this early coherence and significantly improves reasoning performance.

Method	In-Distribution							Out-of-Distribution
Method	AIME24	AIME25	AMC	MATH-500	Minerva	Olympiad	0 0 Avg.	ARC-c	GPQA ⋆	MMLU-Pro	0 0 Avg.
Qwen3-4B-Base	9.6	4.2	34.2	52.6	19.5	28.4	24.8	35.8	14.1	33.3	27.7
Inactive Noisy Label
$\rho=0.1$	21.3	20.4	52.7	83.6	39.7	49.3	44.5	86.3	37.4	59.0	60.9
w/ OLR	22.5	19.6	55.0	83.0	41.2	48.3	$\textbf{44.9}\mathrlap{{}_{\scriptscriptstyle{\color[rgb]{0,0.5898,0}\textbf{+0.4}}}}$	88.9	37.9	59.5	$\textbf{62.1}\mathrlap{{}_{\scriptscriptstyle{\color[rgb]{0,0.5898,0}\textbf{+1.2}}}}$
$\rho=0.3$	12.9	8.3	50.2	75.8	42.0	43.0	38.7	88.1	29.8	56.2	58.0

Table 1: Results on Qwen3-4B-Base under different noise ratios. Each numerical subscript indicates the absolute improvement or degradation compared with naive GRPO without OLR. Bold indicates the better.

Method	In-Distribution							Out-of-Distribution
Method	AIME24	AIME25	AMC	MATH-500	Minerva	Olympiad	0 0 Avg.	ARC-c	GPQA ⋆	MMLU-Pro	0 0 Avg.
Qwen3-4B-Base	9.6	4.2	34.2	52.6	19.5	28.4	24.8	35.8	14.1	33.3	27.7
Unsupervised Methods
TTRL	12.1	8.3	48.2	76.4	36.0	40.3	36.9	86.9	30.3	56.0	57.7
Co-reward	12.1	7.1	44.9	76.0	38.9	40.7	36.6	86.1	29.3	55.8	57.1
Self-certainty	5.8	5.0	28.9	41.8	21.7	20.6	20.6	24.3	12.1	30.6	22.3

Table 2: Results on Qwen3-4B-Base under a 50% noise ratio with different baselines. Each numerical subscript indicates the absolute improvement or degradation compared with naive GRPO. Bold indicates the best in inactive noise scenarios, and underline indicates the best in active noise scenarios.

Method	In-Distribution							Out-of-Distribution
Method	AIME24	AIME25	AMC	MATH-500	Minerva	Olympiad	0 0 Avg.	ARC-c	GPQA ⋆	MMLU-Pro	0 0 Avg.
Active Noisy Label
w/o OLR	12.9	7.5	49.4	76.4	39.0	41.5	37.8	85.1	26.8	54.1	55.3
w/ OLR	20.0	18.3	50.0	78.8	37.1	43.9	41.4	82.9	28.8	55.4	55.7
Inactive Noisy Label
w/o OLR	17.9	12.9	50.2	78.4	41.5	41.9	40.5	88.4	33.3	57.3	59.7

Table 3: Results on Qwen3-4B-Base under a 50% noise ratio with 4K samples. Bold indicates the better.

Panel of Figure 3 — Figure 3: Training dynamics of OLR with Qwen3-4B-Base under an active noise setting (noise ratio = 0.5).

Panel of Figure 4 — Figure 4: Results under a 50% noise ratio on Qwen-3-4B-Base.

Appendix figures & tables9 assets

Supplementary material from the paper’s appendix.

Appendix

Figure 5: Results obtained with 50% inactive or active noisy labels (800 samples) using the Qwen-3-4B-Base model ( Yang et al., 2025 ) . For each sample, we take the majority vote across multiple model rollouts as the model’s prediction. The left and right pairs of columns illustrate the model’s predictions on clean and noisy samples, respectively, under both inactive and active noise. For clean samples, we display the proportion of correct (green) and incorrect (blue) predictions. For noisy samples, we show the proportion of predictions that are correct (green), that match the noisy label (red), or that match neither the true nor the noisy label (blue). The early training phase reveals that the model learns to predict true labels even on noisy examples, indicating a preference for fitting correctly labeled samples and an increasing likelihood of producing correct answers on noisy ones over time.

Panel of Figure 6 — Figure 6: Training dynamic of OLR with Qwen3-4B-Base under the inactive noisy (0.5 ratio) scenario.

Method	In-Distribution							Out-of-Distribution
Method	AIME24	AIME25	AMC	MATH-500	Minerva	Olympiad	0 0 Avg.	ARC-c	GPQA ⋆	MMLU-Pro	0 0 Avg.
Qwen3-8B-Base	10.0	7.5	38.0	61.2	27.2	33.3	29.5	28.8	13.6	46.9	29.8
Active Noisy Label
w/o OLR	14.6	12.5	52.3	80.2	39.7	43.9	40.5	59.6	19.2	60.3	46.4
w/ OLR	16.3	15.0	50.3	80.4	42.6	45.5	41.7	75.5	25.3	60.1	53.6
Inactive Noisy Label

Appendix

Table 4: Results on Qwen3-8B-Base under 50% noise ratio. Bold indicates the better.

