# All-Quadrant Bounded Clipping GRPO: Closing the Unbounded Blind Spot for Stable and Generalizable Training

arXiv: https://arxiv.org/abs/2601.03895 · HTML: https://mlsanity.com/paper/2601.03895/

## 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 21 of its 27 references that are in the map.
- First posted on arXiv 7 Jan 2026.

## Placed in

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

## Builds on (most cited first, 21 of 21)

- [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)
- [Chain-of-Thought Prompting Elicits Reasoning in Large Language Models](https://mlsanity.com/paper/2201.11903/) (2022)
- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [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)
- [Evaluating Large Language Models Trained on Code](https://mlsanity.com/paper/2107.03374/) (2021)
- [Direct Preference Optimization: Your Language Model is Secretly a Reward Model](https://mlsanity.com/paper/2305.18290/) (2023)
- [Measuring Mathematical Problem Solving With the MATH Dataset](https://mlsanity.com/paper/2103.03874/) (2021)
- [Soft Actor-Critic: Off-Policy Maximum Entropy Deep Reinforcement Learning with a Stochastic Actor](https://mlsanity.com/paper/1801.01290/) (2018)
- [Deep reinforcement learning from human preferences](https://mlsanity.com/paper/1706.03741/) (2017)
- [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)
- [FlashAttention-2: Faster Attention with Better Parallelism and Work Partitioning](https://mlsanity.com/paper/2307.08691/) (2023)
- [Trust Region Policy Optimization](https://mlsanity.com/paper/1502.05477/) (2015)
- [Understanding R1-Zero-Like Training: A Critical Perspective](https://mlsanity.com/paper/2503.20783/) (2025)
- [Scaling Laws for Reward Model Overoptimization](https://mlsanity.com/paper/2210.10760/) (2022)
- [Does Reinforcement Learning Really Incentivize Reasoning Capacity in LLMs Beyond the Base Model?](https://mlsanity.com/paper/2504.13837/) (2025)
- [Group Sequence Policy Optimization](https://mlsanity.com/paper/2507.18071/) (2025)
- [Mastering Complex Control in MOBA Games with Deep Reinforcement Learning](https://mlsanity.com/paper/1912.09729/) (2019)
- [Soft Adaptive Policy Optimization](https://mlsanity.com/paper/2511.20347/) (2025)

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

- [Reinforcement Learning for Code Optimization](https://mlsanity.com/paper/2607.25970/) (2026)

## Abstract (arXiv)

Group Relative Policy Optimization (GRPO) has emerged as a popular algorithm for reinforcement learning with large language models (LLMs). However, GRPO inherits PPO's token-level clipping while replacing token-level advantages with a single sequence-level advantage. Through a four-quadrant analysis of the (likelihood-ratio, advantage) space, we show that this combination leaves one quadrant -- negative advantage combined with an increased likelihood ratio (Q4) -- structurally unbounded, so that a few high-ratio tokens can receive very large suppressive updates that collapse entropy and narrow the reasoning boundary. To address this, we propose All-Quadrant Bounded Clipping GRPO (ABC-GRPO), which applies unconditional clipping in all four quadrants through sign-dependent boundaries. ABC-GRPO clips the likelihood ratio before multiplying by the advantage, adding a trust-region floor in Q2 and a cap in Q4 -- its negative-advantage branch coinciding with dual-clip PPO -- to yield bounded per-step policy displacement in every quadrant. On mathematical reasoning with Qwen3 base models, ABC-GRPO attains the highest Avg@64 and Pass@64: it is statistically superior to GRPO, SAPO, and dual-clip PPO and competitive with the strongest baseline (DAPO), while maintaining substantially higher entropy; the gains transfer to MATH-500 and to out-of-domain code (HumanEval). Ablations isolate Q4 as the dominant blind spot.