GCPO: Diagnosing and Constraining Subspace Geometry in Rollout RL for LLMs

On-policy rollout methods such as GRPO are central to post-training of large language models, yet they frequently suffer from training instabilities, cross-task capability degradation, and response-length inflation. Although prior work has characterized the subspace geometry of aggregate updates, the stepwise variation of this geometry and its relationship to model performance remain unclear. We introduce Principal-Subspace Overlap, a dimension-corrected measure of individual rollout updates relative to the dominant singular subspaces of pretrained weights. Despite low average overlap, transient spikes often precede performance degradation. To address this, we propose GCPO (Geometrically Constrained Policy Optimization), which applies hard bilateral orthogonal projections to constrain updates to the complementary subspaces, preventing such excursions by construction. Across mathematical reasoning, code generation, and tool-use tasks on Qwen3-8B and GLM4-9B, GCPO consistently outperforms GRPO and recent variants, including DAPO and GSPO, improving over the base models and the strongest baseline by up to 27.69 and 2.37 points, respectively. Furthermore, GCPO preserves general capabilities, eliminates response-length inflation, and stabilizes policy entropy. Our findings provide a new diagnostic lens and a principled design perspective for stable reinforcement learning post-training.

Trust Your Memory: Verifiable Control of Smart Homes through Reinforcement Learning with Multi-dimensional Rewards

Large Language Models (LLMs) have become a key foundation for enabling personalized smart home experiences. While existing studies have explored how smart home assistants understand user queries to control devices in real time, their ability to perform memory-driven device control remains challenging from both evaluation and methodological perspectives. In terms of evaluation, existing benchmarks either focus on immediate device control or general open-domain memory retrieval tasks, and therefore cannot effectively evaluate a model's ability to perform memory-driven device control. Methodologically, while memory-driven device control can be approached using Reinforcement Learning, conventional RL methods generally rely on outcome-based supervision (i.e., whether the final task is achieved). This lack of intermediate feedback can lead to sub-optimal performance or local failures in fine-grained memory management tasks (adding, updating, deleting, and utilizing). To address these issues, we first release MemHomeLife, built from anonymized real-world long-term user interaction logs. To enable more fine-grained evaluation of different memory-related subtasks, we further construct MemHome, the first benchmark designed to systematically evaluate memory-driven device control in smart home scenarios.