Method	In-Distribution							Out-of-Distribution
Method	AIME24	AIME25	AMC	MATH-500	Minerva	Olympiad	0 0 Avg.	ARC-c	GPQA ⋆	MMLU-Pro	0 0 Avg.
Deepseek-R1-Distill-Llama-8B	15.8	17.9	48.2	72.2	18.8	35.7	34.8	24.9	10.1	38.7	24.6
Active Noisy Label
w/o OLR	21.7	56.2	19.6	72.2	18.4	40.4	38.1	20.6	13.1	41.7	25.1
w/ OLR	25.8	17.5	60.5	73.8	18.4	39.3	39.2	27.2	14.6	41.5	27.8
Inactive Noisy Label

Appendix

Table 5: Results on Deepseek-R1-Distill-Llama-8B under 50% noise ratio. Bold indicates the better.

Method	In-Distribution							Out-of-Distribution
Method	AIME24	AIME25	AMC	MATH-500	Minerva	Olympiad	0 0 Avg.	ARC-c	GPQA ⋆	MMLU-Pro	0 0 Avg.
Qwen3-4B-Base	9.6	4.2	34.2	52.6	19.5	28.4	24.7	35.8	14.1	33.3	27.7
Active Noisy Label
GRPO	10.4	8.8	45.8	74.6	33.1	40.4	35.5	73.9	24.7	48.6	49.1
OLR w/ $\delta_{\text{slope}}=0.0$	13.3	9.2	46.8	76.4	38.2	40.7	37.4	85.4	30.8	56.8	57.7
OLR w/ $\delta_{\text{slope}}=0.025$	10.0	10.0	43.1	76.0	34.2	38.8	35.4	73.5	27.3	50.2	50.3

Appendix

Table 6: Results on Qwen3-4B-Base under 50% noise ratios with different slope threshold

\delta_{\text{slope}}

. Bold indicates the best.

Method	In-Distribution							Out-of-Distribution
Method	AIME24	AIME25	AMC	MATH-500	Minerva	Olympiad	0 0 Avg.	ARC-c	GPQA ⋆	MMLU-Pro	0 0 Avg.
Qwen3-4B-Base	9.6	4.2	34.2	52.6	19.5	28.4	24.7	35.8	14.1	33.3	27.7
Active Noisy Label
GRPO	10.4	8.8	45.8	74.6	33.1	40.4	35.5	73.9	24.7	48.6	49.1
OLR w/ $T=2$	11.3	9.6	46.0	75.8	37.1	42.5	37.1	83.4	28.3	55.4	55.7
OLR w/ $T=4$	20.4	15.4	49.7	81.4	36.4	48.1	41.9	78.5	28.3	54.8	53.9

Appendix

Table 7: Results on Qwen3-4B-Base under 50% noise ratios with different lengths of the early learning stage

T

. Bold indicates the best.

Method	In-Distribution							Out-of-Distribution
Method	AIME24	AIME25	AMC	MATH-500	Minerva	Olympiad	0 0 Avg.	ARC-c	GPQA ⋆	MMLU-Pro	0 0 Avg.
Active Noisy Label
OLR	20.4	15.4	49.7	81.4	36.4	48.1	41.9	78.5	28.3	54.8	53.9
- Positive Convergence Slope	10.8	7.9	46.7	79.0	35.7	42.1	37.0	73.9	24.7	55.5	51.4
- Historical Consistency	13.8	10.4	46.2	77.2	35.3	40.4	37.2	78.5	26.8	54.5	53.3
Inactive Noisy Label

Appendix

Table 8: Ablation results on Qwen3-4B-Base under 50% noise ratio. Bold indicates the best.

Phase	Operation	Compute Complexity	Time
RLVR Training	Policy rollout and GRPO update	$\mathcal{O}(NKL)$	$\sim$ 3.8 h
OLR Update	Majority estimation + statistics update	$\mathcal{O}(NK)$	negligible
Total	RLVR + OLR	$\mathcal{O}(NKL)$	$\sim$ 3.8 h

Appendix

Table 9: Training time and compute complexity of OLR with 800 samples. The additional overhead introduced by OLR is negligible compared with rollout generation.

y^{\text{maj}}_{t}(x)=\arg\max_{c}|\{y\in\mathcal{Y}_{t}(x):y=c\}|

Appendix

Algorithm 1 Online Label Refinement (OLR)

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Noisy Data is Destructive to Reinforcement Learning with Verifiable Rewards

Yuxuan Zhu, Daniel Kang

UIUC · Bridgewater AIA Labs

Reinforcement Learning with Verifiable Rewards Noisy-Label Learning

Open paper AskPDF arXiv

Reinforcement learning with verifiable rewards (RLVR) has driven recent capability advances of large language models across various domains. Recent studies suggest that improved RLVR algorithms allow models to learn effectively from incorrect annotations, achieving performance comparable to learning from clean data. In this work, we show that these findings are invalid because the claimed 100% noisy training data is "contaminated" with clean data. After rectifying the dataset with a rigorous re-verification pipeline, we demonstrate that noise is destructive to RLVR. We show that existing RLVR algorithm improvements fail to mitigate the impact of noise, achieving similar performance to that of the basic GRPO. Furthermore, we find that the model trained on truly incorrect annotations performs 8-10% worse than the model trained on clean data across mathematical reasoning benchmarks. Finally, we show that these findings hold for real-world noise in Text2SQL tasks, where training on real-world, human annotation errors cause 5-12% lower accuracy than clean data. Our results show that current RLVR methods cannot yet compensate for poor data quality. High-quality data remains essential.

Abstract

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