# CARM: Cancellation-Aware Response Masking for LLM Reinforcement Learning

arXiv: https://arxiv.org/abs/2610.02039 · HTML: https://mlsanity.com/paper/2610.02039/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Reinforcement learning for reasoning, one of 17 directions in LLM reasoning.
- Builds on 28 of its 34 references that are in the map.
- First posted on arXiv 1 Oct 2026.

## Placed in

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

## Builds on (most cited first, 28 of 28)

- [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)
- [DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models](https://mlsanity.com/paper/2402.03300/) (2024)
- [DeepSeek-R1: Incentivizing Reasoning Capability in LLMs via Reinforcement Learning](https://mlsanity.com/paper/2501.12948/) (2025)
- [Program Synthesis with Large Language Models](https://mlsanity.com/paper/2108.07732/) (2021)
- [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)
- [HybridFlow: A Flexible and Efficient RLHF Framework](https://mlsanity.com/paper/2409.19256/) (2024)
- [LiveCodeBench: Holistic and Contamination Free Evaluation of Large Language Models for Code](https://mlsanity.com/paper/2403.07974/) (2024)
- [Is Your Code Generated by ChatGPT Really Correct? Rigorous Evaluation of Large Language Models for Code Generation](https://mlsanity.com/paper/2305.01210/) (2023)
- [Program of Thoughts Prompting: Disentangling Computation from Reasoning for Numerical Reasoning Tasks](https://mlsanity.com/paper/2211.12588/) (2022)
- [IMPALA: Scalable Distributed Deep-RL with Importance Weighted Actor-Learner Architectures](https://mlsanity.com/paper/1802.01561/) (2018)
- [CodeRL: Mastering Code Generation through Pretrained Models and Deep Reinforcement Learning](https://mlsanity.com/paper/2207.01780/) (2022)
- [Reinforcement Learning for Reasoning in Large Language Models with One Training Example](https://mlsanity.com/paper/2504.20571/) (2025)
- [REINFORCE++: Stabilizing Critic-Free Policy Optimization with Global Advantage Normalization](https://mlsanity.com/paper/2501.03262/) (2025)
- [Seed1.5-Thinking: Advancing Superb Reasoning Models with Reinforcement Learning](https://mlsanity.com/paper/2504.13914/) (2025)
- [Act Only When It Pays: Efficient Reinforcement Learning for LLM Reasoning via Selective Rollouts](https://mlsanity.com/paper/2506.02177/) (2025)
- [FullStack Bench: Evaluating LLMs as Full Stack Coders](https://mlsanity.com/paper/2412.00535/) (2024)
- [Every Step Evolves: Scaling Reinforcement Learning for Trillion-Scale Thinking Model](https://mlsanity.com/paper/2510.18855/) (2025)
- [BAPO: Stabilizing Off-Policy Reinforcement Learning for LLMs via Balanced Policy Optimization with Adaptive Clipping](https://mlsanity.com/paper/2510.18927/) (2025)
- [Rethinking the Trust Region in LLM Reinforcement Learning](https://mlsanity.com/paper/2602.04879/) (2026)
- [Simple Policy Optimization](https://mlsanity.com/paper/2401.16025/) (2024)
- [Trust Region Masking for Long-Horizon LLM Reinforcement Learning](https://mlsanity.com/paper/2512.23075/) (2025)
- [Contextual Rollout Bandits for Reinforcement Learning with Verifiable Rewards](https://mlsanity.com/paper/2602.08499/) (2026)
- [Efficient Reinforcement Learning for Large Language Models with Intrinsic Exploration](https://mlsanity.com/paper/2511.00794/) (2025)
- [URPO: A Unified Reward & Policy Optimization Framework for Large Language Models](https://mlsanity.com/paper/2507.17515/) (2025)
- [Rethinking the Divergence Regularization in LLM RL](https://mlsanity.com/paper/2606.09821/) (2026)

## Abstract (arXiv)

Recent years have witnessed the rapid adoption of reinforcement learning (RL) in large language model (LLM) post-training, with substantial gains in mathematical reasoning and code generation. In practical systems, however, policy updates and differences between rollout and training engines can make sampled responses off-policy. Sequence-level masking addresses this mismatch by deciding whether an entire response should contribute to optimization. A common masking rule uses the length-normalized geometric mean of sampled token probability ratios. Its signed log-ratios can cancel across positions, concealing substantial bidirectional policy drift. We propose Cancellation-Aware Response Masking (CARM), a sequence-level mask that takes the absolute value of each token log-ratio before averaging, preventing opposing probability changes from canceling. We prove that accepted responses satisfy a joint bound on the fraction of sampled-token ratios outside a prescribed band and their mean log-distance beyond its boundaries. Experiments on mathematical reasoning and code generation show that CARM improves mean@16 averaged over AIME 2024/2025/2026 and BeyondAIME by up to 3.13 percentage points over geometric-mean masking, and increases average pass@1 across four code benchmarks by 2.88 points over the strongest evaluated baseline. These findings support CARM as a theoretically grounded and effective method for response-level off-policy control in LLM reinforcement learning.