# Clipping Bottleneck: Stabilizing RLVR via Stochastic Recovery of Near-Boundary Signals

arXiv: https://arxiv.org/abs/2605.22703 · HTML: https://mlsanity.com/paper/2605.22703/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Placed in Reinforcement learning for reasoning, one of 17 directions in LLM reasoning.
- Builds on 32 of its 36 references that are in the map.
- First posted on arXiv 21 May 2026.

## Placed in

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

## Builds on (most cited first, 30 of 32)

- [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)
- [Qwen3 Technical Report](https://mlsanity.com/paper/2505.09388/) (2025)
- [Gemini 2.5: Pushing the Frontier with Advanced Reasoning, Multimodality, Long Context, and Next Generation Agentic Capabilities](https://mlsanity.com/paper/2507.06261/) (2025)
- [DAPO: An Open-Source LLM Reinforcement Learning System at Scale](https://mlsanity.com/paper/2503.14476/) (2025)
- [Trust Region Policy Optimization](https://mlsanity.com/paper/1502.05477/) (2015)
- [MMLU-Pro: A More Robust and Challenging Multi-Task Language Understanding Benchmark](https://mlsanity.com/paper/2406.01574/) (2024)
- [Understanding R1-Zero-Like Training: A Critical Perspective](https://mlsanity.com/paper/2503.20783/) (2025)
- [Group Sequence Policy Optimization](https://mlsanity.com/paper/2507.18071/) (2025)
- [Beyond the 80/20 Rule: High-Entropy Minority Tokens Drive Effective Reinforcement Learning for LLM Reasoning](https://mlsanity.com/paper/2506.01939/) (2025)
- [SimpleRL-Zoo: Investigating and Taming Zero Reinforcement Learning for Open Base Models in the Wild](https://mlsanity.com/paper/2503.18892/) (2025)
- [The Entropy Mechanism of Reinforcement Learning for Reasoning Language Models](https://mlsanity.com/paper/2505.22617/) (2025)
- [Open-Reasoner-Zero: An Open Source Approach to Scaling Up Reinforcement Learning on the Base Model](https://mlsanity.com/paper/2503.24290/) (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)
- [MiniMax-M1: Scaling Test-Time Compute Efficiently with Lightning Attention](https://mlsanity.com/paper/2506.13585/) (2025)
- [The Surprising Effectiveness of Negative Reinforcement in LLM Reasoning](https://mlsanity.com/paper/2506.01347/) (2025)
- [Soft Adaptive Policy Optimization](https://mlsanity.com/paper/2511.20347/) (2025)
- [A Sober Look at Progress in Language Model Reasoning: Pitfalls and Paths to Reproducibility](https://mlsanity.com/paper/2504.07086/) (2025)
- [Part I: Tricks or Traps? A Deep Dive into RL for LLM Reasoning](https://mlsanity.com/paper/2508.08221/) (2025)
- [Look-Back: Implicit Visual Re-focusing in MLLM Reasoning](https://mlsanity.com/paper/2507.03019/) (2025)
- [Rethinking Entropy Interventions in RLVR: An Entropy Change Perspective](https://mlsanity.com/paper/2510.10150/) (2025)
- [BAPO: Stabilizing Off-Policy Reinforcement Learning for LLMs via Balanced Policy Optimization with Adaptive Clipping](https://mlsanity.com/paper/2510.18927/) (2025)
- [Do Not Let Low-Probability Tokens Over-Dominate in RL for LLMs](https://mlsanity.com/paper/2505.12929/) (2025)
- [Single-stream Policy Optimization](https://mlsanity.com/paper/2509.13232/) (2025)
- [Low-probability Tokens Sustain Exploration in Reinforcement Learning with Verifiable Reward](https://mlsanity.com/paper/2510.03222/) (2025)
- [FIPO: Eliciting Deep Reasoning with Future-KL Influenced Policy Optimization](https://mlsanity.com/paper/2603.19835/) (2026)
- [Sparse but Critical: A Token-Level Analysis of Distributional Shifts in RLVR Fine-Tuning of LLMs](https://mlsanity.com/paper/2603.22446/) (2026)
- [How Difficulty-Aware Staged Reinforcement Learning Enhances LLMs' Reasoning Capabilities: A Preliminary Experimental Study](https://mlsanity.com/paper/2504.00829/) (2025)
- [On the Direction of RLVR Updates for LLM Reasoning: Identification and Exploitation](https://mlsanity.com/paper/2603.22117/) (2026)

## Built on by (most cited first, 1 of 1)

- [Two Clocks: Why Larger Rollout Batches Learn Slower but Fail on Schedule in Reinforcement Learning with Verifiable Rewards](https://mlsanity.com/paper/2610.18853/) (2026)

## Abstract (arXiv)

Reinforcement Learning with Verifiable Rewards (RLVR) has emerged as a central paradigm for scaling LLM reasoning, yet its optimization often suffers from training instability and suboptimal convergence. Through a systematic dissection of clipping-based GRPO-style objectives, we identify the rigid clipping decision induced by hard clipping as a key practical bottleneck in the studied RLVR setups. Specifically, our analysis suggests that informative signals can lie in the near-boundary region just beyond the clipping threshold, and are therefore discarded by the standard hard-clipping rule. Notably, once this bottleneck is precisely identified, even simple stochastic perturbations at the boundary can recover meaningful performance gains. Building on this finding, we propose Near-boundary Stochastic Rescue (NSR), a minimal, plug-and-play modification that stochastically retains these slightly out-of-bound tokens to recover lost signals. While NSR, via stochastic sampling, can be interpreted as inducing an implicit gradient decay in expectation, our ablations reveal that its stochastic, boundary-local rescue mechanism is consistently more effective than deterministic gradient decay. Validated by extensive experiments across model sizes from 7B to 30B and both dense and MoE architectures, as a plug-and-play solution, NSR substantially improves training stability and delivers consistent gains over strong baselines such as DAPO and GSPO.