Preprint reports geometry-based preference tuning gains in LLM math reasoning

A new arXiv preprint proposes Cloud-ScPO, a semi-supervised preference-optimization method that derives training pairs partly from the geometry of a model's hidden-state representations. The authors say the framework combines those signals with answer-level self-consistency to select and filter reasoning trajectories. Across GSM8K and MATH-Numeric in four model settings, the paper reports improvements over ScPO of up to 4.49% and 4.19%, respectively. The findings have not been independently verified.