# GEOALIGN: Geometric Rollout Curation for Robust LLM Reinforcement Learning

arXiv: https://arxiv.org/abs/2606.26917 · HTML: https://mlsanity.com/paper/2606.26917/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 32 of its 36 references that are in the map.
- First posted on arXiv 25 Jun 2026.

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

- [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)
- [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)
- [Let's Verify Step by Step](https://mlsanity.com/paper/2305.20050/) (2023)
- [Training a Helpful and Harmless Assistant with Reinforcement Learning from Human Feedback](https://mlsanity.com/paper/2204.05862/) (2022)
- [FlashAttention: Fast and Memory-Efficient Exact Attention with IO-Awareness](https://mlsanity.com/paper/2205.14135/) (2022)
- [DAPO: An Open-Source LLM Reinforcement Learning System at Scale](https://mlsanity.com/paper/2503.14476/) (2025)
- [Understanding Contrastive Representation Learning through Alignment and Uniformity on the Hypersphere](https://mlsanity.com/paper/2005.10242/) (2020)
- [Solving Quantitative Reasoning Problems with Language Models](https://mlsanity.com/paper/2206.14858/) (2022)
- [OlympiadBench: A Challenging Benchmark for Promoting AGI with Olympiad-Level Bilingual Multimodal Scientific Problems](https://mlsanity.com/paper/2402.14008/) (2024)
- [Scaling Laws for Reward Model Overoptimization](https://mlsanity.com/paper/2210.10760/) (2022)
- [Qwen2.5-Math Technical Report: Toward Mathematical Expert Model via Self-Improvement](https://mlsanity.com/paper/2409.12122/) (2024)
- [Open Problems and Fundamental Limitations of Reinforcement Learning from Human Feedback](https://mlsanity.com/paper/2307.15217/) (2023)
- [Prevalence of Neural Collapse during the terminal phase of deep learning training](https://mlsanity.com/paper/2008.08186/) (2020)
- [PyTorch FSDP: Experiences on Scaling Fully Sharded Data Parallel](https://mlsanity.com/paper/2304.11277/) (2023)
- [A Theoretical Analysis of Contrastive Unsupervised Representation Learning](https://mlsanity.com/paper/1902.09229/) (2019)
- [Interpretable Preferences via Multi-Objective Reward Modeling and Mixture-of-Experts](https://mlsanity.com/paper/2406.12845/) (2024)
- [Regularizing Hidden States Enables Learning Generalizable Reward Model for LLMs](https://mlsanity.com/paper/2406.10216/) (2024)
- [LIMR: Less is More for RL Scaling](https://mlsanity.com/paper/2502.11886/) (2025)
- [What is Your Data Worth to GPT? LLM-Scale Data Valuation with Influence Functions](https://mlsanity.com/paper/2405.13954/) (2024)
- [SEED-GRPO: Semantic Entropy Enhanced GRPO for Uncertainty-Aware Policy Optimization](https://mlsanity.com/paper/2505.12346/) (2025)
- [Reward Shaping to Mitigate Reward Hacking in RLHF](https://mlsanity.com/paper/2502.18770/) (2025)
- [Not All Rollouts are Useful: Down-Sampling Rollouts in LLM Reinforcement Learning](https://mlsanity.com/paper/2504.13818/) (2025)
- [Revisiting Reinforcement Learning for LLM Reasoning from A Cross-Domain Perspective](https://mlsanity.com/paper/2506.14965/) (2025)
- [Stop Summation: Min-Form Credit Assignment Is All Process Reward Model Needs for Reasoning](https://mlsanity.com/paper/2504.15275/) (2025)
- [Regularized Best-of-N Sampling with Minimum Bayes Risk Objective for Language Model Alignment](https://mlsanity.com/paper/2404.01054/) (2024)
- [Policy Filtration for RLHF to Mitigate Noise in Reward Models](https://mlsanity.com/paper/2409.06957/) (2024)
- [Trinity-RFT: A General-Purpose and Unified Framework for Reinforcement Fine-Tuning of Large Language Models](https://mlsanity.com/paper/2505.17826/) (2025)
- [Can One Domain Help Others? A Data-Centric Study on Multi-Domain Reasoning via Reinforcement Learning](https://mlsanity.com/paper/2507.17512/) (2025)

## Abstract (arXiv)

Online reinforcement learning is widely used to align large language models (LLMs) with reward signals, yet training can be unstable under noisy or misspecified rewards. We identify a failure mode we call directional inconsistency: within a batch, a small set of high-reward rollouts induces representation-space preference directions that sharply disagree with the batch majority, resulting in high-variance and destabilizing updates. We propose geoalign, a lightweight plug-in for rollout curation in iterative policy optimization. Geoalign (i) forms within-prompt preference pairs, (ii) learns an online projector on per-rollout hidden states to concentrate reward-ordered displacement directions, and (iii) detects directionally inconsistent rollouts via their angular deviation from a batch consensus prototype and rectifies them with within-prompt stable alternatives. Geoalign is forward-pass only and adds negligible overhead. Across dialogue alignment with a learned reward model and mathematical reasoning with binary verified rewards, Geoalign improves final performance and reduces training oscillation, outperforming PF-PPO, PAR, PODS, and Seed-GRPO. These results suggest latent directional consensus as an effective reliability signal for online LLM RL.