# Beyond Variance: Prompt-Efficient RLVR via Rare-Event Amplification and Bidirectional Pairing

arXiv: https://arxiv.org/abs/2602.03452 · HTML: https://mlsanity.com/paper/2602.03452/

## 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 34 of its 40 references that are in the map.
- First posted on arXiv 3 Feb 2026.

## Placed in

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

## Builds on (most cited first, 30 of 34)

- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models](https://mlsanity.com/paper/2402.03300/) (2024)
- [Evaluating Large Language Models Trained on Code](https://mlsanity.com/paper/2107.03374/) (2021)
- [Let's Verify Step by Step](https://mlsanity.com/paper/2305.20050/) (2023)
- [DAPO: An Open-Source LLM Reinforcement Learning System at Scale](https://mlsanity.com/paper/2503.14476/) (2025)
- [HybridFlow: A Flexible and Efficient RLHF Framework](https://mlsanity.com/paper/2409.19256/) (2024)
- [Understanding R1-Zero-Like Training: A Critical Perspective](https://mlsanity.com/paper/2503.20783/) (2025)
- [Kimi k1.5: Scaling Reinforcement Learning with LLMs](https://mlsanity.com/paper/2501.12599/) (2025)
- [Tulu 3: Pushing Frontiers in Open Language Model Post-Training](https://mlsanity.com/paper/2411.15124/) (2024)
- [LESS: Selecting Influential Data for Targeted Instruction Tuning](https://mlsanity.com/paper/2402.04333/) (2024)
- [The Lessons of Developing Process Reward Models in Mathematical Reasoning](https://mlsanity.com/paper/2501.07301/) (2025)
- [Reinforcement Learning for Reasoning in Large Language Models with One Training Example](https://mlsanity.com/paper/2504.20571/) (2025)
- [VAPO: Efficient and Reliable Reinforcement Learning for Advanced Reasoning Tasks](https://mlsanity.com/paper/2504.05118/) (2025)
- [The Surprising Effectiveness of Negative Reinforcement in LLM Reasoning](https://mlsanity.com/paper/2506.01347/) (2025)
- [LIMR: Less is More for RL Scaling](https://mlsanity.com/paper/2502.11886/) (2025)
- [What's Behind PPO's Collapse in Long-CoT? Value Optimization Holds the Secret](https://mlsanity.com/paper/2503.01491/) (2025)
- [On Designing Effective RL Reward at Training Time for LLM Reasoning](https://mlsanity.com/paper/2410.15115/) (2024)
- [Process Reward Model with Q-Value Rankings](https://mlsanity.com/paper/2410.11287/) (2024)
- [InfoRM: Mitigating Reward Hacking in RLHF via Information-Theoretic Reward Modeling](https://mlsanity.com/paper/2402.09345/) (2024)
- [SRPO: A Cross-Domain Implementation of Large-Scale Reinforcement Learning on LLM](https://mlsanity.com/paper/2504.14286/) (2025)
- [Active Preference Optimization for Sample Efficient RLHF](https://mlsanity.com/paper/2402.10500/) (2024)
- [Active Preference Learning for Large Language Models](https://mlsanity.com/paper/2402.08114/) (2024)
- [Reinforcement Learning with Verifiable yet Noisy Rewards under Imperfect Verifiers](https://mlsanity.com/paper/2510.00915/) (2025)
- [Large-Scale Data Selection for Instruction Tuning](https://mlsanity.com/paper/2503.01807/) (2025)
- [Scalable Chain of Thoughts via Elastic Reasoning](https://mlsanity.com/paper/2505.05315/) (2025)
- [Turn-PPO: Turn-Level Advantage Estimation with PPO for Improved Multi-Turn RL in Agentic LLMs](https://mlsanity.com/paper/2512.17008/) (2025)
- [Asymmetric REINFORCE for off-Policy Reinforcement Learning: Balancing positive and negative rewards](https://mlsanity.com/paper/2506.20520/) (2025)
- [TruthRL: Incentivizing Truthful LLMs via Reinforcement Learning](https://mlsanity.com/paper/2509.25760/) (2025)
- [Data-Efficient Finetuning Using Cross-Task Nearest Neighbors](https://mlsanity.com/paper/2212.00196/) (2022)
- [INTELLECT-2: A Reasoning Model Trained Through Globally Decentralized Reinforcement Learning](https://mlsanity.com/paper/2505.07291/) (2025)

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

- [Unlearnable, or Unmeasured? On the Reliability of Difficulty Labels in RLVR](https://mlsanity.com/paper/2609.40115/) (2026)
- [Prompts Live on an Arc: Gaussian Curricula in Fisher--Rao Coordinates for Rollout-Efficient GRPO](https://mlsanity.com/paper/2609.38018/) (2026)

## Abstract (arXiv)

Reinforcement learning with verifiable rewards (RLVR) is effective for training large language models on deterministic outcome reasoning tasks. Prior work shows RLVR works with few prompts, but prompt selection is often based only on training-accuracy variance, leading to unstable optimization directions and weaker transfer. We revisit prompt selection from a mechanism-level view and argue that an effective minibatch should provide both (i) a reliable positive anchor and (ii) explicit negative learning signals from rare failures. Based on this principle, we propose positive--negative pairing: at each update, we sample a hard-but-solvable q+ and an easy-but-brittle prompt q-(high success rate but not perfect), characterized by low and high empirical success rates under multiple rollouts. We further introduce Weighted GRPO, which reweights binary outcomes at the pair level and uses group-normalized advantages to amplify rare successes on q+ into sharp positive guidance while turning rare failures on q- into strong negative penalties. This bidirectional signal provides informative learning feedback for both successes and failures, improving sample efficiency without suppressing exploration. On Qwen2.5-Math-7B, a single paired minibatch per update consistently outperforms a GRPO baseline that selects two prompts via commonly used variance-based selection heuristics: AIME~2025 Pass@8 improves from 16.8 to 22.2, and AMC23 Pass@64 from 94.0 to 97.0, while remaining competitive with large-scale RLVR trained from a pool of 1209 training prompts. Similar gains are observed on Qwen2.5-Math-7B-Instruct.