# LoGRA: Scaling LLM Reinforcement Learning with Low-Rank Gradient Sketches

arXiv: https://arxiv.org/abs/2610.06647 · HTML: https://mlsanity.com/paper/2610.06647/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 16 of its 26 references that are in the map.
- First posted on arXiv 5 Oct 2026.

## Builds on (most cited first, 16 of 16)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [LoRA: Low-Rank Adaptation of Large Language Models](https://mlsanity.com/paper/2106.09685/) (2021)
- [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)
- [Let's Verify Step by Step](https://mlsanity.com/paper/2305.20050/) (2023)
- [Qwen Technical Report](https://mlsanity.com/paper/2309.16609/) (2023)
- [HybridFlow: A Flexible and Efficient RLHF Framework](https://mlsanity.com/paper/2409.19256/) (2024)
- [Training Deep Nets with Sublinear Memory Cost](https://mlsanity.com/paper/1604.06174/) (2016)
- [PyTorch FSDP: Experiences on Scaling Fully Sharded Data Parallel](https://mlsanity.com/paper/2304.11277/) (2023)
- [GaLore: Memory-Efficient LLM Training by Gradient Low-Rank Projection](https://mlsanity.com/paper/2403.03507/) (2024)
- [Flora: Low-Rank Adapters Are Secretly Gradient Compressors](https://mlsanity.com/paper/2402.03293/) (2024)
- [Offline Training of Language Model Agents with Functions as Learnable Weights](https://mlsanity.com/paper/2402.11359/) (2024)
- [OSWorld 2.0: Benchmarking Computer Use Agents on Long-Horizon Real-World Tasks](https://mlsanity.com/paper/2606.29537/) (2026)
- [ProRL Agent: Rollout-as-a-Service for RL Training of Multi-Turn LLM Agents](https://mlsanity.com/paper/2603.18815/) (2026)
- [GaLore 2: Large-Scale LLM Pre-Training by Gradient Low-Rank Projection](https://mlsanity.com/paper/2504.20437/) (2025)
- [Polar: Agentic RL on Any Harness at Scale](https://mlsanity.com/paper/2605.24220/) (2026)

## Abstract (arXiv)

Reinforcement learning has greatly advanced the capabilities of large language models, but its memory demands remain a barrier to broader adoption. We introduce LoGRA, an approach to RL post-training that reduces memory by retaining useful learning signals in low-rank gradient sketches. These compact representations support both model updates and efficient policy synchronization. To prevent overly large updates from disrupting learning, we complement gradient compression with predicted-KL step control, which estimates policy changes before applying each update and adjusts its magnitude accordingly. With all techniques combined, LoGRA reduces average training memory usage by up to 45.7% across reasoning tasks without compromising performance. It also enables stable training of a 27B-parameter model for over 1,100 steps on a single eight-GPU node, where dense Adam runs out of memory, making previously memory-infeasible RL training practical. Code is available in the hrefhttps://github.com/skzhang1/labs-molt/tree/logra/examples/scripts/lograMolt library.