$S^3$: Spectral Null-Space Swap Makes Reasoning Models Efficient

arXiv:2609.37976v2 Announce Type: replace-cross Abstract: LLMs trained with Chain-of-thought excel in reasoning capability, but often come with excessive token cost. We find that the core of reasoning capacity lies in the Thinking model's weight component within the null space of a projection defined by the corresponding Non-thinking model's dominant singular directions, and removing the subspace component can largely improve reasoning efficiency without hurting the accuracy gained during thinking-mode post-training. Unlike existing efforts that mostly operate within the dominant subspace, we

This content is for informational purposes only and is not professional advice. Specifications, prices, plan tiers, and features change frequently and may differ from what is shown here; verify current details on the manufacturer's or company's official page before purchasing. Ratings are based on analysis of published documentation, not independent lab testing.