# Adaptive Layerwise Perturbation: Unifying Off-Policy Corrections for LLM RL

arXiv: https://arxiv.org/abs/2603.19470 · HTML: https://mlsanity.com/paper/2603.19470/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 32 of its 44 references that are in the map.
- First posted on arXiv 19 Mar 2026.

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

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [High-Resolution Image Synthesis with Latent Diffusion Models](https://mlsanity.com/paper/2112.10752/) (2021)
- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [Denoising Diffusion Implicit Models](https://mlsanity.com/paper/2010.02502/) (2020)
- [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)
- [Diffusion Models Beat GANs on Image Synthesis](https://mlsanity.com/paper/2105.05233/) (2021)
- [Efficient Memory Management for Large Language Model Serving with PagedAttention](https://mlsanity.com/paper/2309.06180/) (2023)
- [Measuring Mathematical Problem Solving With the MATH Dataset](https://mlsanity.com/paper/2103.03874/) (2021)
- [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)
- [Solving Quantitative Reasoning Problems with Language Models](https://mlsanity.com/paper/2206.14858/) (2022)
- [Certified Adversarial Robustness via Randomized Smoothing](https://mlsanity.com/paper/1902.02918/) (2019)
- [Palette: Image-to-Image Diffusion Models](https://mlsanity.com/paper/2111.05826/) (2021)
- [SGLang: Efficient Execution of Structured Language Model Programs](https://mlsanity.com/paper/2312.07104/) (2023)
- [OlympiadBench: A Challenging Benchmark for Promoting AGI with Olympiad-Level Bilingual Multimodal Scientific Problems](https://mlsanity.com/paper/2402.14008/) (2024)
- [Qwen2.5-Math Technical Report: Toward Mathematical Expert Model via Self-Improvement](https://mlsanity.com/paper/2409.12122/) (2024)
- [Group Sequence Policy Optimization](https://mlsanity.com/paper/2507.18071/) (2025)
- [Certified Robustness to Adversarial Examples with Differential Privacy](https://mlsanity.com/paper/1802.03471/) (2018)
- [Provably Robust Deep Learning via Adversarially Trained Smoothed Classifiers](https://mlsanity.com/paper/1906.04584/) (2019)
- [AReaL: A Large-Scale Asynchronous Reinforcement Learning System for Language Reasoning](https://mlsanity.com/paper/2505.24298/) (2025)
- [Randomized Smoothing of All Shapes and Sizes](https://mlsanity.com/paper/2002.08118/) (2020)
- [SimpleTIR: End-to-End Reinforcement Learning for Multi-Turn Tool-Integrated Reasoning](https://mlsanity.com/paper/2509.02479/) (2025)
- [Elucidating the Exposure Bias in Diffusion Models](https://mlsanity.com/paper/2308.15321/) (2023)
- [Revisiting Reinforcement Learning for LLM Reasoning from A Cross-Domain Perspective](https://mlsanity.com/paper/2506.14965/) (2025)
- [Alleviating Exposure Bias in Diffusion Models through Sampling with Shifted Time Steps](https://mlsanity.com/paper/2305.15583/) (2023)
- [Defeating the Training-Inference Mismatch via FP16](https://mlsanity.com/paper/2510.26788/) (2025)
- [rStar2-Agent: Agentic Reasoning Technical Report](https://mlsanity.com/paper/2508.20722/) (2025)
- [Positive-incentive Noise](https://mlsanity.com/paper/2212.09541/) (2022)
- [Trust Region Masking for Long-Horizon LLM Reinforcement Learning](https://mlsanity.com/paper/2512.23075/) (2025)

## Built on by (most cited first, 3 of 3)

- [Revisiting On-Policy Distillation: Empirical Failure Modes and Simple Fixes](https://mlsanity.com/paper/2603.25562/) (2026)
- [Score Centering Stabilizes Off-policy Reinforcement Learning](https://mlsanity.com/paper/2609.20807/) (2026)
- [A Gradient Perspective on RLVR Stability and Winner Advantage Policy Optimization](https://mlsanity.com/paper/2606.16154/) (2026)

## Abstract (arXiv)

Off-policy problems such as policy staleness and training--inference mismatch have become a major bottleneck for training stability and further exploration in LLM RL. The distribution gap between the inference and updated policies grows because of the techniques to enhance inference efficiency, leading to heavy-tailed importance ratios. Heavy-tailed ratios arise when the policy is locally sharp, which further inflates gradients and can push updates outside the trust region. To address this, we propose Adaptive Layerwise Perturbation (ALP), which injects small learnable perturbations into the input hidden states of each layer during updates and uses the resulting perturbed policy as the numerator of the importance ratio against the unchanged inference policy in the objective. Intuitively, by adding controlled noise to intermediate representations, ALP prevents the updated policy from deviating too sharply from the inference policy and enlarges the policy family to cover inference-time mismatch noise. Hence, the flattened distribution can naturally tighten the gap between the updated and inference policies and reduce the tail of importance ratios, thus maintaining training stability. This is further validated empirically. Experiments on single-turn math and multi-turn tool-integrated reasoning tasks show that ALP not only improves final performance, but also avoids blow-up in the importance-ratio tail and KL spikes during iterative training, along with boosted exploration. Ablations show that representation-level perturbations across all layers are most effective, substantially outperforming partial-layer and logits-only variants.