# Learn More with Less: Uncertainty Consistency Guided Query Selection for RLVR

arXiv: https://arxiv.org/abs/2601.22595 · HTML: https://mlsanity.com/paper/2601.22595/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Placed in Reinforcement learning for reasoning, one of 17 directions in LLM reasoning.
- Builds on 24 of its 35 references that are in the map.
- First posted on arXiv 30 Jan 2026.

## Placed in

- LLM reasoning / [Reinforcement learning for reasoning](https://mlsanity.com/lr/reinforcement-learning-for-reasoning/)

## Builds on (most cited first, 24 of 24)

- [GPT-4 Technical Report](https://mlsanity.com/paper/2303.08774/) (2023)
- [Training language models to follow instructions with human feedback](https://mlsanity.com/paper/2203.02155/) (2022)
- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models](https://mlsanity.com/paper/2402.03300/) (2024)
- [Scaling Laws for Neural Language Models](https://mlsanity.com/paper/2001.08361/) (2020)
- [Measuring Mathematical Problem Solving With the MATH Dataset](https://mlsanity.com/paper/2103.03874/) (2021)
- [DAPO: An Open-Source LLM Reinforcement Learning System at Scale](https://mlsanity.com/paper/2503.14476/) (2025)
- [Qwen3 Embedding: Advancing Text Embedding and Reranking Through Foundation Models](https://mlsanity.com/paper/2506.05176/) (2025)
- [Qwen2.5-Math Technical Report: Toward Mathematical Expert Model via Self-Improvement](https://mlsanity.com/paper/2409.12122/) (2024)
- [Beyond the 80/20 Rule: High-Entropy Minority Tokens Drive Effective Reinforcement Learning for LLM Reasoning](https://mlsanity.com/paper/2506.01939/) (2025)
- [The Entropy Mechanism of Reinforcement Learning for Reasoning Language Models](https://mlsanity.com/paper/2505.22617/) (2025)
- [Reasoning with Exploration: An Entropy Perspective](https://mlsanity.com/paper/2506.14758/) (2025)
- [Active Prompting with Chain-of-Thought for Large Language Models](https://mlsanity.com/paper/2302.12246/) (2023)
- [Contextual Diversity for Active Learning](https://mlsanity.com/paper/2008.05723/) (2020)
- [Batch Active Learning at Scale](https://mlsanity.com/paper/2107.14263/) (2021)
- [How to Train Data-Efficient LLMs](https://mlsanity.com/paper/2402.09668/) (2024)
- [Gone Fishing: Neural Active Learning with Fisher Embeddings](https://mlsanity.com/paper/2106.09675/) (2021)
- [Deep Active Learning over the Long Tail](https://mlsanity.com/paper/1711.00941/) (2017)
- [Active Preference Learning for Large Language Models](https://mlsanity.com/paper/2402.08114/) (2024)
- [ActiveLLM: Large Language Model-based Active Learning for Textual Few-Shot Scenarios](https://mlsanity.com/paper/2405.10808/) (2024)
- [Causal-Guided Active Learning for Debiasing Large Language Models](https://mlsanity.com/paper/2408.12942/) (2024)
- [Cost-Effective Proxy Reward Model Construction with On-Policy and Active Learning](https://mlsanity.com/paper/2407.02119/) (2024)
- [Interactive Multi-fidelity Learning for Cost-effective Adaptation of Language Model with Sparse Human Supervision](https://mlsanity.com/paper/2310.20153/) (2023)

## Built on by (most cited first, 2 of 2)

- [When Self-Belief Misleads: Active Label Acquisition for Reinforcement Learning with Verifiable Rewards](https://mlsanity.com/paper/2605.25864/) (2026)
- [IRDS: Interpretable RLVR Data Selection via Verifier-Coupled Sparse Autoencoder Coverage](https://mlsanity.com/paper/2605.28247/) (2026)

## Abstract (arXiv)

Large Language Models (LLMs) have recently improved mathematical reasoning through Reinforcement Learning with Verifiable Reward (RLVR). However, existing RLVR algorithms require large query budgets, making annotation costly. We investigate whether fewer but more informative queries can yield similar or superior performance, introducing active learning (AL) into RLVR. We identify that classic AL sampling strategies fail to outperform random selection in this setting, due to ignoring objective uncertainty when only selecting by subjective uncertainty. This work proposes an uncertainty consistency metric to evaluate how well subjective uncertainty aligns with objective uncertainty. In the offline setting, this alignment is measured using the Point-Biserial Correlation Coefficient (PBC). For online training, because of limited sampling and dynamically shifting output distributions, PBC estimation is difficult. Therefore, we introduce a new online variant, computed from normalized advantage and subjective uncertainty. Theoretically, we prove that the online variant is strictly negatively correlated with offline PBC and supports better sample selection. Experiments show our method consistently outperforms random and classic AL baselines, achieving full-dataset performance while training on only 30% of the data, effectively reducing the cost of RLVR for reasoning tasks.