Cloud-ScPO: Hidden-State Geometry for Semi-Supervised Preference Optimization in LLM Reasoning
Preference optimization improves mathematical reasoning in large language models (LLMs), but reliable chosen-rejected pairs usually require verified answers, human annotations, or external reward models. We investigate whether preference supervision can instead be derived from the model's internal representation geometry in a semi-supervised setting. Our analysis shows that reasoning trajectories generated across different mathematical problems form structured global point clouds in which correct and incorrect trajectories exhibit different geometric organization. Based on this observation, we propose Cloud-ScPO, a topology-guided preference-mining framework that uses a small labeled set ...
| Authors | Yuzhou Liu, Xiyang Hu |
|---|---|
| Primary category | cs.CL |
| Published | 2 August 2026 |
| Last updated at source | 14 August 2026 |
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